Reference to Abstract Objects in Discourse (Studies in Linguistics and Philosophy, 50)

John saw Mary run. Therefore, John saw Mary move her legs in way W.

But this inference is invalid; John might see Mary run without seeing her legs (suppose a waist-high wall separates them over which John cannot see). But if the

26

CHAPTER ONE

object of see in this case is just an event, then such an inference should be valid. The fact that (34) is invalid, as well as a number of other facts, prove difficult to explain for a view that claims NI complements denote events.l 8 Of course, NI perception verbs can take events as objects--as in John saw an arriving of Mary ; they can also take facts--e.g., John observed the fact that Mary arrived. It is thus tempting to conclude that perception verbs count among their objects not only events and facts, but also objects different from either. We might use Barwise and Perry's term for this sort of entity and call it a situation. But the term situation in ordinary language appears to denote a state or some similar such entity.1 9 Since states are not generally recognized objects of NI perception, I will call the latter BPsituations.

1.4 Divisions Among Proposition-like Entities

Various sorts of contexts for improper nominals not contemplated by Kaiser and Vendler lead to further ontological distinctions among abstract entities. Propositional Contexts. A verb phrase like is true, attitude verbs like believe, be certain, doubt, say, and know, and other verbs taking that clauses like imply, and entail. Such contexts take felicitously that clauses in the indicative mood or certain derived nominals as complements; they do not take of-ing gerunds or POSS-ing gerunds. These contexts generate a wide variety of logics. 20 Projective Propositional Contexts: e.g., ask, allow, be necessary. These contexts, in contrast to the group above, take as complements only infinitivals or that clauses in the subjunctive mood from the class of sentential nominalizations. These contexts also generate a wide variety of logics. 21 Factual Contexts. These are contexts generated by verbs like indicate and show. They take all nominals as syntactic subjects; they also take negated nominals. Syntactic objects are restricted to that clauses and POSS-ing and perhaps also ACCing gerunds or certain derived nominals (for states). The rough semantics of the show or indicate context is that a fact, eventuality, or object indicates that a certain fact obtains. Causatives also appear to offer such contexts. Factual contexts appear to support a logic different from that of NI perception contexts or of propositional contexts, the contexts closest in syntactic and semantic analysis. 22 They too permit negated nominals, derived nominals, of-ing geru~ds, and POSS-ing gerunds as subjects and objects. . Pure propositional contexts and projective propositional contexts have complementary distributions among imperf\,:ct nominals. Factive contexts take a wider variety of nominals as arguments than pure propositional contexts. Again using Vendler's strategy, I conclude that within the typology of abstract objects, there are two distinct types--those of propositions and projective propositions. Included within the projective proposition contexts are rogatives like wonder and ask, buletics like want and desire, command verbs like command, plead, entreat, and permission verbs like allow and permit. Propositional verbs include "positive

FROM EVENTS TO PROPOSITIONS

27

factive" and "nonfactive epistemic" verbs like believe and know, and "negative" verbs like doubt and deny.23 These contexts have significantly different logics that, as far as I know, have only been accounted for by positing a difference in the type of arguments these predicates take. For rogatives, the link between the semantics of questions and the semantics of such contexts and the fact that successful, wellestablished analyses of questions treat these quite differently from normal propositions makes it plausible that rogatives take different types of objects from those that are arguments to the pure propositional contexts or those objects denoted by that clauses in the indicative mood. 24 The other projective contexts have a similar analysis to the rogatives. 25 While projective contexts isolate a distinct class of types of projective propositions, the ontological distinction suggested by the division between factive and propositional contexts is more delicate. The distribution of nominals between them is very similar to that given by Vendler's observations about eventuality containers and abstract object containers; the factive contexts handle a superset of the nominals accepted by propositional contexts. If there is a plausible semantic difference between these contexts that is most easily explained by a difference in denotation, then Vendler's strategy will distinguish three types among abstract entities. I tum now to a closer look at factive and propositional contexts. A Vendlerian argument distinguishes between the denotations of ACC-ing and POSS-ing gerund phrases. The examples in (27) repeated below do show that paradigm proposition containers do not readily accept ACC-ing and POSS-ing gerund phrases: (35.a) *Mary hitting Sue is true. (35.b) *Mary's hitting Sam is true. (35.c) That Mary hit Sue is true. Yet the gerund phrases as well as that clauses occur as arguments to supposedly factive contexts like indicate, show, causative verbs, and predicates like is a fact. So by Vendler's argument, there appears to be a semantic distinction between the type of objects denoted by POSS-ing and ACC-ing gerund phrases and the denotation of that clauses in certain contexts. Moreover, if we take factive contexts and propositional contexts to take different types of entities, it would seem that that clauses may denote either facts or propositions. But is there a real difference between facts and propositions in natural language metaphysics? We must examine the different contexts. Factive contexts take as objects that clauses in the indicative tense and POSS-ing and ACC-ing gerund phrases. By looking at the logic of these conteXts, we can again construct arguments to distinguish their arguments ontologically. The arguments assume that indicate and show denote, like propositional attitude verbs, two place relations with a subject and an object argument place. For both types of verbs, the object argument place may be filled by a that clause. As with NI perception contexts, it appears that the objects denoted by that clauses within

CHAPTER ONE

28

indicate and show contexts obey identity principle (1). Consider the valid argument in (28), in which we have two sets of documents A and B.

(36)

Documents A indicate that Cicero was the most highly regarded philosopher of his time. Cicero = Tully. Documents B indicate that Tully was the most highly regarded philosopher of his time. Therefore, documents A and B indicate the same thing.

Factual contexts also validate arguments in which we have substitution of expressions denoting the same property, whereas propositional contexts do not. Consider the argument in (29) (from Cresswell 1985): (37)

The map indicates that it is 7 + 5 kilometers to Upper Moutere. Therefore, the map indicates that it is 12 kilometers to Upper Moutere.

Again (37) is valid, while the corresponding argument with a propositional attitude context substituted for the factual context is not. 26 Similar distinctions in the logic of factive and propositional contexts show up with complex noun phrases of the form the fact that p, the claim that p and the indication that p. These nominals, I will assume, have an analysis on which the objects they denote are arguments of a context introduced by the noun that heads the noun phrase. (38.a) The fact that Cicero was the most highly regarded philosopher of his time is identical to the fact that Tully was the most highly regarded philosopher of his time. (38.b) The belief that Cicero was the most highly regarded philosopher of his time is identical to the belief that Tully was the most highly regarded philosopher of his time. (39.a) The fact that it is 12 kilometers to Upper Moutere is identical to the fact that it is 7+5 kilometers to Upper Moutere. (39.b) The belief that it is 12 kilometers to Upper Moutere is identical to the belief that it is 7+5 kilometers to Upper Moutere. (38.a) and (39.a) strike many speakers as true, while it is in keeping with the pattern of (32) to suppose that (38.b) and (39.b) are false. The discrepancy in truth value indicates that there is an ontological difference between the arguments of factual contexts and the arguments of attitude contexts. Or to put it ontologically: there is a difference between propositions and facts. 27 Differences between contexts as to substitutivity do not point per se to a difference in ontological categories. One could maintain that factual contexts take propositions as arguments but do not distinguish between logically equivalent

FROM EVENTS TO PROPOSITIONS

29

propOsItIonS, just as it is plausible to maintain that truth is a predicate of propositions but does not distinguish between materially equivalent propositions, in the sense that a materially equivalent proposition may be substituted for another within the context is truer ... ) salva veritate. But this would leave distributional data concerning gerunds and that clauses unexplained. There is in any case yet another difference between facts and propositions. As Moore argued, facts and propositions have different existence criteria. Propositions exist "eternally" or at least to exist independently of whether they are true or not. The proposition that

FROM EVENTS TO PROPOSITIONS

CHAPTER ONE

30

easily be explained away. Facts differ not only from propositions but also from events in natural language metaphysics. Suppose that a sentential nominal 0 denotes an event and suppose it contains an occurrence of a singular term a. Now suppose a = p. Let us again assume with Davidson and Lemmon that o[pla] denotes the same event as The death of Caesar is the same event as the passing away of the Roman conqueror of Gaul. Facts differ from events with respect to such identity of reference principles. Suppose that 0 denotes a fact and that it contains a definite description a. Suppose further that a = p. There appear to be readings of o[Pla] such that it does not denote the same fact as O. To see this, let's examine the indicates construction once again:

o.

(42)

The 33 rings indicate that this tree was thirty-three years old when it was cutdown. This tree = the first tree that Jack Webber, woodsman extraordinaire, felled on December 7, 1987. Therefore, the 33 rings indicate that the first tree that Jack Webber, woodsman extraordinaire, felled on December 7, 1987 was thirty-three years old when it was cut down.

There is a reading on which the argument in (42) is not valid, while there is no similar ambiguity for the similar inference on which coreferential proper names are substituted for each other. Indicates has been established to be a factual context, and the that clause picks out a fact. Event descriptions, I am assuming, continue to refer to the same event when one substitutes one coreferring term for another. But the invalidity of (42) then shows that fact descriptions do not have this property. The plausible explanation for this linguistic behavior is that facts have different identity conditions from events.31 Common noun phrases also furnish contexts for distinguishing propositions, facts, and events. Many types of natural language metaphysical entity are also explicitly named in natural language. Facts are one example; they are picked out by the common noun fact (though curiously propositions are not--the term proposition in ordinary language means something quite different from the philosopher's use!). That clauses and other nominals may combine with common noun phrases in a construction called the noun complement construction, and such noun complement constructions may often replace nominals in various contexts. The common noun phrases that are predicable of that clauses and other nominals allow us to extend the Vendlerian argument in the following way: if a statement of the form
31

noun phrase the fact must denote facts, then the infelicity of the sentences in (41) indicate that facts fail to have many of the properties of events--like spatial or temporal location. (43.a) #The fact that Mary fell down occurred in the park at noon. (43.b) #The fact of Mary's falling down occurred (obtained) in the park at noon. (43.c) #Mary falling down occurred at noon. Once again facts appear to differ from events. The arguments distinguishing eventualities from facts leave us with a puzzle. Given that facts do not have spatiotemporal locations, how do facts have causal efficacy? I'll retum to this problem in chapter five, when I analyze fact denoting constructions. Having introduced the common noun fact as a sort of context or container in our discussion of facts, we must countenance a whole host of such common noun contexts. Many sentential nominalizations combine with noun phrases as NP complements. The common noun phrase components in such constructions may also act as containers. Here is a sample of the sort of common nouns that may combine with that clauses, for instance: (44)

That Mary is happily married is a fact (proposition, truth, falsehood, supposition that her husband erroneously makes, hope of her mother's, fear of her suitor's, a possibility, a necessity, etc.)

The extended Vendlerian argument, introduced in conjunction with example (44) distinguishes further types by examining how head noun containers and predicate containers "fit together." For instance, (45.a) but not (45.b) is felicitous. (45.a) John announced the fact that he was married. (45.b) #John announced the thought (claim) that he was married. So one infers that announce may be satisfied by facts but not by thoughts or propositions. Similar examples force us to acknowledge a distinction between possibilities and facts, as well as between propositions and possibilities. (46.a) (46.b) (46.c) (46.d)

John feared the possibility that Mary had left without him. ?John feared the claim that Mary had left without him. John believed the claim that Mary had left without him. ?J ohn believed the possibility that Mary had left without him.

The sentences in (46) suggest a difference in type between propositions and possibilities. (47) reveals a similar pattern among possibilities and facts. (47) ?John feared the fact that Mary had left without him.

FROM EVENTS TO PROPOSITIONS While (46.a) sounds fine, (47) is not very felicitous. These observations suggest a further division among abstract entities--among possibilities, facts, propositions, and projective propositions. The Vendlerian observations concerning eventuality and abstract entity denoting nominals are as much a study of the contexts to which these nominals supply arguments as they are a study of the nominals themselves. Many of these predicates seem to pick out distinct ontological types which lie on a scale of world immanence. For instance we have distinguished a variety of eventualities; these lie toward the concrete end of the spectrum as they all have spatiotemporal properties and causal efficacy. On the other hand projective propositions and propositions arguably have none of these properties. Propositions also exist in all possible worlds, whereas our intuitions concerning eventualities is that they are, for the most part, contingent entities. Facts fall somewhere in between in the spectrum of world-immanence. They are contingent entities in the same sense as eventualities; but their identity conditions are still to some extent dependent upon our descriptions of them, as is evident from the inference pattern in (42). There are further, finer distinctions between various types of abstract entities--e.g., between possibilities and facts. As we shall see, this complex typology receives support from other data, such as that involving quantification and anaphora.

2. QUANTIFICATION, ABSTRACT OBJECT ANAPHORA AND THE TYPOLOGY OF ABSTRACT OBJECTS

2.1 Quantification One way of testing whether the types of predicates isolated in the previous section are satisfied by different types of objects is to quantify over the relevant argument places in complex open sentences. To state the test formally, suppose
33

have a rather different feel. (48.c) lacks a truth value altogether; it is unacceptable, as is any variant with another quantifier substituted for nothing. According to my intuitions, (48.c) indicates a category mistake. Such sentences are unacceptable, though it is impossible to attribute the unacceptability to a syntactic source; both belief and temporal contexts allow such quantification when they occur in isolation. And also the unacceptability cannot be attributed to a simple incompatibility of predicates as in (48.a-b). The unacceptability of (48.c) indicates a semantic incompatibility between the types of objects that such contexts take as arguments; the same type of object does not satisfy both contexts, in this case a belief context and a temporal location context. Let us now apply our quantificational test to the division between eventualities and propositions. A sentence like (48.c) above indicates a distinction between the two types of objects. Objects of belief are not the sort of things that can (at least in any straightforward sense) take time. So the quantficational test does distinguish between objects that have a temporal location or extension and those that do not. The quantificational test also distinguishes projective propositions from pure propositions. Projective propositions and propositions are both at the abstract end of the spectrum of world immanence, but the quantificational test distinguishes between them. One cannot quantify over projective and ordinary propositions at the same time. Contrast for instance (49.a-b) with (49.c-d): (49.a) (49.b) (49.c) (49.d)

#John desires everything that Mary believes. #Everything Mary asks for is true. John asks for something that Mary wants. Everything that John believes is true.

On the other hand, (49.c) shows that the quantification test does not distinguish between different types of projective propositions; although questions and desires would seem to be very different sorts of objects, quantification binding an argument in both contexts simultaneously seems fine. The quantificational test also reveals that the syntactic tests for projective proposition contexts are not absolute. Expect is a verb that can take either a normal that clause in the indicative mood or an infinitival phrase. So it and similar verbs would appear to straddle the categories of propositional and projective propositional contexts. In the case of expect, however, the quantificational test appears to indicate that its objects are projective propositions: (50.a) ? John expects something that Mary knows. (50.b) You can expect whatever you ask for (desire, permit). The moral we should draw from these anomalies is a familiar one. The distinction between projective propositional contexts and propositional contexts is a semantic one, and syntactic tests for context classification are not in general absolute. There are limits to the quantificational test. It does not distinguish between the

---------------

34

FROM EVENTS TO PROPOSITIONS

CHAPTER ONE

various eventualities when the usual contexts are used. The contexts used to distinguish among eventualities are temporal modifiers. The temporal modifiers for states like lasted for an hour and those for punctual events like happened in an hour are incompatible. So are modifiers for extended events--e.g., beginning at five, ending at five--and predicates for punctual events--e.g., occurred at seven. But these incompatibilities appear to be merely predicate incompatibilities. (51.a) Nothing that lasts for an hour happens in an hour. (51.b) Nothing that begins at five had occurs at seven.

(51.c) John saw something that lasted an hour and took place in the park. Finally, the quantificational test does not reliably distinguish between the objects satisfying factive and NI perception contexts. (51.d) (51.d) Everything John saw is a fact. Finally, let us consider factive and proposition contexts relative to the quantification test. Consider (52) in comparison to (5l.d). Clearly (52.b) is better than (52.a), which seems decidedly odd. But even attitude verbs with factive presuppositions like know do not seem to yield perfectly felicitous sentences--witness (52.b-c) (52.a) ?Everything John believes is a fact. (52.b) ?These photographs indicate what John knew. (52.c) ? These tapes indicate nothing of what John knew. The intended readings of (52.b-c), where what is indicated are the facts toward which John has some attitude, is not available. Thus, the quantificational test also supports the distinction between facts and propositions. Similar quantification tests to those I have already discussed will distinguish between facts and projective propositions and facts and eventualities.

35

not just sentential nominals but other constructions like verb phrases or even whole sentences introduce abstract objects and eventualities into a discourse and may serve as referents for anaphoric pronouns. The study of anaphora considerably broadens the scope of natural language metaphysics, and it also refines and verifies our provisional typology of abstract objects with another sort of data. Before discussing anaphoric examples, I need to sketch how I conceive of abstract entity anaphora. I illustrate with eventualities. Anaphoric reference to events may involve sentential nominal antecedents as in (53). (53)

The quantificational test also does not distinguish between the denotations of Nl complements and events. Consider the riddle-like but acceptable sentence.3 2

--~------

[The destruction ofthe citY]i amazed Fred. Iti had been bloody.

But events may be introduced into a discourse by other than nominal elements. Verbs, or more precisely the tense and aspectual components usually associated with an inflection or I node in the syntax, introduce events as objects in a discourse. These events may be referred to anaphoricaily in subsequent discourse. Ramsey (1927) first proposed that verbs might be predicates of events as well as the arguments contributed by their subjects, objects and indirect objects. Davidson (1967) argued that action verbs had a hidden argument place for events. According to Davidson a sentence like (54.a) has the logical form of (54. b): (54.a) John kicked Sam on Monday. (54. b) 3e (kick(e,j, s) & past(e) & on(Monday, e)) Now (54.a) can be extended to a sentence in which anaphoric reference is made back to the event introduced by the first clause. (55)

John kicked i Sam on Monday, and iti hurt.

The coindexing on the verb represents an anaphoric link between the event entity characterized by the verb hurt and the denotation of the pronoun. The coindexing here and throughout the book is to be interpreted semantically; the denotation of the pronoun and its antecedent are semantically related in some way. Davidson's logical form for (55), given in (56), illustrates the general semantic effect of anaphora in traditional terms; the anaphoric pronoun introduces a variable which is either bound by or somehow related to the semantic value of the antecedent NP or in this case bound by the existential quantification introduced by the verbal complex.

2.2 Anaphora (56) Another linguistic construction with which we make reference to abstract entities is anaphora. In anaphora, intuitively we refer with a pronoun to an object that has already been introduced into the discourse by some other linguistic construction. If we take anaphora to be a relation between the denotations or the semantic values of the linguistic antecedent and the pronoun, it can be very profitable to study abstract entity anaphora. Abstract entity anaphora reveals that

3e 3e'(kick(e,j, s) & past(e) & on (Monday, e) & past(e') & hurt(e', e))

The semantic approach to anaphora is right, but the Davidsonian analysis is inadequate and incomplete for a number of reasons. A full analysis of intersentential anaphora will have to await the development of DRT, coming in chapters 2 and 3. I will defend the semantic analysis of anaphora in chapter 6 using the DRT framework.

36

FROM EVENTS TO PROPOSITIONS

CHAPTER ONE

One can anaphorically refer not only to eventualities but also to purely abstract objects like propositions and facts. Consider, for instance, the examples at the beginning of the introduction. The acceptable patterns of abstract entity anaphora thus may offer another source of information concerning the diverse sorts of abstract objects. There are two ways to use the anaphoric data to uncover distinctions of natural language metaphysics. Suppose that the linguistic antecedent of an anaphoric pronoun occurring within a context C is a nominal A occurring in context C. If the anaphoric link is felicitous, then C and C may be satisfied by the same sort of entity. Further, the denotation of A may satisfy both context C and C'. If the anaphoric link is infelicitous, then this is an indication again that C and C are not satisfied by the same type of entity. Because of the general analysis of anaphora, the anaphoric test is a semantic one. The anaphoric connection made between C and C' is at the level of denotations, not syntactic expressions. The anaphoric data concerning perfect and imperfect nominals supports the hypothesis that semiconcrete objects like events and abstract objects like propositions should be distinguished. Nominals that denote events cannot be anaphorically linked to pronouns that occur in contexts that don't admit such nominals. (57.a) ?[The destruction of the citY]j took several hours. Fred hadn't believed it;, when he had first heard about itj. (57.b) [The destruction of the citY]j took several hours. Fred hadn't believed that itj could happen. Even though it makes sense to link anaphorically the first occurrence of the pronoun in (57.a) with the derived nominal phrase, it sounds bad to many speakers. I explain this by appealing to a clash of type requirements. The relation of believing takes a proposition as an object; it forces the pronoun to refer to a proposition. If of-ing gerundives always refer to events, then to identify the semantic value of the pronoun with that of the gerundive would yield a clash of types. On the other hand, (57.b) is a context whose preferred arguments are events, and that sounds fine. If we distinguish between propositions and events, then we can explain why (57.a) is bad and (57.b) good. These examples show that eventualities and propositions are to be distinguished, even when neither is introduced by an NP or a noininal. Consider for instance the pair, (58.a) Susan's boyfriend has graduated. But Sally does not believe it. (58.b) The worst student in the graduating class has graduated. But Sally does not believe it. In principle, there are two choices for the anaphoric antecedent of it in (58.a), since as we have already seen sentences may introduce both eventualities and propositions into a discourse. The first is that it refers to the proposition expressed by the first sentence in (58.a). A second possibility would be that it refers to the

37

event introduced by the first sentence. In many contexts, it may in fact be difficult to tell whether a pronoun picks out a proposition or an event. But from what I have said the second possibility is not a real one. For suppose that Susan's boyfriend = the worst student in the graduating class. Then the first sentences in (58.a) and (58.b) introduce the same event (on many if not most views of events), but it appears that (58.a) may be true while (58. b.) is false. If it picks up the proposition expressed by the first sentence in (58.a-b), then the argument sketched above with regard to events does not go through. The proposition determined by the first clause in (58.a) will not on most plausible theories of propositions be identified with the proposition determined by the first clause in (58.b). Anaphora also distinguishes between various sorts of eventualities. For instance, we cannot felicitously refer anaphorically to states with paradigm event contexts like it took place. Compare (59.a), for instance, with (59.b): (59.a) ?John lovedj Mary. Itj took place in the park. (59.b) John loved Mary. It lasted many years. Also if an anaphoric pronoun occurs in a context that attributes an extended temporal interval, it cannot refer to an achievement. (60)

?Alexis reachedj the summit. Itj took several minutes.

The other types of eventualities impose similar constraints on anaphora. Among the abstract entities, the anaphoric data only partially reflects the distinctions developed with other tests. The anaphora test distinguishes between facts and propositions, or facts and projective propositions, though the data is perhaps not as firm here as one would like. The predicate is a fact, I have assumed, is a factual context and ACC-ing gerunds supposedly denote facts, while verbs like doubt and believe take propositions as objects. Although what the sentences in (61) attempt to express is perfectly sensible, these sentences still sound quite odd to me. (61.a) ?John doubts [that Susan got an A on the test]j. But itj is a fact. (61.b) ?Mary wonders whether [she got an A on the test]j. But it j (that j) is a fact. (61.c) ?[Fred kissing MaryL was too much for Sam to bear. But John didn't believe itj. Propositional verbs, on the other hand, happily share anaphoric connections between their complements: 33 (62)

John believed [that Mary would leave himJi. Fred was certain of iti, was certain of itj, knew itj, expected itj).

The anaphora test does not distinguish projective propositions and propositions

38

CHAPTER ONE

when the normal containers are used. In general, projective propositional and simple propositional verbs do not share anaphoric connections between their complements very well--witness (63.a-b). (63.a) ? John asked (wanted) [to go to the parkJi. His mother believed itj. (63.b) ?? His mother will allow [John to go to the park]j. But he doubts that j. Yet other examples with anaphoric links between projective propositional and propositional contexts are fine. (63.c) John believes that he will go to the park. His mother will allow itj. (63.d) The Danes believe [that the Germans will reunite]j. The French fear it j. The Germans themselves desire itj. (63.d) shows that sometimes the anaphora test does not distinguish between possibilities (the objects of fear), propositions, and objects of buletic verbs. Nevertheless, the similar (63.b) is unintelligible, though the scenario is perfectly straightforward: John's mother will allow him to go to the park, but he doubts that he will go to the park. Of course, the anaphoric link between that in (63.c) and the proposition expressed by the entire first sentence is a possible anaphoric antecedent; but that is simply an instance of anaphoric linking between two propositional contexts. Once we look at complex nominal antecedents where an NP dominates an S' or Complement Phrase (CP), however, we see a better reflection of the typology of abstract entities. With such antecedents the anaphora test distinguishes between facts, possibilities, propositions, and projective propositions. The following examples show that that clauses in a complex NP cannot act as antecedents to pronouns when the pronouns occur in a context that takes as argument a distinct type of abstract object from the type taken as an argument to the predicate introduced by the head noun of the complex NP. The first clauses on their own, however, seem to me to be fine. (64.a) ?John believed [the claim that Mary would leavehim]j, and he feared itj. (64.b) ?John feared [the possibility that Mary would leave him]j. Fred believed itj. (64.c) ?John feared the possibility [that Mary would leave himJi.The signs indicate thisj. (64.d) ?John believed the claim [that he would go to the park]j, but his mom wouldn't permit itj. (64.e) ?John doubts the claim [that Mary got an A on the test]j, but itj's a fact. (64.t) ?Mary wonders about the question whether [she got an A on the testl. But it j (thatJ is a fact Especially telling is the contrast between (64.g) and (63.b). Though the first

FROM EVENTS TO PROPOSITIONS

39

sentence of (64.g) is fine, the discourse as a whole is decidedly odd. (64. g) ?The Danes believe the claim that the Germans will reunite. The French fear it, while the Germans themselves desire it. The anaphoric test does not strongly confirm a difference between propositions and the objects of NI perception (BP situations). Statements like (65) are natural in which the anaphor is linked to the antecedent verb phrase: (65.a) John believes that Mary [hit a home runl. After all he saw her do SOj (it j ). (65 .. a) John saw [Mary cross the finish line first in the marathon]j. Two days later, he still didn't believe itj. In contrast with (65.a-b), however, (66) is not felicitous. (66)

??John saw [Mary cross the finish line first in the marathon]j. Two days later, he still didn't believe this claimj.

As with the distinction between projective propositions and propositions, the anaphora test distinguishes propositions and objects of NI perception only when complex NP constructions of the form the N that p are used. In general, the anaphora test upholds the divisions in the typology already introduced in earlier sections. But the anaphoric data also indicate that the boundaries of the kinds in the typology are more fluid than we might perhaps suppose. We can sometimes make reference in a context whose arguments are typically of type X to an entity which we would judge to be of type Y given its context, for X '# Y. It seems that only with complex noun phrases in which the NP dominates a CP do we get the relevant type distinctions. Also we get puzzling asymmetries--as in the contrast between (65.a-b) and (66) or between various projective attitude contexts as in (67) below. Projective attitudes include desires, questions and commands. Desires differ from commands and both differ from questions, in that pronouns within buletic contexts cannot easily pick up antecedents within rogative and permission contexts.34 At least (67.a-c) sound worse than an anaphoric link between two buletic contexts as given in (67.d), and much worse than the VP ellipses in (67.e-t) (67.a) ?Eva asked [whether she could go to the park]j. She had wanted thatj all day. (67.b) ? Eva's mom allowed her [to go to the park]j. But she didn't want that j. (67.c) ?Eva asked [to go to the park]j. She had wanted thatj all day. (67.d) Johanna wanted [Eva to go to the park]j. Eva wanted thatj too. (67.e) Eva asked whether she could [go to the park]j. She had wanted to ¢j all day.

40

CHAPTER ONE (67.f) Eva's mom allowed her [to go to the park]j. But she didn't want to ¢j.

There is a curious asymmetry here between buletic contexts and the others. One can pick up antecedents within buletic contexts for pronouns in permission or rogative contexts, but not vice-versa. Rogative and permission contexts happily allow anaphoric links in either direction. (68.a) (68.b) (68.c) (68.d)

Eva asked [whether she could go to the park]j. Her mom permitted itj. Her mom allowed Eva [to go to the park]j. She had asked about thatj. Eva wanted [to go the park]j. But her mom wouldn't permit itj. Eva wanted [to go the park]j. But she didn't dare ask her mom about itj.

Why are some anaphoric links between two contexts C and C' good while links between C' and C are for the most part uniformly bad? This is a puzzle of natural language metaphysics that we cannot yet resolve. The anaphora test yields other intriguing puzzles. It shows that there is an unexpected fluidity to the typing in the typology of abstract objects and suggests that at a more fundamental level, many distinct types of natural language metaphysics may be very similar, if not identical. The analysis of these phenomena will come in chapters 5 and 8, but I will touch again on this theme once we have examined the typology from a third perspective--the perspective of closure principles.

3. PRINCIPLES OF SUMMATION AND STRUCTURED DOMAINS FOR ABSTRACT ENTITIES The last way of examining types of abstract objects in natural language metaphysics concentrates on their logical closure principles. The investigation of closure principles answers questions like this: If 8 denotes an object of type T, does -,8 also denote an object of type T? If so, then objects of type T are closed under some sort of operation of complementation, corresponding to the meaning of negation. The closure principles for an entity of type T define an algebraic structure for the domain of objects of type T. Different closure principles will differentiate between various sorts of abstract objects and provide us with a more systematic treatment of natural language metaphysics to conclude this investigation. An answer to the question of what is the structure of the domain of propositions or events, however, depends on what we are postulating a structured domain for. I can think of two possible reasons. The first concerns the possibilities for propositionhood, eventhood, facthood; etc. That is, what sort of abstract entities does natural language allow us to talk about? This is, I believe, the sort of question that has motivated those interested in the "algebra of events." Such theories of the structure of an ontological domain should ensure that the entities to which one can refer anaphorically exist. Second, they should provide denotations for combinations

FROM EVENTS TO PROPOSITIONS

41

of expressions that each denote an entity of a particular kind. I shall refer to such domains with bold letters in italics--e.g., P, E ,etc. A second concern is to characterize the domain of propositions put forward by a bit of natural language discourse. That is, the task is to discover just what propositions, events, or other types of objects are introduced by a particular bit of natural language discourse. This is a concern of theories like Discourse Representation Theory. A text has a complex logical and rhetorical structure that complicates our understanding of the domain of entities made available by a text. A text may simply assert the existence of some object. It may also contain the supposition that such an object exists and then contain a number of assertions based on this hypothesis. And there are many other rhetorical devices or modes that a text contains besides simple assertion and supposition. Thus, we might think of a text as generating a set of domains--or better yet a set of domains and assertions about objects in those domains, i.e., a set of partial models--which is structured in a particular way to make clear the logical and rhetorical structure of the text. I shall call such structures spaces, if T is a text, then JP(T) and E(T) are the spaces of propositions and events constructed from T. I shall be able to make this much more precise using DRT, but for now spaces will be defined as a structure <'M, ~ >, where 'M is a set of partial models and ~ is a partial ordering such that if M ~ M' and x E 1:(M), where 1:(M) is the domain of M, then x E t£(M'). The ordering encodes the relevant structure of the logical and rhetorical relations of a text but it abstracts away from the content of those relations, as this is not needed to express closure principles for spaces. I will assume that a satisfaction relation for formulae may be appropriately defined for models M in 'M. I will also suppose that these partial models form a context for the processing of elements of the text. So we may speak of a particular phrase introducing an object into a particular partial model in the structure--the one that serves as its most local context. Most local is defined with the help of~: M is the most local context for a phrase

3.1 Events I will begin again with events, for they are more familiar ground. Linguists like Bach (1981, 1986), Link (1983), Ter Meulen (1984) and Krifka (1987, 1989) have studied the structure of the domain of events. One interesting aspect of the domain of events is that events can be summed together to yield new events. Of course the same is true of the domain of individuals.

FROM EVENTS TO PROPOSITIONS

CHAPTER ONE

42

(69.a) Fred, Mary, and Jane met Sam at the store. They went to the movies together. (69.b) Every man on this block owns an expensive sports car. They are all Ferraris. Kamp and Reyle (199+) discuss such examples at length. I shall look at their DRT analysis in chapter 2. For now I simply point out that examples suggest that individuals may sum together to form plural entities or groups. The summation principle undergoes a substantial change for event and proposition anaphora. Events do not pluralize easily in the following sense. One cannot use a plural anaphoric pronoun alone to pick up a group of events, in the way that one can use a plural pronoun to pick up a group of individuals--e.g., people, rocks, trees, etc. Consider the following example (due to Link):36

accomplishments, which behave similarly, as Krifka (1987) has argued, to co~nt noun denotations. If this is right, then it appears that we have two ways of forrmng collections for events--a principle that takes individual events and fuses them into a larger individual event (the mass-like summation principle), and a principle that takes individual events and forms a plural group from them (the "count" summation

(71)

Many runners drank wateri from the stream flowing by the finish line. It i made them quite sick.

(69.b), (70.b), and (71) have a similar logical form. The singular pronoun in (71) picks up all those quantities of water drunk by the runners--i.e., those quantities satisfying the conjunction of the two properties related by the denotation of the determiner many. The pronoun in (70.b) appears to pick up a collection produced by the same principles as the collection in (71). This principle of "summation" appears to work generally with all kinds of events--even achievements and

.

~~~.

It appears that the domain of eventualities allows the mass type of sumn;atIon

over diverse types of eventualities. Example (72) shows that one can anaphoTIcally refer to a sum of events and states introduced over several clauses. The definite description the outing in the last sentence refers to the sum of all the events that are introduced in the previous sentences. (72)

(70.a). Three men raised i the flag of the republic. TheYi took the ruling junta by surprise. (70.b) Three men raised i the flag of the republic. Iti took the ruling junta by surprise. (70.a) cannot be used to mean that there were three events of raising the flag, the group of which took the junta by surprise. One can use the plural definite description these events to pick up the group, a fact familiar from plural anaphora generally. On the other hand, in using the singular pronoun to refer to this group of events as in (70.b), an acceptable sentence with the same intended anaphoric interpretation results. This anaphoric data provides some support for the notion developed recently by Bach (1981), Ter Meulen (1984), Link (1983) and Krifka (1987,1989) that events in natural language metaphysics are a structured domain, closed under a summation operation. On such a conception, events sum together to form a new event. More precisely, the space of events is closed under a "join" or sum operation. The linguist's algebraic view of events refines an older philosophical theme that events are subject to mereological principles. 36 This feature makes event expressions akin to mass nouns, where many "lumps" of the same stuff may sum together to form a larger, singular "lump" of the same stuff:

43

John went to pick Mary up for the dance. But he had forgotten the corsage. That made him late. The food at the dance was terrible, the music mediocre. Then John spilled some punch on Mary's dress. She said she never wanted to see him again. The outing was in short a disaster.

In contrast to closure under summation, the domain of events is not closed under complementation. The reason for this is the following. Assuming a c~mpositio~al semantics for event expressions, this means that the negation of a nOmInal denotIng an event does not necessarily also denote an event. To use Cresswell's (1985) example, the train's arrival may be an event, but whatever the train's non-arrival denotes, it does not denote an event. The non-arrival of the train does not accept the standard perfect nominal containers--as witnessed by (73): (73)

*The non-arrival of the train occurred at 10 am (lasted many hours, took place at the station in Victoria).

So in virtue of Vendler's criteria, the denotation of the non-arrival of the train should not be classified as an event. Further, the non-arrival of the train can be paraphrased by a that clause; the positive derived nominal phrase the arrival of the train cannot be--that the train arrived is not synonymous with the arrival of the train. At best, events obey the following law of relative complementation. This law says that for any subevent e of an event e', written e c e', there exists a third event that summed together with e yields e' and is disjoint with e. In symbols where 0 represents overlap and E9 sum and leaving off the outside universal quantifiers: (EO)

e c e' .... 3e" (e" E9 e = e' & --,e" 0 e).

The principle of relative complementation does not predict that the non-~val of the train is an event, if one assumes that there isn't any larger event of WhICh the train's arrival and the train's non-arrival are components. This assumption appears reasonable. Suppose we think of some description of an extended event e'--e.g., the

44

FROM EVENTS TO PROPOSITIONS

CHAPTER ONE

1988 campaign for the U.S. presidency by the Democratic candidate. We may also single out a particular event e, the acceptance speech at the Democratic convention. The phrase the rest of the campaign certainly appears to have a denotation that is the relative complement of e' in e. It is also very unclear whether the disjunction of two event descriptions yields another event. A sentence like (74)

John's kissing Mary or his pinching her led her to knock him unconscious with her handbag.

appears to indicate not that some sort of disjunctive event led her to knock him unconscious, but that one or the other event (perhaps the speaker doesn't know which) did. What could a disjunctive event even be? We seem to have no such conceptual category. If such observations hold in general for events, we should tentatively with Link (1983) and Krifka (1987) assign events a domain structure whose two closure principles are (EO) and (El)--the former concerning relative complementation, the latter concerning summation. (E1)

::le" e"= effie'.

Krifka and Link go on to develop a lattice structure for events characterized by the universal closure of the following axioms besides (EO) and (E1): (E2) (E3) (E4)

effie = e. effie' = e' ffi e, (e ffi e') ffi e" = e ffi (e' ffi e").

Without further discussion, some of these axioms--for instance (E3)--seem suspect. The event of John's taking his shoes off and going to bed, as van Benthem (1991) has argued, is not the same event as John's going to bed and then taking his shoes off; the latter might have quite different causal consequences for instance--like John's getting his bedsheets dirty. Moreover, these axioms yield more events than are warranted for anaphoric purposes. To see what is anaphorically warranted, let us investigate the space ]B(T). Immediately suspect in the algebraic characterization of events is the axiom (E1). Not every sum of events yields another event. The mereological summation principles for events in domains of elements of ]B(T) appear to be much more limited--at least if we are looking at mereological principles for events and not groups of events. Outside of a determinate context, it appears that a pronoun cannot refer to the sum of two disparate, unconnected events. Consider for instance (75): (75)

Fred went shopping for a new pair of sneakers. Mary went to her office to prepare some reports. It took a long time.

45

Of course matters are here difficult to judge, since interpreters will put (75) in a context so that the sum of the two events may be a possible antecedent.37 Example (75) suggests at least that it is not the case that in every context any group of events may be summed together. That is, given a text T that mentions two events, their sum may not be an object of ]B(T). This is not so surprising if we look at the facts about plural anpahora; there too not every sum of individuals is available to be the referent of a plural pronoun. Consider for example (77): (76)

John first picked up Jaime, then Mary, and finally Susan for the double date to the movies. They had a nice time.

Frey and Kamp (1991) contend correctly that it is impossible to get Jaime and Mary to be the referent of they, unless they are already given as a group by the context. Similarly, mereological principles for mass terms are, upon closer examination, more limited than some discussion in the literature suggests.3 8 One must be careful about the implications of such examples as (75) and (76). No one, for example, would deny that some events are more salient in a given context than others, and so more likely to be chosen as referents for pronouns, than others; and there is no doubt that one could interpret the data in (75) and (76) as a matter of salience in context. On a salience oriented theory, the explanation of the data would claim that while such events were in principle available as referents for pronouns, they are assigned such a low salience that they are never chosen as referents. But there is evidence against the view that the domain of events is closed under summation which the salience theory does not explain. Conjunctions of event denoting nominals do not always denote one event. Sometimes they denote a group of events. Contrast for instance (77.a) with (77.b): (77.a) John's hitting of Fred and Mary's getting married were the main events of the week. (77.b) John's hitting of Fred and Fred's subsequent returning of the punches was the main event of the week. It is impossible to talk about the sum of the two events denoted by the nominals in the conjoined subject NP in (77 .a). It seems, however, just possible to s~eak of (77.b) as an event in the singular. The possibility of doing so depends on bemg able to fit the events into a coherent whole event--in this case a fight. The salience theory does not explain this failure of summation. So (E1) does not hold for event spaces, ]B(T), created by texts T. The advocate of (El) may still be unconvinced by the example in (77 .a). He can always force the two events in (77 .a) to merge together by using the expression, the event of Thus,

(78)

the event of John's hitting Fred and Mary's getting married

47

FROM EVENTS TO PROPOSITIONS would, according to him, denote the sum event. The use of such event descriptions however, can be explained by a much weaker principle: if e, e' E 1:(M) for some M in B(T), then e €a e' E 1:(M), if it is explicitly introduced by an event description that is a conjunction of a description for e and a description for e'. These conjoined event descriptions are not terribly felicitous in any case, unless the context supplies some reason for connecting the events. Thus, it may be that (E1) is an artifact--a natural generalization from texts, but not one that is fully supported by our linguistic practice. If one is persuaded by these judgments, one might reject (E1) as a principle of E as well as rejecting it as a principle of B.39 One can also cast doubt on (EO) from the perspective of B. While (EO) might be appropriate for a certain philosophical approach to events, it is certainly too liberal from the perspective of B. The set of events introduced by a natural language text does not satisfy (EO). To see this consider (79): (79)

#Dukakis made a great acceptance speech at the Democratic Convention. It was the highlight of his campaign. It suffered from complacency.

(79) is bad, if we assume the only available event antecedents for occurrence of it in the last sentence are the events of Dukakis's speech and of his campaign. Since (79) is bad, it seems impossible to assign as an antecedent to the pronoun the event that is the complement of Dukakis's speech relative to his campaign for the Presidency, which intuitively is what is desired. Of course, this event is easy to pick up with the phrase, the rest of his campaign; if we insert that phrase in place of the occurrence of it in the last sentence, the discourse becomes perfectly felicitous again. The rest of his campaign gives the listener the license to construct the event and introduce it into the universe of discourse, but otherwise the event is not taken to exist in B(79), the space of events generated by (79). A superior description of the domain of events of a text B(T) is one on which B(T) is closed under several principles of comprehension of the form if
(EO)

Suppose the phrase the rest of the fP, where

is an event space. Suppose also that 3M E :M such that M ~ Mo, and 3e', e E 1:(M) such that M ~
As Krifka (1987) and Bauerle (1987) have noted, there is a problem with events and negation if events are not closed under complementation. It affects both a

theory of events that has only (EO) or only (EO). Suppose that we adopt the general account of a large class of adverbial modifiers in the way proposed b~ Davi~son, and suppose we analyze for two hours as a predicate of events. But If that IS the case and events are not closed under negation, how can we make sense of (80) .on the reading where the adverb is understood to have wide scope over the negatIve quantifier no one? (80)

No one talked for over two hours.

If we try to carry out the standard event-based approach40 to such adverbial modifiers, we cannot write down a coherent logical form for (80) that captures the intended reading. For the logical form for No one talked would ~e --,3x3e t.alk(x, e), and if we make for two hours a predicate of e, we must end up WIth the lOgICal form --,3x3e(talk(x, e) & for two hours(e», which assigns (80: incorrect truth co~ditions. I shall expand on this difficulty in the next sectIOn when I examme the complementation principle for states. I turn now to the counterpart of (E1) for the space B(T). I will assume that the domain B(T) contains events explicitly introduced by event descriptions. But this is not enough to characterize those sums of events that are elements in B(T). Example (77.b) indicates that sums of events that are of the same type, or whose types are "naturally connected together" in some sort of script-like world knowledge, are elements of B(T). These connections might be thought of as a path of events types; intuitively, such a path is supposed to connect events of a particular type in a natural or stereotypical sequence. Such paths are part of the common sense knowledge of the competent speaker and are exploited in text understanding. 41 Such rela~ons on event types define derivative relations on events. I will use a two place predicate epath(e, e') whose interpretation is that e and e' are instantiations of two event-types belonging to the same path. Paths are typically temporal sequences of events (these include causal sequences of events too), but they may sometimes be temporally simultaneous and spatially contiguous or related. I hypothesize a collection principle that sums ~ven~ in the ~ame e-path and also any events in the same e-path temporally or spatIally mtervemng between the two events. Let €a again stand for 'sum', 0 'overlap', c 'is a part of. Let u, v range over individuals, e, e', etc., range over events. Let M E :M for any structure <:M, ~ > built up from a text. Then

(B 1)

(E-Path Collection): \fM 3M I(M I extends M & 3e" E 1:(M) (E-path(e, e') -+ (e, e' c e"

».

E

1:(M I) \fe, e'

The notion of an E-path is very vague; it is also provisional. In chapter 8, I will use notions from discourse structure to make event summation more precise. In view of examples like (70), one might also suggest that B(T) is closed under another limited principle of comprehension, on which all the events satisfying one

~-----zrii:~~~=~~~-~--riTTA~-~-~-~---:;-----~-----P--------~------------------------------------

CHAPTER ONE

FROM EVENTS TO PROPOSITIONS

of a certain conventionally determined class of event descriptions sum together into one event. One way of doing this would be to sum events according to their participants; if their participants form a group entity in the text, then so do the events they participate in. I will assume that such actors can play certain roles in events--RJ, R 2 , etc. In what follows let R range over such roles.42 (lB2)

(Thematic Event Collection): \fM 3M 1 (M 1 extends M & \fy -+ e C e')).

E

'L(M) 3e'

49

that events do. The pronoun appears to pick up the proposition that combines everything Mary says.43 One could also refer to everything that Mary says with the plural description these claims. Thus, propositions seem to have very similar summation principles to those for events. There is also the less constrained summation familiar from events. The following example shows how several, separate sentences in a text may combine to form a proposition that is the anaphoric referent of a pronoun or definite description.

E 'L(Ml) \fe E 'L(M) \fx(x E Y& R(x, e))

(82) The. principle of .thematic event collection relies on separate axioms for groups (~hI~h would anse from the study of plural anaphora). But given these, the pnnciple accounts for the examples in (77), as well as (70.b). In (77.a), the two events ~en'~ of the same type nor do their types fall into a natural path. Further, they fall to mvolve elements of an antecedently given group. So it is difficult to connect them together to form a spatiotemporal path and a single event. Once the group ~s antec~dently given as in (77.b), however, the principle of thematic event collectIOn predicts correctly the sum to be available. As for (70.b), we can plausibly s~ppose from the facts of plural anaphora that three men introduces a group into the discourse. . These principles of restricted comprehension and collection define a very dIfferent structure for the domain of events in comparison with the Krifk:a-Link treatment. The event building operations described by (lBO)-(lB2) create for a given set of atomic or "urelement" events a cumulative hierarchy that includes ever more complicat~d events.. This view reflects a different metaphysical persuasion from that of Krifk:a and Lmk. Of course for events of a certain type--for instance, events of some?ne's drinki!1g wi~e--on~ can easily derive with some plausible, additional assumptIOns, the Krifk:a-Lmk lattIce structure. The textual perspective encoded in ]B takes sums and composite events to be essentially the product of human thought. Events .are construct.ions--particular regions of space-time singled out by a conventIOnal!y deterrnmed ~lass of event descriptions and event building operations. The appropnate mathematical structure for the space ]B(T) is not an algebra but rather a weak set theory, with axioms (lBO)-(lB2). If E is identified with the set of all events introduced in ]B(T) for some T, then in general none of the Link-Krifk:a axioms hold.

3.2 Propositions

Proposition anaphora reveals that the domain of propositions too has a structure. Consider for instance (81): (81)

John believes everything Mary says. Further, it is all true.

(81) suggests that groups of propositions "sum" to form a singular entity in the way

The "liberation" of the village had been bloody. [Some of the Marines had gone crazy and killed some innocent villagers. To cover up the "mistake," the rest of the squad had torched the village, and the lieutenant called in an air strike.]j At first the battalion commander hadn't believed itj.

Though similar with respect to summation properties, the domain of propositions and the domain of events also differ from each other. Most philosophical or linguistic theories of propositions (including something like the possible worlds theory or a Russellian theory) take he domain of propositions to be closed under these operations of a Boolean algebra: complement, join and meet. 44 We have already seen that the domain of propositions appears to be closed under a summation corresponding to conjunction. The disjunction of two propositions also forms a proposition; and further the negation of a proposition is a proposition, to which we may refer anaphorically. (83.a) Sam suspects that [either Fred is at a party or he is at a bar]j. Jenny thinks thatj too. (83.b) [It's not true that Mary will lose the racel; Fred believes this j too. Already these closure principles suggest that events and propositions are quite different sorts of objects. It is far from clear, however, that tidy structures like Boolean algebras are precisely what is wanted to characterize the domain of propositions in natural language metaphysics. Although the closure principles for a Boolean algebra might be plausibly applied to the domain of propositions, it is quite unrealistic to assume that the identities of a Boolean algebra hold as well. To assume that the identities held would imply that all logically equivalent propositions express the same proposition. But this view is not compatible with the demands of natural language metaphysics, or, for that matter, with a viable natural language semantics for propositional attitudes. 45 We have established that the Boolean closure principles are plausible for the domain P. But what, for instance, are the generators of the algebra? What identities if any might such an algebra satisfy? From the perspective of natural language metaphysics and the needs of semantics for attitude constructions, the generators might be the propositions expressed by simple, assertoric sentences. Of course we

50

CHAPTER ONE

must allow that in some cases an assertoric sentence will not express a proposition __ for example, if it contains an anaphoric pronoun and that pronoun has no antecedent. As some have argued,46 that the relevant antecedents exist is a presupposition of the sentence. In that case, we may take the following single axiom schema for our theory of propositions. 47 As notation, I will use' A , as an operator on sentences; if cp is a sentence, then Acp is the proposition cp expresses. (PI)

(Simple Propositional Comprehension) If S is an assertoric sentence, then given a context where all of S's presuppositions are fulfilled, AS E P.

Even though many of the propositions within this space are logically equivalent, natural language metaphysics still distinguishes them because of their different roles in attitude contexts. Their behavior in attitude contexts makes clear that logically equivalent propositions may still be distinct propositions. If we are committed to a principle of diversity in natural language metaphysics, we may as well be liberal: (P2)

(Diversity) There are infinitely many distinct but logically equivalent propositions.

With Fine (1981), we might say that on such a theory there will be infinitely many distinct propositions all true in the same possible worlds. 48 Fine shows that a theory which includes (a limited form) of propositional comprehension (for a formal language), diversity, an axiom specifying the necessary existence of propositions, and one relating propositions to possible worlds is logically very simple; it is sound and complete with respect to a simple semantics and it is decidable. One might take these two axioms to define the domain of propositions. But this really tells us very little about propositional identity. One might add to our pitiful stock of axioms idempotence of conjunction: (P3)

(Idempotence) p & p = p.

But it is not clear that one could add the same operation for other operators under which the space of propositions is defined. In DRT, for instance, it will tum out that while the operation corresponding to conjunction is idempotent, the operation corresponding to disjunction is not. From a characterization of P, I tum now to the space ]peT). Many of the observations about JB(T) apply also to the domain ]P(T) of propositions generated by a text T. If we take the anaphoric data seriously to indicate what are the available abstract entities that natural language discourse posits, then we have very strong reasons to doubt that ]peT) is closed under arbitrary intersection of constituent propositions. Consider (82) again: (82)

The "liberation" of the village had been bloody. Some of the Marines

FROM EVENTS TO PROPOSITIONS

51

had gone crazy and killed some innocent villagers. To cover up the "mistake," the rest of the squad had torched the village, and the lieutenant called in an air strike. At first the battalion commander hadn't believed it i . While some conjunctive propositions are available as referents for the pronoun, some are not. In particular, the conjunction of the first and second sentences alone does not appear to furnish an antecedent, nor, perhaps, the conjunction of the second and the third sentences. Also it would be difficult to argue that ]P(T) is closed under relative complement; the relative complement of the proposition expressed by all of (82) except the last sentence, for instance, is not an acceptable antecedent to the pronoun. So the domain of propositions ]peT) cannot have the closure properties of a Boolean algebra. If it were, we should be able to make anaphoric reference to these propositions, but we cannot. The structure of ]peT) is intimately connected with interpreters' intuitions about discourse structure. The conjunctive propositions that are posited by a text are those carved out by these mysterious principles of discourse structure. One of these principles is the propositional analogue of (E3). But there are others too that depend on the topical organization of the discourse. The space ]peT) is not cumulative in the following sense. Once the sums of propositions are formed, the propositions from which they were formed are often no longer available. To get smaller constituents, the space of propositions]P also is closed under certain "separation" or "segmentation" principles that carve up the content of a discourse in distinct ways-the inverse in effect of collection principles. Support for these principles about ]P(T) and a fuller study of them, however, must await a more thorough characterization of propositions and proposition anaphora in chapters 7 and 8. . If we identify P with the propositions of UT ]peT), again a set theoretIcal conception of the domain of propositions emerges, one governed by various comprehension principles ranging from the simple (PI) to the segmentation axioms mentioned in the previous paragraph. These principles leave a great deal of work to be done on the logic framework of propositions. For instance, they entail that even sentences like This proposition is false. express propositions in natural language metaphysics. More on this in chapter 10.

3.3 States Some have argued that states are identical to propositions. 49 But given our discussion of the previous two sections, states surely have a different logical structure from purely abstract entities. First, the domain of statesSO is not closed

52

CHAPTER ONE

FROM EVENTS TO PROPOSITIONS

under an operation of complementation, while the domain of propositions is. A state is always a state of some object.51 If the object ~ exists, it is not in the state

Suppose

(C) is a principle of conversion for eventuality types. The "property negation" of an event predicate is a state predicate. We can think of types here either as real properties or simply as extensional sets. (C) places an interesting constraint on the domain of states and events. It is a principle that relates the two domains together. (C) says that if't is a type that is a subset of E, then the complement of 't in the universe of eventualities is a subset of S, the space of all possible states. This interpretation of (C) assumes a complement operation on types corresponding to the negation sign. One can exploit (C) to define a principle of closure under complementation for states. Let s range over states, and suppose

53

are too strong. They must be restricted to certain eventuality types. At least negations of state descriptions seem to produce new state descriptions. Suppose it is false that John knows where the ball is. So it is the case that there is no state of John's knowing where the ball is. But then it seems very natural to say: John is in the state of not knowing where the ball is. That's just what John does not know where the ball is means. We can also assign typical stative adverbial modifiers to the eventualities introduced by the verbs, and we can refer to them anaphorically as states: (85.a) John didn't know where the ball was for over an hour. (85.b) John didn't knowj the answer to the problem. This j lasted until the teacher did the solution on the board. The negations of states behave like states with respect to adverbial modifiers--unlike accomplishments or achievements. 53 (85.a) (85.b) (85.c) (85.d) (85.e) (85.f) (85.g) (85.h)

After Mary was in the hospital, John went to visit her. After Mary wasn't at the hospital, she was at home. ?After Mary didn't eat the cake, John left. After Mary didn't swim, she went home. While Mary was at home, John washed the dishes. While Mary wasn't at home, John cleaned up the house. ?While Mary didn't eat the cake, John washed the dishes. While Mary didn't swim, John talked to her non-stop.

In contrast to the negations of statives and stative predicates themselves, the negations of accomplishment predicates in (85.c) and (85.f) sound odd. Negations of achievement predicates are also bad with these adverbial modifiers, whereas states go fine with them. Negations of activity predicates seem much like statives with respect to these test adverbials. So we might extend (Sl) to: (Sl')

Suppose x is a state or activity variable. Vu

E

0 (-.3x
--->

3s -.
u)).

(Sl)

(Argument Relative Complement): Vu

E

0 (-.3e
--->

3s -.
u)).

(S 1) says that whenever an actor, 0, of a possible event

?The non-arrival of the train lasted for hours.

If the non-arrival of the train denoted a state as it would under an unrestricted (Sl), then (84) would be predicted to be perfectly acceptable. Consequently, (Sl) and (C)

Because of (84) it is not possible to extend (S 1') to allow

No one got on base for over an hour.

Such a sentence would be typically uttered in a context in which the subject NP makes reference to a contextually salient background group of individuals whose existence is not in dispute. 54 Getting on base in baseball is an achievement, and achievements don't normally take durative adverbial modifiers like for two hours.

54

CHAPTER ONE

FROM EVENTS TO PROPOSITIONS

States normally take such durative modifiers (as well as activities). This seems to indicate that there is a state described by (86). We can pick up this state anaphorically too, by continuing (86) as in (87.a), and we can exploit the state's temporal location to situate the next event in the discourse as in (87.b). (87.a) No one got on base for over an hour. This occurred during the first game. (87.b) No one got on base for over an hour. Then Reggie hit a home run. The word then in second sentence in (87.b) exploits the temporal extension of the state mentioned in the first sentence and helps us locate the event of Reggie's hit. Krifka (1987) does offer a solution to account for the evidence in (86)-(87). He supposes that the logical form of a sentence like (80) involves reference to a maximal event as follows: (88)

3e (maximal(e) & for-two-hours(e) & -,3x 3e' C e laugh(x, e'))

55

reference to a maximal event. If that is the case, then the logical form in (87.b) cannot be correct, and that casts doubt on (88) as the logical form for (80). In the final analysis, I believe that one must handle adverbial modification--like that in (86) and (87)--in a quite different way. A defense of (S 1') as the right characterization of the complementation characteristics of the domain of states and a solution to the problem of event negation and adverbial modification is given in chapter 5. Relativizing (S 1') to the models in a given state space yields an appropriate axiom for S. Suppose 'AxAU. (511)

VM E '.M ifM ~ -,3x
Ur SeT), then (SI') is simply a consequence of (511). With respect to the other closure axioms, states behave similarly to events. States do not have an operation corresponding to the Boolean operation U. There aren't disjunctive states, just as there are no disjunctive events in ordinary English. The argument against the closure of the space of all possible events under join should carry over to the space SeT). But it also appears that OBI) - OB2) hold for the space SeT). If S is identified with

Krifka's solution is wrong, because it postulates the existence of a maximal event. No such maximal event is available for anaphoric reference with either a pronoun or a definite description. At least not if we think of an event in the ordinary sense of natural language metaphysics. One would expect that maximal events should have spatial parts like other large events; for instance a large battle may have one part waged in a valley, another on a hill top. If the event is really maximal, then it should include all (perhaps all accessible) spatial regions at that time. So if we can say things like,

3.4 Facts (89)

The battle raged across several counties. It included small skirmishes in the hills and a cavalry charge on the plains.

Then one ought to be able to say, (90)

?No one laughed for two hours, but it (this event) included Mary's washing of the dishes next door as well as a sunset on Neptune.

If Krifka's proposal really gave the logical form of (80), then there should be no difficulty with the anaphoric link in (90); the pronoun could refer back to the maximal event introduced by the logical form of the first sentence. Following the analysis of anaphora of events in the previous section and the hypothesis about logical form, one should naturally come up with the following logical form for (90):

(91)

3e (maximal(e) & for-two-hours(e) & -,3x 3e' C e laugh(x, e) & 3e" Mary wash dishes(e") & 3e'" C e sunset on Neptune(e"'))

C

Facts are one of the abstract entities occupying an intermediate position on the spectrum of world immanence. The logical structure of the domain of facts indicates that facts differ from events. "Conditional events" appear not to be a possible category of natural language metaphysics; the noun phrase the event of jf Mary comes to town, then Jack will be happy or a gerundive phrase construction like Jack's kissing of Mary jf she comes to town. do not denote events. Event descriptions or event denoting nominals simply cannot have the form of a conditional. Some of the anaphoric evidence surveyed earlier also suggests that there are no negative or disjunctive events, for it appears impossible to anaphorically refer to them. The syntax of that clauses allows us to speak happily of "conditional", "negative", or "disjunctive" facts, just as we speak of conditional propositions and negative propositions.

e (92.a) The fact that if Mary came home late, John would be in a bad mood forced her to leave work earlier than the others.

But (91) is completely anomalous; it does not appear as though one can make any The presence of conditional facts in natural language metaphysics also potentially

CHAPTER ONE

56

distinguishes facts from BP situations; conditionals are not acceptable complements of NI perception verbs. 55 Similarly, our language allows us to construct expressions that denote facts that are the complements (or the contradictories) of other facts, just as it does for propositions. (92.b) That no one bothers any more about doing a good job is not a legitimate excuse for distributing goods of poor quality. Natural language metaphysics also countenances some facts as "generalizations" of other facts. Reference to disjunctive facts in natural language also seems fine-witness for instance (93). (93)

The fact that the children were either asleep or playing quietly in their room allowed Mary to get some work done.

Unlike a disjunction of event descriptions (cf. example 75) the fact described in (93) involves as constituents facts described by either disjunct. So true disjunctive facts appear to exist. The structure of the domain of all possible facts, F, appears subject to the same comprehension axiom scheme as the one given for propositions (PI). In view of our discussion of substitution inferences in section I of this chapter, however, the principle of diversity would not apply to F. The space IF of facts generated from a text is, as in the case of propositions or of events, much more limited than F. In a discourse, the definite descriptions this fact and these facts may pick up only a limited number of possibilities. These available facts appear to be closely correlated with individual or atomic events or with complex but not compound sentences. They do not follow the discourse structure principles that govern the structure of spaces of type lP(T). Consider a slight variant of (82): (94)

The "liberation" of the village had been bloody. [First on a sweep through the town some of the Marines had gone crazy and killed some innocent villagers. To cover up the "mistake," the rest of the squad had torched the village. To cap it off, the lieutenant called in an air strike.L #This facti (these factsj, the factsJ made the senior officer call for an investigation.

The intended anaphoric link in (94) is not possible, if the singular NP this fact is used. The singular NP may only refer to the fact associated with the topic event \3r perhaps with the fact determined by the penultimate sentence. On the other hand, the intended anaphoric connection is fine with the plural NP these facts. It appears that atomic facts may not sum together to form singular facts, at least not in all cases. Fact locutions act more like count nouns than mass nouns in terms of their summation properties. As (94) indicates, events are more mass-like than facts. By

FROM EVENTS TO PROPOSITIONS

57

the event comprehension principles, the events denoted by the text within the square brackets should constitute an entire event--the event of the liberation. Nevertheless, even compound sentences denote single facts; insofar as facts obey a comprehension principle like (PI). Surely we can say the fact that Mary came home and that Sam stayed home and notbe forced to say the facts that Mary came home and that Sam stayed home. Thus, it appears that only a principle of comprehension governs the domain of facts; there is no separate summation principl~. ~hus, f~cts have different closure principles from propositions and events, a fmding whIch reinforces the conclusions of the previous two sections. There are two remaining types of abstract objects the structure of whose domains has not been discussed: projective propositions and BP situations. The domain of BP situations, however, seems much like that of events, and the domain of projective propositions is quite heterogeneous. Rather than characterize generally a space of projective propositions, it appears as. though we oug~t to consider separately a domain of intentions, a domain of questIOns, and a domam of desires. I won't pursue those analyses here, however.56

4. PROVISIONAL CONCLUSIONS The study of diverse linguistic contexts, anaphora and logical structure have led to a rich metaphysical picture.The divisions suggest the following phylum tree with the basic types at the leaves of the tree arranged from left to right in increasing order of abstraction along the spectrum of world immanence:

Saturated Abstract Objects

-----------~

Eventualities

~States

Purely Abstract

Events

Proposition-like Objects achievements accomplishment processes

PureProA Projective Propositions

Fact-like Objects ~

possibilities I facts situations states of affairs?

~ questions conunands desires

Spectrum of Abstractness

>The diagram reveals a basic distinction between event-like and proposition-like

58

FROM EVENTS TO PROPOSITIONS

CHAPTER ONE

entities. But a closer investigation of the spectrum of world immanence reveals a much more complicated typology. At the next level of detail, we may distinguish between events and states under event-like entities--and then further between states, activities, processes, accomplishments, and achievements. Among the propositionlike entities we have distinguished a group of fact-like entities with causal efficacy and a group of pure proposition entities. Both of these groups have further subdivisions. Here is a summary of the characteristics of the major divisions in natural language metaphysics. Eventualities: Spatiotemporal modification (states and events sharply distinguished by a variety of classifications of spatiotemporal modifiers), causal efficacy, no closure under complementation (states support modified complementation, events support relative complementation). Logical behavior: substitutability of coreferential expressions preserving reference to the same event or state. Limited comprehension principles dictate limited mereological summation properties. Simple Propositions: No spatiotemporal modification, no causal efficacy, highly intensional entities (no substitution of logical equivalents or of coreferential terms to preserve denotation to same proposition). Summation dependent on discourse structure. Projective Propositions: No spatiotemporal modification, no causal efficacy, highly intensional entities (no substitution of logical equivalents or of coreferential terms to preserve denotation to same proposition). Complex anaphoric properties occur among different types of projective propositions. Limited comprehension principles dictate limited summation properties. Facts, Possibilities, States of Affairs: No spatiotemporal modification. Probable causal efficacy. Logical behavior: substitutability of coreferential names, definite descriptions may get an opaque reading, questionable substitution of logical equivalents salva veritate, Sentential Comprehension Principle. My examination of abstract entities in natural language metaphysics has revealed a complex typology but also some puzzles. First, there is the problem of the structure of the domains of these abstract objects. The domains of events, propositions, and facts each seem to possess a rich structure with much as yet unsolved, at least as far as their interaction is concerned. That structure appears to bear some relation to the space of such entities created by a text, but much more needs to be said, especially in the case of propositions. Also, many of these domains are fraught with paradox in natural language metaphysics. This poses a traditional problem that natural language metaphysics cannot solve on its 6wn. How can we have a theory of propositions which admits paradoxical propositions? And how do other abstract domains avoid paradox, if they do? A second raft of difficulties concerns the typology itself. The typology of abstract entities is fluid. We have already seen that anaphoric links can exist between contexts that admit incompatible types of abstract objects--e.g. between

59

objects of NI perception and objects of propositional attitude. The selectional restrictions determined by various contexts do not appear to always apply. Further one can "relabel" as a possibility or a conjecture what someone believes: (95.a) John is certain that the universe was created in a big explosion, but as far as I know that is only a possibility, a conjecture, not proven fact. (95.b) Fred fears the possibility that Mary may leave John. But as far as John is concerned it is already a fact to be lived with. Of course, one can also disagree about the status of ordinary objects, as (96) attests: (96)

John believes he saw a cat run into the sewer, but I swear it was a rat.

There is, however, a different feel to (96) in comparison with (95.a-b). In (96), the nature of the object is in doubt. In (95.a-b), the content and even the structure of the abstract object at hand is completely determined; the characterization of the abstract entity by the that clause is not in doubt. What is being contested is the type. of abstract entity. A more apt comparison is to recast the discussion in (96) as bemg about the question of whether the cat John believes he saw was real or a figmen~ of his imagination. But unlike imagination and reality; identifying the abstract object type is often a matter of fiat or decision. Another consideration related to the fluidity of this typology is that different sorts of abstract entities like facts and propositions may "agglomerate" together to form uniform wholes that may be picked up by anaphoric pronouns. For instance, consider the following example: (97)

The fact that Sam ran off with his secretary surprised no one. Mary's expectation that he would be unfaithful is also a pretty grim commentary on his character. All of it makes plain the typical, sad state of modem marriages.

This, as well as the data in section 2.2.2 suggests that abstract entities like facts and propositions may not be so different that they cannot merge together to form another proposition. . The fluidity of the typology is revealed in the linguistic forms of sententlal nominalization as well. An unusual feature of my classification is that some sentential nominals, viz., that clauses, and to some extent POSS-ing gerunds, have a polymorphic or chameleon-like quality; like the color of chameleon~, their true nature depends on their surroundings. They may serve to charactenze abstract entities of different and even incompatible types. For instance that clauses may denote several different types of abstract entities: facts, propositions, and possibilities. This suggests that that clauses introduce structures that are ~ot themselves of any particular type in the typology of natural language metaphYSICS but which may serve to characterize many different types of abstract entities. '

------------------------.-~--~-."~.-~~"~--

60

CHAPTER ONE

The typology for abstract entities differs markedly from a typology for concrete entItles. But the fluidity of the abstract object typology makes sense to a conceptualist. For while the realm of concrete entities appears to have fixed and determinate boundaries, there are no such boundaries that need be respected when categorizing the products of thought. For the conceptualist, the distinctions between abstract entities need not answer to fixed and determinate distinctions in nature or external reality. Abstract objects are our own creations and our categorizations of them answer to our own pragmatic needs; as our needs change, so may our categorizations. Furthermore, our needs for categorization may be local, so the typology may not be complete or altogether worked out. Finally, we may suspend our categorization for certain purposes or when giving another perspective on some abstract object. Natural language metaphysics reflects these conceptualist tenets faithfully. The next chapters will tum to a more careful linguistic analysis of these matters. 1Mental states, however, which relate together propositions and agents, may very well have causal efficacy. More on this later. 2Philosophers like Davidson have claimed that events are concrete individuals. According to Davidson (1967), however, events are to be individuated by their causes and effects (so they are not individuals like rocks, trees, animals, or space shuttles, altJiough they may share some properties with ordinary individuals). 3For unsaturated entities too there is a similar distinction between world-immanent and abstract objects. Natural kinds and event types are examples of world-immanent properties; such properties have causal efficacy, and kinds even have a kind of spatiotemporal extensIOn as in: (1) platypi are found in Australia but nowhere else. (2) dinosaurs lived for about 400 million years. Many predicate nominals, on the other hand, denote abstract properties with no causal efficacy or spatiotemporal extension. So it is odd to say something like: (3) Goodness caused the world to be saved. except in a highly metaphorical sense. But I will not examine predicate nominals or natural kinds here. 41 use the term gerund phrase to refer to the complex construction employing a verbal for like loving or having loved or even the form being about to Jove. This seems to oe standard usage in at least some of the syntactic literature, but there are many variations of terminology in this area. I also made up the term of ing gerund to denote those gerunds in which one argument IS or would be expressed with a prepositional phrase beginning with of. 51 use these somewhat barbaric terms, ACC-ing gerunds and POSS-ing gerunds, because they have become standard in the linguistic literature on sentential nominals. ACC-ing and POSS-ing stand for the different cases of the subject of the gerundized verb. 6See "Unfair to Facts" in Austin (1961). 7Temporal adverbial PPs also hold of perfect nominals, as in Fred's kissing of Mary on Monday. 8For a discussion, see Smith (1991). 9This suggestion is picked up by Bennett (1988). 1°1 differ here from Vendler in my judgments about the acceptability of the container true with yerunds and derived nominals. 1Vendler's arguments for distinguishing these types of eventualities rests on an examination of verb classes, although as Verkuyl (1972) pointed out, verb classes themselves do not uniquely determine the type of eventuality that the sentence will eventually introduce. 12For a detailed discussion of these categories and problems involving them see Dowty (1979), Krifka (1987), Smith (1991). 13See Barwise (1981), Barwise and Perry (1983), Asher and Bonevac (1985a-b), Higginbo'~lam p985a). 4Kaiser introduces two other contexts that I will not here. They consist of verbs of hapJJening and duration-- e.g. begin, stop, and last, and emotive and cognitive verbs-- e.g., infuriate, bOther, anticipate and regret. It seems to me that these classes of verbs do not distinguish between other types of abstract entities; the first group of verbs does playa peculiar role in that they take imperfect nominals like POSS-ing gerund constructions and apply temporal properties to them. More on this in chapter 5.

FROM EVENTS TO PROPOSITIONS

61

15Barwise (1975) and Barwise and Perry (l?78, 1983) argue.persuasively on these grounds that the objects ofN! perception are not sets ofP9ssIble worlds ..TheIr arguments, ~owever, do not distinguish the naive notion of a proposluon from the objects of N1 percepuon. 16 This argument is given in Asher and Bonevac (1985.a). . 170 [!3/a] is the result of uniformly substituting the term !3 for every occurre~ce. of the term am 0: ·18 For a discussion see for example Asher and Bonevac (1985a, 1985b). Higgmbotham (1985a) IS a defense of the view that NI complements denote events. . 19Consider for instance His desperate situation forced him to gamble all he had on a vel)' nsky plan. 20S ee Asher (1987). 21See Asher (1987) again for a discussion. 22See Bonevac (1984). 23 In Asher (1987) I give a relatively detailed account of these categories. 24The semantics of questions that I have in mind is ~e s~mantics of questions using their direct or correct answers. ThIS view is held by a number of lIngUISts and phIlosophers. See Karttunen (1977), and Groenendijk and Stokhof (1982). 25 Again see Asher (1987) for a discussion and bib~ography. . 26S ee also Gupta and Savion (1987) for confirmauon on the faIlure of the property argument form .. .. . for projective propositional contexts. . 27These differences are too simple when we examme contexts m whIch propOSItIOnal and facUve contexts share arguments. There are highly intensional ~ontexts that appear to take ~acts ?S arguments and they would seem to sugzest that facts mIght also have those sorts of Idenuty conditions'that we have suggested are llie mark ofpropositi~ns. C~nsequently, (I) ~annot ~ used to distinguish between facts and propositions. There IS a readmg, for mstance, on whIch (l.a) IS true while (1.b) is false: (1 a) The fact that Superman was vulnerable interested Lex Luthor. (1:b) The fact that Clark Kent was yuhIerab~e interes~d Lex Lutl!or. . This objection however is not conclUSIve. Denved nommal, POSS-mg and of-1f1g gerund phrases, however, also behave non-extensionally in such contexts. The sa'!le contrast as, m (l.a) an.d. (l.b) obtains if we substitute instead of the pair of complt?x NPs, the parrs Superman s vulnerabilItya.nd. Clark Kent's vulnerability. On their own these nommals apJJear to denote ~e same state, b!lt wIthm the context of a verb like interest, these ~ominals aJJl~ar 19 denot~ somethII)g mu.ch '!lore lIke a proposition. Superman's spurning of LOIS and ClaiK Kent s spurmng .of LOI~, ~hICh m normal contexts would denote events also behave as if they denoted projJoSItIons wIthm the con~xts . described in (27). Names of individuals such as Superrp.!Ifl and Clark Kent al~o behave m the subject position of interest as if they were within s~me propOSIuonal ~ontext. Thus, mterest generates a propositional context, and tJierefore, one mIght argue.. always mvolves some appeal to .mental states, propositions or some other intentional object related m some way to the actual deno~u9n 9f the noun phrase or nominal in subject place. Propositional contexts can even be generated WIth mdIcate. Consider the pair: (2.a) This proof indicates to me that xn + yn = zn has n~ solution in the whole numbers. (2.b) This proof indicates to me that Fermat's theo~em IS true. . . It seems as though the frrst of this pair could be true WIthOUt the second bemg true, If I.am not aware of the contents of Fermat's theorem. Attitude contexts m?y ~orce such an ?ccommoda~on as the data concerning the various types of nominals would seem to mdIcate. The unif~rm beh~vI~r of all . nominals m such contexts makes it plausible that the more complex semantIc analYSIS IS .appropnate and so these sorts of observations do not vitiate the distinction oetween facts and propOSItIOns. 28This reconstruction of Moore's argument is .giv~n in Fine (1981). Note that sho~ and il}dic:ate do not require their object arguments to be facts m thIS sense; maps may show somethmg or mdIcate sometJiing but then they may also be wrong. Thus, such contexts seem to take not on1y facts but possible facts or possibilities as arguments. 29Many philosophers who adopt a corres~ndence theory of truth take this argument to support the view that facts ground the truth of propoSItions. For a discussion, see Hochberg (1978). 30This example is due to Peter Lasersohn in conversation. . 31 There is an interesting question as to whether one can use the argumel!t P!ltterns. m (2~) to make distinctions between BP SItuations and facts. It does seem t~at the substItuuon of mtensIOnally equivalent property descriptions wit~in a fact den~ting nqmm?l preserves the reference of that nominal whereas we have seen that It does not WIth BP SItuatIons. 32 The ~cceptability of events as well as NI complements as objects of NI perception verbs would .. explain why the quantificational test fails.. 33The data in (62) is sensitive to the presence dlscours.e partIcles lIke bur or tOf!. ~ese add considerable complexity to the analysis of abstract enuty anaphora. TheIr role IS dIscussed at length in chapter 8. . . 34Contrast (70) however with the perfectly acceptable VP ellipSIS: John asked [whether he could go

62

CHAPTER ONE CHAPTER TWO

to the park);. He wants to. Of course here there is no clash in types; the anaphoric construction picks up a concept expressed by the VP in the previous clause. I shall analyze such constructions in chapter 5. 35It was given in a talk by Link at a conference on Discourse Representation Theory, Stuttgart, Gennany, 1987. 36Davidson (1967) states that events are subject to mereological principles. 37For instance, when we create a context in which these two events become thematically connected, then the anaphoric link becomes quite good: Fred and Mary drove into town together. Fred went shopping for a new pair of sneakers. Mary went to her office to prepare some reports. It took a long time. 38 Earth and water when mixed together make mud, but what of hydrogen and nitrogen? The mereological principles for mass tenns work only on quantities of a particular kind of stuff. 390f course one might here distinguish between singUlar events, which is what I have been talking about, and plural groups of events. Events can be summed to fonn a plural group along the usual principles of gn;mp fonnation. Such groups would be referred to witli the complex demonstrative these events as m: John hit Mary. Sam got married. These events would prove momentous in the history of Smallsville. 40rhis approach too is due to Davidson (1967). 41Such appeals to common sense knowledge in text understanding have a long history within the AI commumty-- see for instance Schank & Abelson (1977) or in computational lInguistic analysis Dahlgren (1988). ~2I .w.ill al..yays suppos~ that among the groups of individuals are singleton groups for every mdividual m the domam. 43The detenniner all then forces a distributive reading over this conjunction. I'll return to this curious anaphoric phenomenon later. 44A possible worlds theory of propositions identifies propositions with sets of possible worlds. Proponents of such a view are Stalnaker (1976, 1984), Lewis (1970), Montague (1970). A Russellian view of propositions, defended recently by philosophers like Salmon (1986), Soames (1987) and Barwise ana Perry (1983), claim that propositions are structured com,l'lexes that include individuals, relations that have those individuals as arguments and some sort of' polarity" indicating whether the relation holds or does not hold of the individuals. 45The view that prop()sitions are sets of possible worlds completely describes the al~ebra and gives it a Boolean structure. It also verifies all the Boolean identities. I here do not include Stalnaker's (1976, 1984) suggestions for a semantics in which linguistic facts about what word referred to what object as well as non-linguistic situations would be encoded into the possible worlds structure. For a discussion see Stalnaker (1984). 46See R. van Sandt (forthcoming) for a discussion of this issue. 47With sentential quantifiers, propositional comprehension, which could be written as 3p p =
A CRASH COURSE IN DRT

The last chapter introduced a typology of abstract entities in natural language metaphysics. To investigate and analyze the typology further, I need to give a detailed semantics of sentential and verbal nominals. In order to do this, I will introduce the semantic framework, Discourse Representation Theory (DRT), within which the analysis will take place. That is the task of the present chapter. Much of this chapter rehearses material and motivation in DRT that has already surfaced elsewhere. All of this fragment, for instance, is covered in Kamp and Reyle (199+).1 But unlike the top-down analysis of Kamp and Reyle, the analysis and construction procedure of the DR-theoretic structures presented here is bottom up. It describes a program that has been implemented in LISP and PROLOG.2 The principal novel contribution of this chapter is to give a semantics for the bottom up construction procedure that shows the construction process is semantically coherent and gives the right results. This semantics yields insights into the possibility of a compositional treatment of DRT, and it also lays the foundations for the semantic analysis of sentential nominals. DRT contains two components: the DRS construction procedure, a procedure for constructing semantic representations, and the correctness definition, the method by which these representations are interpreted. I will first give a brief review of these components within the basic DRT fragment of Kamp (1981). DRS construction will proceed from the bottom up perspective. In the following sections, I will sketch two extensions to the basic fragment that will be very important for the analysis of nominals denoting abstract entities and abstract entity anaphora: the analysis of verbs as event predicates and tense and aspect, and plurals and plural anaphora.

1. A PHILOSOPHICAL OVERVIEW OF THE AIMS OF DISCOURSE

REPRESENTATION THEORY DRT was the first of a group of theories to develop a dynamic notion of meaning. The proposal for a dynamic semantics is, however, already present in Stalnaker (1976). The group of dynamic theories includes the situation semantics of Barwise (1985) and the Dynamic Predicate Logic of Groenendijk and Stokhof (1990).3 These theories all view the meaning of a sentence as a function from contexts to contexts. DRT analyzes meaning in two steps. The first, the DRS construction procedure or so called DRS construction algorithm, is a set of rules for constructing a semantic representation for a discourse. This representation is called a discourse representation structure or DRS, and it is built up sentence by sentence. If j sentences have been

63

64

CHAPTER TWO

processed to yield the DRS Kj , then the processing of Sj+l will yield a DRS that The second part of DRT mterpretatlon, the correctness definition, provides instructions for homomorphically embedding a DRS in a model so as to yield correct truth conditions for a discourse. The interpretation of a discourse in DRT then takes two steps: first the construction of a DRS, then the proper embedding of the DRS in a model. Combining the correctness definition with the construction procedure yields a dynamic, truth co~ditional interpretation of discourse. The dynamic meaning of Sj+l is that function WhICh takes us from the truth conditions of Kj to the truth conditions of K·+ 1. .Several pr.oponents of dynamic semantics have eschewed this two st~p approach to mterpretatIOn. 4 They have voiced various objections to the use of DRSs the intermediate level of representation in DRT. One objection is that the exploitati~n of an intermediate level of representations threatens a certain view of compositional semantics familiar from Montague Grammar. This is the doctrine of direct interpretation, on which the rules for semantic interpretation must exactly follow the s~ntactic rules of phrasal construction (thus allowing the syntactic rules .to be dispensed with in principle). Another difficulty for the two stage view concerns the seman.ti.c interpretation of the DRS construction procedure itself. In previous expOSItIOns, the DRS construction procedure seems to have no semantic interpretation; it is simply a formal procedure for getting the right truth conditions for a discourse without appealing to any intuitive notion of meaning of the lexical items in the disco~rse. In the last section I address this criticism and show how the meaning of a DRS IS a function of the meanings of its parts. Perhaps the principal challenge, however, is to say precisely what is the role of ~he inte~mediate level. What does it buy us? Various interpretations of the ~ntermedlate level have been suggested during the development of DRT: (1) the DRS IS a level of "logical form," (2) the DRS is a "partial model" of what is said in the discourse, or (3) the DRS is a "mental representation" of the content of a discourse formed by a recipient of it. Which of these views is correct? The "narrow" view of DRT (usually espoused by those who do not like DRSs or representations), construes a DRS only as a representation of logical form for dynamic semantics. I believe that a broader view of DRT is warranted on which all three characterizations of ?RSs a:e correct. ~ut in order to defend this claim, some remarks concerning the phIlosophIcal foundatwns of truth conditional semantics are in order. Much of the subsequent linguistic investigation in this book does not hinge on these philosophical points. But I mention them to make clear what I take to be the aims of DRT. Formal semantics has proceeded for the most part independently of philosophical concerns ~at attempt to link meaning with use. 5 The version of DRT that I present here begms to address these concerns by situating semantics within a more compr~hensive theory of verbal communication. Such a theory might take the followmg shape. Contents are at bottom properties of cognitive states. In co~~unication, speakers attempt to convey these contents (among other things) to :eclplents who attempt to reconstruct these contents from the verbal message. A DRS IS an abstract, partial, and non-linguistic specification of the information a recipient ~ombines .with Kj to form an extended DRS Kj+l.

A CRASH COURSE IN DRT

65

recovers from the processing of a discourse. Or more precisely, the information the recipient recovers must have a structure homomorphic to that of a DRS. Thus, DRSs are to be distinguished from inscriptions in the DRS language, which is, as the reader will soon find out if he or she does not already know, full of "boxes." The sort of information of which a DRS is a partial specification also serves as a component of cognitive states; the belief that
...

",,--------------------------------------11'~~~----~~.

~~-~---

CHAPTER TWO

A CRASH COURSE IN DRT

full analysis of pronominal and temporal anaphora. Such an analysis may prevent the full compositionality required for the direct interpretation of natural language. But I reject the claim that a semantics must necessarily directly interpret natural language. It

elements of the domain ofM such that f(x) is a boy in M, fey) is Fred in M, and f(x) kicks f(y) in M. If we define (1) to be true in M just in case (K1) has a proper embedding in M, we get the right tmth conditions. We have now seen a DRS and the truth conditions it detennines for a simple

66

seems completely unilluminating to do so when one is interested in the meaning of pronouns. The intennediate level of representation allows us to defme processes like pronominal and temporal anaphora resolution in a simple and clear way that is not

open to those who espouse direct interpretation. This does not show that the use of representations is inescapable, but it constitutes prima facie strong evidence in their favor. One can almost always save the strong view of semantic compositionality and eschew an essential appeal to representations at the expense of baroque and unlike! y semantic values. But I shall not pursue it here.

2. TIlE BASIC FRAGMENT

67

sentence. The next step is to extend the treatment to multisentence discourse. Let us add to (1) another sentence to get the discourse: (2)

A boy kicked Fred. Fred cried.

We know what stmcture the first sentence yields; it is (K1). To get a DRS for all of

(2), the DRS created from the first sentence serves as a context for processing the second sentence. In processing the second sentence, the conditions and discourse referents introduced by the second sentence are entered into the condition list and universe a1ready created in processing the first sentence. This is the result x,y,z

The original fragment of DRT discussed in Kamp (1981) contained Common nouns, verbs, the determiners a and every, and the English conditional expressed by if

(K2)

.. . then. In this section, I introduce a construction procedure and correctness definition for this fragment, extended with rules for processing definite noun phrases and negation.

boy(x) Fred(y) kick(x,y) cry(z) Fred(z)

The advantage of using the DRS built up from previous discourse as a context for the

2.1 DRSs and Truth Conditions The best way to get acquainted with DRSs is to look at an example. The DRS for (1) below, ignoring the semantic contributions of tense, appears as (K1): (1)

A boy kicked Fred. (Kl) ffX,-u,Y'o-;---j

boy(x) Fred(y) kick(x,y)

(K1) describes graphically an abstract, information stmcture, a DRS, with two parts. One part is called the universe of the DRS, the other its condition set.. A DRS is an

ordered pair consisting of its universe and condition set, written as .

interpretation of the next sentence arises in the process of anaphora resolution. Anaphoric pronouns introduce a peculiar sort of condition. Many conditions come with a determinate, context free-content, but others do not In particular those that are introduced by anaphoric pronouns introduce a discourse referent that must be linked with some other discourse referent in order to give the condition a complete meaning. I write such conditions as being of the fonn z =? Such conditions are incomplete conditions. All other conditions are complete conditions. The distinction between incomplete conditions and complete conditions carries over to DRSs. Complete DRSs are those containing only complete conditions; incomplete DRSs contain at least one incomplete condition. The condition contributed by the pronoun he in (3), z =?, is responsible for the DRS (K3) being incomplete. (3)

A boy kicked Fred. He cried.

The DRS depicted in (K1) has as its universe two "discourse individuals," x and y,

and as its condition set a collection of property ascriptions to x and y. The conditions in ConK l are formed from n-place DRS predicates and n discourse referents as arguments. In this fragment, DRS predicates are generated from nouns or verbs. The condition set says that x is a boy, y is Fred and x kicks y. To give the tmth conditions for (1), we need to define a proper embedding for (K1). Informally, a proper embedding for (K1) in an (extensional) model M = , consisting of a domain D and an interpretation function [I, is a function f that maps x and y onto

x,y,z (K3)

boy(x) Fred(y) kick(x,y) cry(z)

z=? The question mark in this condition needs to be replaced by a discourse referent, in

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order to complete the DRS. The task of anaphora resolution is to find an appropriate discourse referent other than z and to tum z = ? into an identity assertion. In the example at hand, y is an appropriate discourse referent introduced by the processing of the first sentence; i.e., the discourse referent is an element of the DRS that serves as a context for the processing of the second sentence of (3). After identifying y with z, we have the following completed DRS for (3):

(K'3)

x, v. z boy(x) Fred(y) kick(x,y) cry(z) z~v

(K5) ~

69

x,y John(x) Fred(y) like(x, y)

(K5) has a proper embedding just in case there are no obj~cts x and y such that x is John, y, Fred, and x likes y. We could also add disJunc!lon as an operator to this fragment, but since disjunction will not figure prominently in what follows, I wIll make do with the original DRS operators'? We have seen some examples of DRSs for very simple natural language texts. In the next section, we will see how to build DRSs from DR-theoretic meanings of basic expressions.

(K '3) has a proper embedding in a model M just in case M contains Fred and a boy

such that the boy kicked Fred and Fred cried. There are more complex DRSs that themselves contain DRSs. Any condition containing one or mOTe DRSs as a constituent is called a complex condition. (4) gives rise to one: (4)

Every girl kicked Fred. (K4)

Igir~X) I

"* Fred(y)

kick(x, y)

The DRS for (4) has two DRSs that are constituents of a complex condition. Such constituents are called subDRSs. I will caIl the one on the left (K4.1) and the one on the right (K4.2). The notion of a proper embedding for such a DRS must take these subDRSs into account. It does so in the following way: fis a proper embedding for (K4) in a model M iff every extension (superset) off that properly embeds (K4.1) in M can be extended to a proper embedding of (K4.2) in M. Not only do many determiners like every introduce such complex DR-theoretic structures, but conditionals and other operators do as well. In particular, besides the "* operator on DRSs, I will use one corresponding to negation, -,. Thus. a sentence like (5) yields the DRS below it: (5)

John does not like Fred

2.2 The Basic Construction Procedure The DRS construction procedure builds up a DRS for a discourse in a stepwise fashion,- sentence by sentence. The actual inputs to the construction procedure are parses of sentences. reflecting their syntactic structure. Th~ syntac~c theory ass~ed in this section is a simple fragment of X' theory and a leXICon WhICh subcategonzes argument positions of the verb. The negation particle not and conjunctions like or ~d and not are assumed to combined with sentences, verbs, and verb phrases. ThIS fragment does not have boolean combinations of noun phrases or detenniners. The syntactic assumptions will be expanded in section 3. 8 . Let us begin with a simple natural language discourse, a simple sentence like (I) repeated below: (I)

A boy kicked Fred.

To construct (KI) we need look only at one sentence. Sentence (I) has the following syntactic structure if we ignore tense.

NP

/~

Det

I

a

N

I

boy

kick

Fred

The DRS construction procedure that I shall describe works bottom up, translating the terminal nodes of the syntactic tree into DR-theoretic structures that are then

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combined together according to a process called DRS conversion to produce a DRS. This process has been implemented in both PROLOG and LISP and is described in a variety of papers.9 The translation of a common noun or a verb yields a DRS predicate. So the translation of person, which I shall sometimes write as person ~ is AX person(x), while kick' = AX AY kick(x, y). These predicates can be represented as DRS structures known as predicative DRSs. The italic letters represent variables over discourse referents or dr variables, and the A operator is a variable binding operator.,_

Accordingly I shall introduce predicative DRS variables and bind them with a A.operator. A partial DRS also may have a declared discourse referent. A declared discourse referent is a discourse referent that is to serve as an argument of a premcative DRS that will be assigned to one of the predicative DRS variables during the operation of DRS conversion. When a predicative DRS variable P is assigned a discourse referent as an argument, P is a variable over n-place predicative DRSs for n ~ 1, whereas when P is not assigned a discourse referent as an argument, then it may vary over n-place predicative DRSs for n ;, O. Partial DRSs are converses to predicative DRSs. Predicative DRSs are formed from DRSs by taking out discourse referents, while partial DRSs introduce discourse referents. In order to make sure that a partial DRS does not introduce a discourse referent that has already been introduced into the DRS K for a discourse, we require that the discourse referent x it introduces be not already an element of UK or the universe of any DRS that occurs within K. To state this precisely. we must suppose that the translation of a determiner like. is always relative to a DRS context. The translation of the determiner. then relative to a context DRS K is the partial DRS:

Definition: For a sequence of dr variables x" ... , x. and DRS K such that x" ... , x. E UK, Ax" ... , AX.«UK-{X" ... , x.J), ConK(x.!x" ... , x./x.» is a premc.tive DRS. Here are predicative DRSs corresponding to person' and kick' expressed in the graphical DRS langnage:

AxF====11 .

person(x)

AX AX jl--ki-'c-k-(x-,-y-)--1

The interpretation of predicative DRSs is quite familiar from algebraic treatments of properties and propositional functions. The A. indicates an operation of "discourse referent abstraction," in which a discourse referent is removed from a DRS. Thus a predicative DRS is a DR-theoretic object which is a function from discourse referents into DRSs. Predicative DRSs combine with one or more discourse referents to yield a DRS. Nevertheless, discourse referent abstraction works much like A-abstraction; and like A-abstraction (which operates on formulas), object abstraction has a converse--DRS conversion, in which a n+ l-ary predicative DRS combines with a discourse referent to produce an n-ary, predicative DRS. DRS conversion is analogous in part to the wayan ordinary A abstract applies to a constant. But DRS conversion differs from A-conversion; the form of its partial and predicative DRS arguments do not detennine the output of DRS conversion, as is the case with 1..conversion. DRS conversion is able to fill in any of the A-abstracted discourse referent places in a predicative DRS. DRS conversion exploits syntax and other information sources encoded in the form of linking rules to tell it which discourse referent fills in which argument place. This gives DRT great flexibility in accounting for different possible scopings of operators and quantifiers, something that is usually taken care of in the ordinary type theory of Montague Grammar with type raising. The flexibility of DRS conversion makes the predicative DRS expressions in the DRT language equivalent to A-expressions of the lambda calculus with a polymorphic interpretation. The translation of the NP and the determiner of sentence (I) is more complicated but familiar from the work on quantifiers of Montague (1968, 1970) and van Benthem (1984). A determiner introduces a partial DRS. A partial DRS is what remains from a DRS when one or more predicative DRSs is abstracted away from it.

71

APAQ t-u"-c-:--! P(u) Q(u) where u is a new discourse referent relative to K. This means that the translation of a detenniner is context sensitive; the discourse referent it introduces may only be determined within the context of constructing a particular DRS. In this notation, P and Q combine with predicative DRSs, while u is a declared discourse referent. Thus, determiners are to be understood semantically as functions from predicative DRSs to DRSs. But the function introduced by the determiner in a given context also performs the function of introducing a new discourse referent, a new discourse object, into the infonnation structure. The round brackets denote the application of . the predicative DRS to a discourse referent. Typically, the translation of the common noun phrase in an NP is assigned to P; u is assigned as an argument to that predicative DRS during DRS conversion. I will sometimes write partial and predicative DRSs in linear notation to save space. For example the partial DRS above would be written as, A.PAQ <{uj, {P(u), Q(u)}>. I will further abbreviate partial and predicative DRSs by using variables for DRSs--e.g., AQAP K A proper name like Fred introduces a partial DRS too, but it is one that is partially filled in. If determiners introduce relations between properties or rather concepts, proper names introduce one place properties of concepts. Thus the translation of Fred is

A.P t-v~_ _1 Fred(v) P(v)

72

Partial DRSs can be easily understood in operational tenns as supplying the discourse referent arguments to turn predicative DRSs into DRSs.1 o But in offering a semantics for the construction procedure, we must assign some extensions to partial DRSs and predicative DRSs and show how DRS conversion comes up with the right extensions for DRSs. The semantic extension of the output of the DRS construction algorithm relative to a model M should be a set of embedding functions--those embedding functions that properly embed the output DRS in M. The partial DRSs and predicative DRSs that go into building the output DRS constrain the set of ~roper embedding functions for the result of DRS conversion. If we are to do this correctly, the contribution of each condition will have to be understood dynamically. Given a set of embedding functions or some embedding function, the semantic extension of a condition will be to return a more constrained set of embedding functions. There are a variety of ways one could proceed here, I I Most natural from this bottom up perspective is to treat predicative DRSs similatiy to propositional functions and thus

assign to them extensions that are functions from discourse referents and a given embedding function to sets of embedding functions. Partial DRSs will then be functions that may combine with predicative DRS denotations and a given embedding function to yield sets of embedding functions. For the interested reader, I make this more precise in section 5.3 of this chapter. As our semantics for the construction algorithm implies, DRS conversion is similar to 13 conversion of the lambda calculus. It merges partial DRSs and predicative DRSs together, assigning the appropriate arguments to the appropriate places and returning a DRS. Aoperators in effect always have widest scope in the conversion routine, for the combination of a one place partial DRS and an n+ 1 place predicative DRS yields an n-place predicative DRS. Though ugly to state (see the last section of this chapter), DRS-conversion is easy enough to understand once one has seen an example. Having translated all the terminal nodes of the tree for (1), we now combine these translations together in DRS conversion. Let us first combine the predicative DRS that is kick' with the translation of Fred. According to the rule of conversion together with the infonnation that the discourse referent introduced by Fred fills the object argument place of kick " we get the predicative DRS:

AX

f-cv'-cc-.,-~

kick(x,v) Fred(v)

We now combine a' with boy'to get the following partial DRS:

AQ

u

boy(u) Q(u)

This partial DRS may now combine with the predicative DRS constructed for the VP in DRS conversion to give us the final result.

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CHAPTER TWO

u v

boy(u) F~~v) ..\ kicklU, v

2.3 DRS Consl111ction, Multiple Sentence Discourse, and Intersententia! Anaphora Let us now turu to the more complex example (3), repeated here. (3) A boy kicked Fred. He cried.

The translations of the expressions in the second sentence are familiar except for he. The translation of he is a partial DRS of the fonn

The condition z = ? is an incomplete condition. Anaphora resolution will make the condition complete. But first we have to construct the DRS for the second sentence. It is this:

We now must update this DRS with the DRS for the previous sentence. This amounts just to taking the union of the universes and the condition sets of the two DRSs. I also call this operation DR-theoretic union, symbolized by !,d. DEFINITION: DRS-update(Kj, K 2 )

= «UK,

U UK'), (ConK, U ConK.»

= Kr

!,d K2 x. v.z boy(x) Fred(y) kick(x, y) cry(z) z=? The task of anaphora resolution is to find an appropriate discourse referent other than z with which to replace the ? in z = ? After using the process of anaphora resolution to identify y with z, we have the following, completed DRS for (2):

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x,v,z boy(x) Fred(y) kick(x, y) cry(z)

A CRASH COURSE IN DRT

The partial DRS introduced by every combines with the predicative DRS that is the translation of girl to yield tltis partial DRS:

1..Q

z=y Anaphora resolution is a distinct process from DRS construction proper. The reason for distinguishing them is that the structure of a DRS imposes a constraint on anaphora koown as accessibility. But to define accessibility, we need to de,'c\op the DRS construction procednre a little forther.

2.4 Every and if. .. then

D-D The sentential operator and the deterntiner introduce slightly different structures when we look more closely. The sentential operator yields a partial DRS with a complex condition and no declared discourse referent.

The determiner yields a partial DRS with a complex condition and a declared

discourse referent

r============

This combines with the farniliar translation of the VP to yield the DRS: (K4)

The deterntiner every and the sentential operator if . .. then complicate the picture of DRSs by introducing conditions with subDRSs, DRSs within DRSs. These conditions are known as complex conditions. Sentences with occurrences of every and if. . .then yield DRSs with complex conditions of the following shape, containing a pair of DRSs and an operator.

75

Ig~(X) I-

v Fred(y) kick(x, y)

It is worth remarking that while detenniners have uniform translations as partial DRSs, partial DRSs are a quite diverse group. The partial DRS that is the translation of. , as well as the partial DRS that corresponds to a proper name, have the functIOn of introducing a discourse referent into the DRS--an object that we can taik about and refer to in subsequent disconrse by means of anaphoric pronouns. A definite NP also yields under translation a partial DRS that introduces a discourse referent into the discourse. This discourse object. however, is presupposed to be familiar to the

interpreter, at least in the sense that the takes the noun phrase to refer to a specific individual that the speaker takes him to koow something about.!2 Such partial DRSs differ considerably from the partial DRS introduced by every. This partial DRS looks much more like an ordinary quantifier. A disconrse referent

is also introduced in this case, but since it occurs in an embedded DRS, we shall see that in general it cannot be referred to in subsequent discourse. The discourse referent introduced by every functions like a variable, and in the complex condition of the partial DRS there is a tripartite structure familiar from the theory of general!zed quantifiers. The box on the left of the complex condition corresponds to the restnctor property; the one on the right is the nuclear scope; the arrow is the quantificati?nal relation.13 A detenniner is quantiiicational just in case it yields a p~~~.U?"~§};ylth a tripartite structure and intrOduces a 'newruscoilisefeferefiriirffie~re'strictor: _~·"."'_W~""'"_~-·'·'.""_

..". _"'._.

~,_

2.5 SubDRSs, Accessibility, and An.phora

In building the DRS for (4), we use a partial DRS like the one above. (4)

Every girl kicked Fred.

The treatment of quantificational deterntiners and logical operators introduces a complex logical structure into DRSs. This structure affects anaphora and helps us to understand the constraint of accessibility, which exploits tltis logical structnre. Again let us proceed by way of an example which contains anaphoric pronouns and yields a DRS with complex conditions.!4

A CRASH COURSE IN DRT (6)

If a high school student owns a Mustang, he works on it every day.

77

Accessibility is a relation on discourse referents in the universes of DRSs. Roughly. the constraint says to find all the accessible discourse referents accessible to some

The clause in the antecedent yields the DRS,

discourse referent x, one must look in those universes of DRSs to the left or superordinate to the universe in which x is declared.

x,V

The accessibility constraint allows us to complete the DRS for (6) by identifying

high-school student(x) Mustang(y) own(x, y)

Zl

with x and Z2 with y. According to the definition for accessibility, x is accessible

to z, and y to z,. This yields the following finished DRS for (6):

while the clause in the consequent yields the DRS: x High-school student(x) Mustang(y) own(x, y)

Zl ? '0. =?

...

Zl, Z2 Zl=X

z,,=y

Work-on-every-day(zj,

Z2)

work-on-everv-daY(ZI,Z2) The two DRSs above furnish the arguments to the structure introduced by if then. So pnor to anaphora resolution the DRS for (6) looks like this:

(K6)

X

high-school student(x) Mustang(y) own(x, y)

...

Zl. :q

zl

?

Z2=

?

work-on-every-day(zj,

Z2)

The DRS for (6) above cont';;ns incomplete conditions within a subDRS. The completion of the conditions in DRSs with subDRSs is subject to a semantic constraint, accessibility. To define accessibility, I need fitst to define the notion of subordination. recursively. Definition: (Subordination): If K is a constituent of a complex condition of K', then K is subordinate to K'. If K. is a constituent of a complex condition of Kn-l and Kn-l is subordinate to K, then K. is subordinate to K.

(6) is a so called "donkey" sentence, and the DRS above is equivalent to the one for evel}' high school student who owns a Mustang works on it evel}' day. One of the successes of DRT was to yield this predicted equivalence, using unifonn rules to process the indefinite article, the detenniner evel}', and the conditional operator. The accessibility constraint together with the DRS construction rules, however, forbid the anaphoric links that are suggested by the coindexings in the following

sentences (Le., when an NP is coindexed with a pronoun, that indicates that the discourse referent introduced by the NP and the discourse referent introduced by the pronoun are to be identified in the anaphora resolution process).15 (7.a) (7.b) (7.c)

*Every man who owns every Mustang i likes i~. *Every man who owns a Mustang j praises it. It, runs very well. If a professor were to own a Mustangi. he would not be able to maintain it. It, would cost him too much to fix.

Let us look at (7.a) to see how the accessibility constraint rules out the suggested

anaphoric connection. One new element in (7.a) is a relative clause; the construction procedure translates a relative clause as a predicative DRS and combines it with the predicative DRS derived from the head of the common noun phrase, identifying the

I now define the accessibility of a discourse referent x to a discourse referent y in a DRS Ko by an enumeration of cases: Definition: (Accessibility): Let K = Ko or K be subordinate to Ko. Then: (i) If x, y E UK, then y is accessible to x in Ko: (ii) if K' is subordinate to K and x E UK' and y E UK, then y is accessible to

x in Ko; E UK', x E UK" and K' ... K" is a complex condition of K. then y is accessible to x in Ko; (iv) otherwise, y is not accessible to x in Ko.

(iii) if y

two A-operator bound discourse referents. This new predicative DRS now becomes an argument to the partial DRS introduced by the detenniner of the NP.1 6 The DRS for (7.a)

x man(x)

Z

Z=?

like(x, z)

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has a structure in which y, the discourse referent representing the intended antecedent for Z, is inaccessible to z according to the definition of accessibility; y occurs in a subDRS of a DRS that is to the left of the one in which z occurs. Thus, the anaphora resolution module will not be able to identify y with z. Note that accessibility is not merely a configurational principle. It reflects a constraint imposed by the trnth ~onditional interpretation of DR-theoretic structures. Any attempt to identify z with y In th~ DRS above makes its embedding conditions incoherent. An embedding funcMn f that embeds the subDRS on the left side of the arrow does not itself assign an object to y; so there IS no embedding function of the right hand subDRS extending f .that maps z to an individual that is identified with fey). The accessibility of a disco~se referent entails that.it gets a value assigned by an appropriate embedding function. AccessIbilIty thus differs from syntactic constraints like those of "precede and command," which syntacticians have proposed. 17 First, it is defined on semantic structures and has a semantic justification, whereas the syntactic constraints do not. Further it has different empirical consequences; syntactic precedence and command constraints in conjunction with principles of a binding theory rule out sentences like JOhni likes himi. whereas accessibility does not. Precede and command constraints do not distinguish between the semantic content of detenniners or operators and so cannot by themselves account for the phenomena in (6) and (7.a) and (7.a-b). Note, however, that while (7.a-b) are unacceptable, (7.c) is fine. Craige Roberts's (1987) notion of modal subordination offers a DR-theoretic account of such examples. The modal, she argues, indicates that the second sentence is to be interpreted relative to the context created by DRS-update of the left subDRS with the right subDRS derived from the fIrst sentence of (7.c). This seems right in (7.c). The would of the second sentence indicates a causal link between the inability to maintain ~ Mustang and its costliness; a professor who owns a Mustang is not able to maintain It because. it costs h~m too much to fix. However. one can also get acceptable sentences like (7.c) WIthout overt modals. Consider (8): (8)

Every professor who owns a Mustang j is unable to maintain it. It. costs him too much to fIx. I

I believe that a DR-theoretic explanation of (8) must follow similar lines to that suggested by Roberts for the modal sentences. Causal links implied by a text, as we shall see In chapter 8, do not require an overt modal or other lexical indication. Since modals are not a part of thi~ fragment, I give the DRS for (7.c) with the anaphoric equations filled m. All the links made are consistent with the accessibility constraint I have represented the causal link by a conditional. This is inadequate, but this is aiJ that can be done within the bounds of this fragment.

x

Zl, Z2 Zl x

=

professor(x) Mustang(y) own(x, y)

=y is-not-able-to-maintain (z 1, Z2) Z2

x. . Zl. Z2 Professor (x) Mustang(y) own(x, y)

...

Zl =X z2 =y

is-not-able-to-maintain (

79

"3=x z'=y

cost-too-much-to fix(z3' z') )

2.6 Scopes for Quantifiers in DRT and Other Constraints on Anaphora The principal innovation in the DRT analysis of anaphora is the constraint of accessibility. Accessibility, however, is dependent upon the scopes assigned to the translations of noun phrases. The scopes determine the exact logical strncture of the DRS constrncted. The interaction of scope assignment and DRS constrnction has implications not only for anaphora resolution but also for more general issues like compositionaiJty. As an example of a sentence with several possible scopes for the noun phrases. consider a case in which noun phrases within the VP take wide scope over noun phrases in subject position. For example, (9) has a reading in which this holds. Imagine that the cOntext is one where people are discussing the success of a county fair. (9)

Many people visited almost every booth.

Within this context, the wide scope reading of (9) is preferred and implies that for almost every booth many people visited it. Determining the scope of quantifier expressions and operator expressions in ~aturallanguage is complex. Various factors affect scope: among them are syntactic configuration, lexical semantics, grammatical position, and, in speech, phonological stress. Because scope affects the logical strncture of a DRS and because accessibility is determined by the logical strncture of a DRS, DRS constrnction and scope assignment must fIx the strncture of the DRS prior to exploiting that structure as a constraint on anaphora resolution. In the present description of the DRS constrnction procedure (and in most implementations), different scope assignments are made possible by the fact that the argument position of a discourse referent in a predicate is specified independently of the linear order of applications of DRS conversion. Thus, regardless of when the partial DRS introduced by an NP is used in DRS conversion, the discourse referent it contributes as an argnment to the matrix predicate of the sentence will end up in the right place.

80

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,

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The linear order of applications in DRS conversion. on the other hand, determines the scope of a particular NP translation. While this allows the construction procedure to handle different scopes for quantifiers, it also opens the question of rule to rule compositionality. If the syntax incorporates a rule like "quantifier raisingl1 that places an NP higher up on the syntactic tree than its customary position,18 then one can use the position of the NP in the syntactic tree to detennine its scope and thus also its place in the linear order of application of partial DRSs to predicative DRSs. With such a syntactic rule and its semantic correlate, one would get a determinate, seoped reading for each syntactic structure; the DRS construction procedure for this fragment would be an "algorithm," a function from syntactic structures to DRSs. The DRS construction procedure would be compositional in accordance with the Montagovian rule to rule hypothesis concerning compositionality. On the other hand, the syntax might not have such a rule. Even so, our definition of conversion allows us to apply the translation of the NP in a different order than the one the syntactic configuration might suggest. This allows us to give different scopes to the translation of the NP, relative to various quantificational elements or operators. 19 But this gives the DRS construction procedure the potential to yield potentially several DRSs for each syntactic structure, and this violates the requirements of the rule to rule hypothesis. One could perhaps recover functionality and the strong form of compositionality by specifying other factors besides the syntactic structure that detennine scope. Besides scope, which affects accessibility, anaphora is dependent on a number of other syntactic and discourse factors. The anaphora resolution process employs syntactic information of various kinds. For instance, the discourse referent x introduced by an anaphoric pronoun may only be identified with a discourse referent y in the anaphora resolution process if the antecedent noun phrase and the pronoun agree in gender and number. Further, if x is introduced by a full noun phrase. x may only be identified with y in the anaphora resolution process, if the antecedent noun phrase and the pronoun obey syntactic constraints like disjoint reference. 2o But these will be largely of peripheral interest to the present study and are much discussed in the current syntactic literature. Of more interest in the study of anaphoric reference to abstract entities are the constraints on anaphora based on discourse principles. I discuss the discourse constraints briefly here and then at length in later chapters. There have been several studies arguing persuasively for constraints on anaphoric reference to ordinary individuals based on discourse structure. 21 These appear to be of two general kinds. One sort of discourse constraint exploits a variety of cues in order to determine a salience ranking on accessible discourse referents relative to some other discourse referent z that occurs in an anaphoric equation; the greater the degree of salience of a discourse referent x relative to z, the more likely is the process of anaphora resolution to identify x with z.22 The other, central to this book, exploits principles about the structure of the discourse to yield certain configurational constraints on the anaphora resolution process, similar in nature to accessibility or syntactic configurational constraints. We have seen already one such example of discourse effects in the DRS

for (7.c). The discourse structure of (7.c) is such that discourse referents that would not ordinarily be accessible are so. It seems hopeless to make sense of such discourse structure effects within the framework of a strongly compositional mapping from syntax to semantics, especially when there are no clear lexical triggers like a modality. In (7.c) it is clearly not the syntax that determines when subordination is possible. The factors that make modal subordination a possibility are complex and ill understood; they depend on world knowledge as well as on grammatical details like the interaction of tenses. I shall argue in chapters 7 and 8 that discourse structure is very important to a correct analysis of anaphoric reference to abstract entities; and there, once we have some idea of discourse structure, I shall review the constraints on individual anaphora imposed by discourse structure.

2.7 Other Determiners and Operators in the Basic Fragment We have treated one quantificational determiner, every, and one logical operator, if. .. then. The basic fragment contains one other truly quantificational determiner and two other operators. no is the other quantificational determiner. It introduces a discourse referent which is in effect "bound" by occurring within a subDRS. A negation on this subDRS reveals the determiner relation, and the DRS itself is the union of the restrictor clause and nuclear scope. So no introduces the following partial DRS:

According to the definition of accessibility, the discourse referent introduced by no within the subordinate DRS will not be accessible to a discourse referent introduced within a superordinate DRS. DRT predicts (10) to be bad, for instance. (10)

'No girl; slept. She; was then very cross.

Just as in this fragment the lexical element ifintroduces the operator ~ on its own (without, that is, the introduction of a discourse referent), the lexical element not introduces the negation operator on its own and has the translation:

Negation may have multiple scopes in this DRT fragment--in particular scopes over V, VP, or S.23 Semantically, then, negation will take either a predicative DRS or

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DRS as an argument. But since DRSs are in effect O-place predicative DRSs, we need only the translation for the negation operator given above.24

X.V

boy(x) Fred(y) kick(~: y) «x, a>, }

2.8 External Anchors and Definites

One unsatisfactory feature of the original fragment as I have described it thus far is the treatment of definite singular tenns. Philosophers like Kripke (1972) and Kaplan (1977) have persuasively argued that proper names, indexicals and demonstratives contribute the same denotation in every possible world, no matter in what non-quotational context the expression occurs. Their views fann the "direct

theory of reference." DRT adopts their insights, reflecting the directly referential character of such expressions at the level of DRS interpretation. A special device fixes the assignment to the discourse referent; it is a partial function, which is called an external anchor, from discourse referents in the universe of a DRS to objects and times in the domain of the model. A DRS with an external anchor is said to be externally anchored. I also call a real individual that is the value of tltis function with the input of a discourse referent x in a DRS K the external anchor for x. Proper names are directly referential expressions. So since (1) above contains a proper name, (KI) should have an external anchor; the pair consisting of the discourse referent introduced by Fred and the object Fred is the external anchor for (KI), as indicated below: x,V boy(x) Fred(y) kick(~: y)

«y,Fred>}

83

The device of external anchoring forces us to rethink the status of conditions that a directly referential singular tenn introduces in a DRS. Since such a tenn gives rise to an externally anchored discourse referent. the condition it contributes is otiose for detennining the real individual that is the value of the discourse referent un~~r a proper embedding of the DRS. But then what infonnation might such ~ condillOn convey? Clearly the use of the tenn conveys certain ~nfo~~ti.on to th: mterpreter. For example, the use of a name seems to convey metahngUlstIc informatlOo--e.g., the infonnation that the discourse referent introduced by the name a stands proxy for an individual with the name (1.. But attempting to incorporate this sort of infonnation directly into the truth conditional content that a name contributes to a discow;se le~ds to trouble. Suppose we try to process the sentence Kripke IS necessan!y Identlcal with Kripke. If the condition 'named(x, 'Ktipke')' is assumed to contnbute to ~e content of the DRS and noun phrases are processed in the nonnal way, the followmg DRS (where D, not part of our current fragment, stands for the modal operator) results:

x named('Kripke', x) y D x y named('Ktipke', y) «x, kripke>, }

External anchors constrain the intetpretation of the DRS in the following way: if K is a DRS containing a discourse referent x and <x, b> is in the external anchor for K, then f is a proper embedding of K only if f(x) = b. Proper names are not the only directly referential expressions. The pronouns this and that are often read as deictica11y referring to some salient individual in the environment of the speaker and audience, as are complex demonstrative phrases like this man and that airplane. So consider for example the sentence, (11)

This boy hit Fred.

Since this boy is also a directly referential expression, (11) generates two external anchors, ODe for the discourse referent introduced by this boy and one for the discourse referent introduced by Fred. The complex demonstrative this boy also introduces a condition--just as an indefinite would.

DRT then appears to predict that this obviously true statement expresses ~he falsehood that the individual named Kripke necessarily has the property of bemg named 'Kripke'.25 . . One might eliminate the conditions introduced by directly referenual expressIOns entirely to avoid this problem. But conditions introduced by proper names an~ other directly referential expressions do serve a purpose. They supply the agent WIth the means for connecting up the content of a message in which such expressions occur with his antecedent beliefs in the right way; the infonnation conveyed by a proper name a for instance, allows the agent to integrate the infonnation about the bearer of ex with ~ther information he has about the bearer. The construction of such "internal connections" is an essential part of interpretation and of belief fonnation, since only by integrating the content of the message with his antecedent beliefs can an agent evaluate the new material. Similarly, the semantic contribution (for the agent) of a definite NP, like a defmite description or a complex demonstrative. is often simply to single out some mdivldual

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for which a discourse referent has already been introduced in the processing of the discourse or which is otherwise available from context, not to contribute to the set of

property ascriptions attributed to the individual picked out. Nevertheless, the descriptive conditions of the definite in this case still make a contribution--the

furnishing of internal connections between elements of the agent's cognitive state. The internal connections introduced by all defmites end up playing a crucial role in gauging the behavior of singular terms within belief contexts, as we shall see in

chapter 3. This way of characterizing the conditions introduced by names (but also other definites) pertains to DR theory's fonnalization of the fantiliarity theory of definites. According to the familiarity theory of definites, it is a presupposition of a definite NP a that the recipient of a discourse containing a be familiar with a's

denotation. The familiarity with definites also is a presupposition of bearers of propositional attitudes, if the definites occur within the report of the attitude,z6 It is thus essential to the DRT account of names, indexicals, demonstratives, and other directly referential expressions that they do introduce some conditions on discourse referents--inc1uding perhaps such metalinguistic information as is

suggested by the use of the condition 'named( , )'. But these conditions are to be understood in a different way from other conditions. An acceptable account of the contribution of proper names and other definites to DRS construction must

distinguish between two sorts of conditions: those that directly contribute to the truth

85

3. EXPANDING THE FRAGMENT: EVENTS IN DRT There are three expansions of the original fragment that are important to later developments: work on events and tense, plurals, and belief contexts. Belief contexts have a special importance in that their treatment already lays down some of the

fundamental precepts of the semantics of abstract entity denoting constructions. They merit a separate chapter. Events and plurals I will cover in the next two sectlons.

Some of the earliest papers on DRT (e.g., Kamp 1979, Kamp and Rohrer 1981) set out to develop a DR-theoretic account of temporal reference and ~emporal anaphora using event discourse referents. 3o Since we will be analyzin? n?~nals that denote events and event anaphora in the next two chapters, this matenalis Important to review.

A paradigm example of an event or state introducing construction in DRT is the tense or aspectual component of a sentence often syntactically realized as an ending on a finite verb. Following recent syntactic theory, I will associate this component with the syntactic constituent I, the inflection node. The translation of this constituent introduces in DRS construction a discourse referent of a different type than we have seen before; it is an event discourse referent, a discourse referent that an embedding function must map onto an event in the model. Event discourse referents and conditions on them carry the temporal and aspectual infonnation of a discourse.

Following the suggestions of Davidson (1967) on which adverbs are predicates. of

conditions of a report, and those conditions that are relevant to the interpretation of the report by the agent. I'll call the two sorts of conditions attributive and referential respectively, in honor of Donellan's similar distinction for definite descriptions?? Conditions produced by names are almost always referential, while conditions derived from other definites may be referential or attributive. By treating the conditions of definite descriptions as either attributive or referential, one in effect

events, conditions on event discourse referents may also convey the mfonnanon contained in adverbs and adverbial clauses in a discourse. Detailed DRS construction procedures for the temporal systems of French,

reproduces the familiar scope distinctions for definite descriptions and operators like those introduced by modalities. This discussion leads to the following processing rules for the definite determiner the. The definite determiner introduces the same basic DRS structure as the indefmite. But it brings with it uniqueness and familiarity presuppositions, which have various effects on the DRS construction process. Typically, fantiliarity and

DRS construction with events. First we must make some additional syntactic assumptions. In current X' syntactic theories, the site for temporal and aspectual infonnation ~s the inflectio? node (I) of a syntactic structure. 31 X' theory says that given any baSIC category X, It

including temporal adverbs, exist in Bras (1990) and Kamp and Rohrer (forthconting). A relatively comprehensive construction procedure for Enghsh also exists in Kamp and Reyle (199+). I only sketch here some of the leading ideas of

accessible discourse referent satisfying all the conditions attributed to x. 28 Definite descriptions, however, may also have a functional reading, when the head noun of the

has a maximal projection XP and an intennediate node X' such that XP c,,? be rewritten as YP X' and X' may be rewritten as X ZP, where YP and ZP are maxunal projections of basic categories Y and Z.32 IP is the maximal projection of I and is the syntactic fonn of a simple sentence. I have five basic categories: V (verb), M (modifier), N (noun), C (complement), D (detennmer), and I (mflectlOn). I also assume for all categories a pair of features concerning nouns and verbs .. I wIll say

noun phrase denotes a functional property--i.e. a property AxAYCP(X,y) such that for every x if x is a possible argument for cP, then there is a unique y such that cp(x, y).

that a category is +n just in case it is nounlike, +v just in case it is verb-like. Some basic categories may come with either feature. Modifiers may be of the +~ o~ the +v

This reading is often present with e;vent or state nominals, as we shall see in chapter 4. In this case, the meaning of the~head noun fulfills the uniqueness and familiarity

variety depending on whether they attach to N' (in which case ~ey are adJecnves) or to V' (in which case they are adverbs). Here are the rules the X theory Imphes for I

uniqueness presuppositions are satisfied by requiring that the discourse referent x

introduced be identified by the anaphora resolution module with some most salient,

presuppositions. 29

and its projections.

VP - MP(+v) V'

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A CRASH COURSE IN DRT

V' - V (NPobjecu, (NPobject2), (CP) I'-IVP IP-NPI' (NPobjecu, (NPobject2), and (CP) all stand for possible arguments of V, where CP is a maximal projection of a complement--e.g., a that clause. The subcategorization frame for the verb will detennine what syntactic category of arguments the verb must take. With I are associated several features: Tense, Aspect, Modal, and Agreement, which encode properties of the verb such as whether it is in the past or pluperlect tense, has perfective or imperfective aspect, or is accompanied by a modal auxiliary like can or must These syntactic rules yield the following structure for a simple sentence: IP

NP~r

I~VP

~

Tense, AGR, / Aspect, Modal

V' /

~ ADJ

V~NP I yields one or more event discourse referents and a variety of conditions expressing temporal and aspectual information. 33 Thus, I plays a semantic role much like the detenniner in a noun phrase, reflecting the syntactic similarity. A simple tense like the simple past or present functions very much like an indefinite or definite detenniner. More complex tenses function more like quantificational detenniners introducing complex conditions and discourse referents within subDRSs.34 DRT thereby predicts that event anaphora should follow the patterns of individual anaphora. I shall look at event anaphora in chapter 5, when I discuss abstract entity anaphora I introduces a discourse referent of a different sort from individual discourse referents introduced in chapter 2. DRT distinguishes between sorts of discourse referents--in particular between individual discourse referents and state and event discourse referents. I introduces state or event discourse referents. State discourse referents are denoted by S, s" etc. while event discourse referents are denoted. bye, e" etc. To save the orthography at the price of some ambiguity, I will use e, e, etc. as eventuality discourse referents when I do not need to distinguish between the different types of eventualities. Here is a natural translation of I:

AP

IP(e) I
87

In the partial DRS above, 'I' represents the condition(s) derived from the temporal and aspectual information contained in I. This translation of I does not reflect the function argument structure implicit in the syntax. I is the head of the whole sentence, but my translation reflects a syntax in which the subject NP is the head. One could reflect the function argument structure of the syntax in the semantic translation of 1. But nothing is gained semantically by this move, and some aspects of DRS construction become more awkward with the more complex translations. 35 Thus, I shall stay with the simpler translation above. The conditions derived from temporal and aspectual information are often quite complex. They involve temporal anaphoric relations between the events introduced in the inflection node and events and times already introduced into the discourse by previous material. DRT here follows in broad outlines the Reichenbachian treatment of tenses. One special discourse referent introduced is the temporal discourse referent that stands for the moment of uttering or writing down of the discourse--the "now of the discourse context." Past tenses introduce an equation that says that the action occurred previously to the time of the discourse (e < n). Present tenses introduce an equation that says that the event overlaps the now (e ~ n), while future tenses introduce an equation that says that the event is later than the now (0 < e). But there are other temporal relations that obtain as well. For instance, the simple past tense introduces a temporal relation between the event discourse referent e it introduces and the event discourse referent introduced in the previous main clause e'; the relation is that ~(e < e').36 A pluperfect tense typically introduces the equation e < e'. The rules governing the use of these equations in DRSs are quite complex; they depend on lexical, semantic, and syntactic information as well as on the structure of the discourse built up to that point. 37 In DRT, the task of introducing these equations has traditionally been left to an augmented anaphora resolution module. Since the analysis of tense lies outside the scope of this book, I will not go into details here.3 8 Besides rules concerning the temporal properties of events, a DRT must also provide rules for calculating aspect. In DRT, aspect is determined at the level of the DRS (Smith 1991, Bras 1990). This requires distinguishing not only between states and events at the level of discourse referents, but also between accomplishments, achievements, activities and processes. As Verkuyl (1972), ter Meulen (1984), Krifka (1987, 1989) and others have noted, whether a sentence introduces an accomplishment or an activity may depend on the entire VP or even the entire sentence. Not just features of the verb but also features of its arguments must sometimes be used to detennine the type of event or state that eventually fIlls in the event argument place in the predicate introduced by the verb. We will look at details in chapter 4. The parallel between I and D forces us to revise our translation of VPs. The semantic translation of an N' is a property; its DRS translation is a predicative DRS applying to the discourse referent introduced by the translation of the D. The translation of a VP is also a property. But it must be a two-place predicative DRS-one argument place to be filled by the subject of the whole sentence and the other to be filled by the event discourse referent introduced by 1. How does this work? We

1I1!r~------------------------------------',""""_--'-----

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must change the entries for verbs given in the previous section. Following Davidson and others like Parsons (1989), we add to the translation of each verb an eventuality

A CRASH COURSE IN DRT to yield, according to the definition of DRS conversion:

argument place and introduce eventuality discourse referent variables e, e l .. etc ..

Thus intransitive verbs cp become two place predicates of the form lee lex cp', where cp' is the DRS predicate corresponding to the verb; transitive verbs", become three place predicates of the form lee lex ley cp', and similarly for ditransitive verbs. The translations of transitive and ditransitive verbs convert with the translations of their indirect and direct objects in the way discussed in previous sections. But once the translation of the VP is built up, we see that it is a two place relation rather than a one place property. Its translation is of the form lee lex cp; so it may combine with the translation of the I. Thus the semantic translation of a YP is a property of eventualities; it is an event- or state-type. Our choices so far also dictate the form of the translation of adverbial phrases. Following Davidson, many of these form predicates on events. In the DRS construction procedure, then, adverbial phrases should form predicate ascriptions to

lee! Ax

~u'":,~ y",,=:o::<1

named ('Sam', y) erkick (x, y) school(u) at(u,e, )

«y, Sam>}

The I component contributes an event discourse referent and conditions reflecting the

assertion that the event has already happened. 4! 1 will summarize all these conditions with just one, e < n, where n is a discourse referent representing the "now" of the discourse:42

the event discourse referents introduced by the inflection node. To do this and to

AX e,u,Y,n

combine with the translation of V' to yield an event type, the translation of an adjunct cp must be of the form

e
named ('Sam', y) e-kick(x, y) school(u) at(u, e)

APlee P(e)

cp' (e) This is the right sort of structure to combine with the property of events given from the trartslation of the Y' to yield another property of events.39 Let us now look at an example of how we might introduce and treat event

«y, Sam>} This predicative DRS may now combine with the translation of the subject NP in the familiar way to yield the DRS (K12): (KI2)

discourse referents.

89

e,u,Y,v,n

named('John', v) e
(12) John kicked Sam at school.

Let us look at the processing of (12) in detail. kick Sam yields the predicative DRS: y

leelex~n~am~e'd~('~S~am~",y')~ e -kick(x , y)

«y, Sam>} This now combines with the translation of the adjunct adverbial,40 which is

lePlee 1 p-ue:--:----i P(e l ) school(u) at(u, e l )

named('Sam', y) e'-kick(v, y) school(u) at(u, e) (,} This DRS is not quite complete. When amalgamated with already accepted information, the conditions of the form named(a, x) will disappear; their role is to guide the updating correctly. But we must await the next chapter to see how this is done. But (KI2) serves to derme truth conditions for (12); (KI2) has a proper embedding just in case there are objects correlated with u, v, y, e--call them l!, Y, y, !e-such that: y is John,!! is a school, y is Sam, ~ (the event-type discourse referent introduced by the finite verb) is an event of Y kicking y, and !e occurs at l!. Thus, (K12) confers the right truth conditions on (12). When a VP contains a quantificational determiner, it may turn out that an event discourse referent is declared in a DRS superordinate to the one in which the

condition derived from the verb is introduced. But this causes no particular difficulty.

11

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A CRASH COURSE IN DRT

Consider (13.a) and the DRS for it derived according to our construction procedure.43

we must appeal to some other principle to explain (13.c) besides the usual method of reflecting wide scope readings in the DRS construction procedure.

90

(13.a) Mary hit every boy. 4. PLURALS IN DRT

x e n named('Mary', x) e
§--~ {<x, Mary>}

Because of the way DRS conversion nonnally proceeds, the event discourse referent is declared in the universe of the principal (topmost) DRS, along with its temporal conditions. Nevertheless, the event discourse referent is an argument of the predicate derived from the verb. 44 An event description e-, y for x, y respectively. In (13.a) the event described is an event in which Mary hits x, for every boy x. This event is the sum of all these events in which Mary hits a particular boy. This treatment implies quite permissive substitution principles within event descriptions. In (13.a), for example, were the quantifier phrase every boy to be coextensive in a model M with the students who were bad in class, then the event introduced by (13.a) in which Mary hits every boy and the event introduced by Mary hit the students who were bad in class would be the same. This analysis predicts that event descriptions must always be transparent to substitution of coreferential singular terms, unless these descriptions occur within the scope of an intentional operator. This is welcome in view of the discussion in chapter 1. But notice that the approach to (13.a) won't do in every case. (13.b) Mary hit no boy.

The preferred reading for this sentence is to have negation take wide scope. To get this reading, we need to postulate that the negation in the VP always percolates to I and takes wide scope over the eventuality introducing components of 1.45 A further question is whether eventualities introduced by the inflection node may take wide scope over the subject noun phrase. Can we say that there is one event described in the following sentences, for instance?

The next extension to the DRS construction procedure I consider concerns plurals. The DRT view incorporates many of the observations and analyses of Link (1983, 1987), Krifka (1987), and Landman (1988) on plurality. A comprehensive treatment of plurality with DRT is given in Kamp and Reyle (199+).47 I will sketch here only their general approach and the DRT treatment of plural anaphora. The observations about plural anaphora are important for my analysis of abstract entity anaphora 4.1 DRS Construction for Plurals and Basic Plural Anaphora

Plural NPs sometimes act as terms referring to sets, groups or kinds, and these plural NPs may act as linguistic antecedents for plural pronouns. (14)

The students went camping. They enjoyed it.

During DRS construction, plural NPs, like singular NPs, introduce conditions and discourse referents. 48 Various difficulties concerning dependent plurals and NP conjunction have led some to suggest that there should be a uniform type of discourse referent for plural entities and individuals.49 If we follow the suggestions of Link and Krifka, a uniform type for individuals and groups would reflect the uniformity of individual and plural entities as elements of a lattice in the model theory. While I shall adopt at least provisionally the lattice-theoretic models for plurality common in this research, I shall ignore the complexities of dependent plurality and adopt a conceptually simpler theory in which plural discourse referents form a distinct type denoted by capital letters 'X', 'Y', 'XI " etc.; embedding functions always map plural discourse referents onto non-atomic parts of the lattice of groups and individuals in the model, while mapping individual discourse referents to atoms in the lattice.50 With our decision made, we can now represent a discourse like (14) with the following DRS:5!

Ye Z z e' (13.c) Every boy kissed his mother. (13.d) No one kissed their partner. The consensus about (13.d) is that the event discourse referent introduced by the processing of I is not entered into a DRS universe outside the scope of the negation implicit in the quantifier no one .46 With (13.c) matters are not so clear. Most likely,

students(Y) e-go-camping(Y) e'-enjoy(Z, z) Z=Y

z=e The new elements in the DRS above are the plural discourse referents Y and Z, and

1lII----------------------~-~,~---~--

CHAPTER TWO

A CRASH COURSE IN DRT

the identification between them. The plural discourse referents are introduced by plural NPs. The plural pronoun also introduces a condition that the anaphora resolution process must fill in. A new constraint on anaphora is that the process of anaphora resolution may not identify a plural discourse referent ~ith an individual discourse referent. Not all plural quantifiers introduce plural discourse referents. Many incorporate instead instances of quantificational determiners introducing individual discourse referents. For example, determiners like few, mos~ and many are almost always read distributively; that is, when such a detenniner occurs as part of an NP, it is interpreted as quantifying over elements satisfying the common noun phrase which is its head. Thus sentences like (15.a-b), in contrast with (15.c),

is the sum of Susan and Bill. These examples indicate that the antecedents for plural anaphors may be constructed from other discourse referents or DR-theoretic structures in the text This is also a fundamental feature of abstract entity anaphora, to which I return in chapter 5. The operation needed to construct new discourse referents from old discourse referents in (16.a) and (16.b) sums over previously introduced discourse referents. I define it as follows:

92

(15.a) Many men lifted a piano. (15.b) Most men lifted a piano. (15.c) The men lifted a piano.

!

I

do oot have collective readings. When the head common noun phrase is interpreted as a property of individual discourse referents. it types the discourse referent introduced by the determiner as being an individual discourse referent. Kamp and Reyle (199+) extend the DRS language to incorporate many different quantificational relations; these are enclosed diamond-like shape, occurring between the DRSs representing the restrictor and nuclear scope. A sentence like (15.b), for instance, will yield thus the following DRS: n

~~ man(x)

most x

e,V e
This is a straightforward rewriting in the DRT formalism of a generalized quantifier representation for (4) like that to be found in van Benthem (1984). Quantificational determiners other than every will introduce quantificational relational predicates into the DRS language.

4.2 Plural Anaphora

DRT has some new and interesting insights about plural anaphora. Plural NPs are not the only kind oflinguistic antecedents plural anaphora exploits. Consider, (16)

Susan went camping with Bill. They enjoyed it

On the most salient reading of the plural pronoun in (16), they refers to the group that

93

(PSUM) Given any fmite number of discourse referents ~" .. " ~n' where each 13i may be a plural or singular discourse referent, we may form the sum 131 + ~2 + ... + ~n and use it to replace a ? in an incomplete condition of a DRS K, if the ~i are all accessible from K. Suppose Z = ? is a condition in an incomplete DRS K. Then if ~" ... , ~n are all accessible to Z (in K), then one may identify Z with ~1 + ~2 + ... + ~n to complete K. The import of the operation of sum for the examples (16.a-b) is clear. The last clause of the definition is needed to handle the contrast between examples (17) and (18), which are due to Hans Kamp. (17)

Bob is mean. Each student he takes out for a beer ends up paying for every pitcher they order.

The pronoun they in (17) can refer to the sum of Bob and a particular student he takes out The definition (PSUM) permits this since the discourse referent introduced by 'Bob' and the discourse referent introduced by 'every student' are accessible to Z, since it is introduced in the subordinate DRS. In (18), however, (18)

Bob is mean. Each student he takes out for a beer ends up paying for every pitcher they order. They don't get on now.

the second occurrence of they introduces a discourse referent Z in the main DRS to which the discourse referent introduced by every student is not accessible. So (PSUM) rules out the anaphoric link between Z and any group consisting of Bob and some student he takes out for a pitcher. This accords with speakers' intuitions; the reading of the second occurrence of they as bound by the quantifier in the second sentence is not generally accepted. Sometimes sums are explicitly marked by means of conjoined noun phrases, but sometimes they are not An interesting and important aspect of plural anaphora is that not all of the sums that can be formed are acceptable as anaphoric referents. Consider, for instance, the possible readings of a sentence like (19): (19)

Suzie kissed John. Sam was wedded to Mary. They are both very happy.

(PSUM) predicts that there are six possible interpretations of (19), one for each

1I"'r-----------------~_,~------.

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possible group with two members that can serve as antecedent to the anaphor. But (19) has fewer than six readings. Consider, for instance, the following variants of (19): (20.a) #Suzie kissed John. Sam was wedded to Mary. They are both very happy, although Suzie and Mary are not. (20.b) #Suzie kissed John. Sam was wedded to Mary. They are both very happy, although Sam and John are not. Given the adverbial clauses, they should have as antecedent in (20.a) the sum John + Sam and in (20.b) the sum Suzie + Mary. But these groups are not acceptable antecedents for the pronoun. What do seem to be acceptable antecedents for the they in (19) are the sums Suzie + Sam and John + Mary. The elements of these groups do not share the same thematic role or even the same syntactic position. It is a delicate matter what to make of examples. Perhaps the unacceptability of Suzie + John as an antecedent is just a matter of salience, this group being so much less salient than other groups. But were it simply a matter of salience or world knowledge, we should be able to play with the context to alter salience. Certainly this works with individual anaphora: (21)

Sue invited the physicist over for dinner to John's house. He kepttalking incomprehensibly about gravitrons, while the rest of us tried to get away to watch the football game.

But now when we tty to do something similar with plural anaphora to pick up a group like Mary and Suzie as in (20.a) or (20.b), we fail. It should be perfectly possible to refer to the group Suzie + Mary by means of a definite descriprion. (20.c), for instance, is completely felicitous. (20.c) #Suzie kissed John. Sam was wedded to Mary. The girls are both very happy, although Sam and John are not.

95

The plural pronoun in (22) refers to the group of all those students in the class who went on the camping trip. But since the individual students are not explicitly introduced into the discourse as discourse referents, (PSUM) cannot be used to form the appropriate sum. I assume that the quantificational structure of (22) does not introduce a plural discourse referent, since many always has distributive readings. 52 What we need is a particular operation to yield groups; it is called abstraction. Abstraction exploits a condition introduced by a quantificational determiner like most, every, and many. If the condition is of the fortn ct <> ~, then abstraction allows us to form a group of all those objects satisfying an alphabetic variant of ct I,l ~, the DRS update of ct with ~.53 The group is denoted by the term LX ct U ~, where L takes the DRS ct I,l ~ and a discourse referent declared x in ct I,l ~ and returns the group of all those objects y that satisfy the property Ax ct I,l~. Such a group is the intended antecedent of the pronoun in (22). We will see more of abstraction when we develop the account of anaphora of abstract objects in chapter 6. The appendix defines truth conditions for conditions of the form X = Lx ct I,l ~. In conclusion, it is noteworthy that the DR-theoretic treatment of plural anaphora assimilates plural pronouns much more closely to definite descriptions. The operations of (PSUM) and abstraction can be viewed as ways of determining pertnissible descriptions for which the plural pronoun stands proxy. Evans (1980) developed the view that pronouns stand in for contextually supplied definite descriptions. DRT's view of singular pronouns is quite different; it takes them to function essentially as bound variables, but DRT gives a different notion of binding and scope than traditional linguistic theories. On the other hand, DRT seems more inclined to agree with the Evans view of pronouns insofar as plural pronouns are concerned. This area of DRT is, however, still quite unsettled.

5. APPENDIX: FORMALIZATION OF DRS CONSTRUCTION AND DRS INTERPRETATION

5.1 Definition of DRSs These observations indicate first that pronominal anaphora and definite description anaphora differ. Second, they indicate that collections must fall under a certain description, or they must be constructed by reference to infOrtnation like role, or topic and focus, since the elements in the group share the property of being topicalized. One should modify (PSUM) so as to reflect these constraints. But at present we lack a framework in which we can develop precise constraints to predict these observations. We shall see in chapter 8 that principles of discourse structure will give us such a framework There is one other sort of plural discourse referent introducing operation that should be briefly mentioned. The operation (PSUM) is unable to account for the anaphoric phenomena in a discourse that is quite similar to (18.a-b): (22) Many students in my class went on the camping !tip. They enjoyed it.

I adopt the following conventions for variables over different types of discourse referents. x. y, etc., range over discourse referents of any type; c. Ct. etc. over discourse referents of event type; t 1• t2 for temporal discourse referents; and X. Y, etc., for plural discourse referents. Temporal discourse referents include the "now" discourse referent, n. I define DRSs and their conditions by means of the following double recursion: DEFINITION:

(i) (ii)

If,!, is an n-ary DRS predicate and x" "', x. are discourse referents, then V(x b ...• xn) is an atomic condition. If x" X 2 are discourse referents of any kind, e I, e 2 are eventuality

96

(iii)

discourse referents, t a temporal discourse referent, then Xl = X2. Cl < e2, e 1 < t are conditions. If K" K, are DRSs, x is a discourse referent, e is an event discourse referent, and '" is a quantifier relation symbol, then the following are conditions: -,K, Kl =* K 2 • e-K, and

K1 (iv)

(v) (vi)


el EB e2 = mine {e': el C e' & e2 C e'}, if there is such an e' = 0, otherwise Note that without additional axioms on the domain of eventualities EB is neither commutative nor associative. 54 There are several ways we can set up the definition of a proper embedding. The simplest defines the concept of a proper embedding of a DRS K in a model M with respect to a function from discourse referents into objects in DM <w, I> I will call any such function from discourse referents into OM an embedding function. Define an embedding function g to extend an embedding function f relative to K in M at <w, t> ( written g 21< f) just in case Dom(g) = Dom(f) U UK, g 2 f. I will also say that g extends f relative to a set of discourse referents X. Define an external anchor for Kin M to be a partial function from UK into (U<w,1> E W X T (Dom«w,t») U T, such that if n E UK then A(n) = the utterance time of the discourse, and if i E UK A(i) = the speaker of the discourse. Now we define a proper embeddingf ofK in M at <w, t> (written If, K]Mw U with respect to a possibly empty external anchor A for K in M and satisfaction of a condition in M relative to an embedding function f for the DRS in which the conditions occur at <w,t> (written (M, w, t) ~f).

K1

If x is a discourse referent in UK, and K E DRS, then X = LX K is a condition. If Xl •.. "X n are discourse referents, then X = Xl+ ...+ Xn is a condition. A DRS is a pair , where U is a set of discourse referents, and Con a set of conditions.

Conditions that contain subDRSs are complex conditions; those without constituent conditions are simple or atomic conditions. An atomic DRS contains only atomic conditions; otherwise it is complex.

5.2 Model Theory

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The original model theory of this fragment was extensional. In order to talk about meanings in DRT, however, I introduce intensions with respect to worlds and times. They will become crucial in the section in which I add attitude descriptions to the DRT language, but they are also useful to talk about the semantic concepts for the extensional fragment of the language. Further, the easiest tack for the model theory would be to follow Krifka and Link and assign the domain of eventualities and sums a lattice structure. In view of the discussion in chapter 1, however, it appears that the domain of eventualities does not have a tidy algebraic structure. This is reflected in the models below. Define an intensional DRS model M to be a quintuple <W, T, D, E, II>. (i) W and T are non-empty sets (the set of worlds and times respectively). (ii) D is a function from W X T into a non-empty, atomic lattice (D<w,t> is the "domain of individuals and sums of individuals in w at t"). (iii) E is a function from W X T into a set of objects (eventualities) partially well ordered by inclusion such that: (a) if 'I' is an E-path description (see chapter 1) VetE E<w,t 1> Ve2 E E<w,t z>' .. Ven E E<w,tn> ("" eo) - 3e' E E<w.t.> (el C e' & ... & eo C e') and (b) if '" is an eventuality description, then 3e' E E<w, t> Ve E E<w, t>Vxt. ... xn'l'(e, Xl. ... , xn) - e C e'). E<w,t > is the "domain of eventualities in watt". Dom«w,t» = D<w, I> U E<w, 1>. (iv) II is an interpretation function that assigns to DRS predicates functions 0 such that for <w. t> EW X T o«w, t» E go (Un E ",(Dom«w,t»)n). To quantifier relation symbols, II assigns functions 'Y such that for <w, t> E W X T into y( <w, t» E go go (Un E ",(Dom«w,t»n», where: Dom«w,t» = D<w I>U E<w 1>. Since C on eventualities is a partial well ordering, we may 'extend the summation operation Ell defmed by the lattice for pluralities to eventualities:

DEFINITION (Proper embedding and Satisfaction): (i) If '" is an atomic condition of the form : 3g 21<, f (g(x) = b & [g, Kd~.t.f) I. (iv) If", is of theform e-KI , then(M, w, t) ~f'" iff3g 21<, f[g, KdMw,t,f). (v) If",is a condition of the form KI "'" K" then (M, w, t) Fr ",iff'lfg21<, f ([g, Kd~,t.f - 3h 21<, g [h, K,]~,t,g).

K1

ffi

K1

If", is a condition of the form then (M, w, t) ~f '" iff <{b: 3g 21<, f [g, KI]Mw,t,f& g(x) = b}, {b: 3g 21<,f [g, KdMw,t,f & 3h 21<, g [h, K,]Mw,t,g h(x) = bl> E 1
I.

W

,

rr------:-:-fe-r-en-c-e-t-o-w-o-r-ld-S-i-n-th-e-defi-m--i-ti-o:-H-o-:-~-p-ro-:-e-~-e-mO-be-ddin-.-g-a-b-ov-e-.5-5-----------..·r"'·. ~~-, .. "'iill!.A""""

The notion of proper embedding yields a definition oflogical consequence (in fact several notions of consequence, but I only give the most familiar here). Let us write M low, t K iff 3f [f, K]Mw,t, and M I' K iffVw E WM 'It E TM (M, w, t) I' K. We may now define a DRS K to be a logical consequence of K' iff for every DRS model M (M, w, t) I' K'"* (M, w, t) I'f K, for all w, t of M. We write K is a logical consequence ofK' as K' I' K. Validity is defined by taking K' to be the empty DRS.

5.3 The Construction Procedure and its Semantics I restrict myself here to extensional models for simplicity. It will be obvious how to extend the discussion here to intensional models. I will show in this section how to supply denotations to partial DRSs and predicative DRSs so that one can verify that the construction procedure yields the correct output set of embedding functions for given inputs. The extension of a DRS is a set of embedding functions relative to an embedding function g (g may be the empty function!). Our denotations for partial DRSs and predicative DRSs will reflect this fact First I define the language of DRS conversion precisely and then specify the operation DRS conversion, updating and anaphora resolution. Here are the expressions of the language: Vocabularv of the DRS Language. Object Language Symbols: X,y,Xh ...

e, el •...

P, Q, P" Q" ... li, X, y. Z, Xl> .. loves( , ), boy( ),etc.

"'*. I , V Metalinguistic Symbols. x, y, Z, Xl •... e,eh" , x, y, .. ' e, el •...

K,K',K .... . P, Q, Q" .. .

individual, eventuality or plural discourse referent variables. eventuality discourse referent variables predicative DRS variables discourse referents (individual type) DRT predicates DRS operators

variables over individual, eventuality or plural discourse referents variables over eventuality discourse referents variables over discourse referent variables variables over eventuality'discourse referent variables variables over FDRSs variables over predicative DRS variables

'l'-'-'-

<11, '¥, <11" •••

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99

variables over DRT predicates variables over DRT conditions and sets ofDRT conditions

I will use ConK to denote the conditions of a DRS K and UK to denote the universe ofK. I now extend the basic DR-theoretic structures with some new kinds. These are various types of l1incomplete" DR-theoretic structures, or structures containing variables. Out of these will emerge DR-theoretic structures representing quantifiers and propositional functions. I use a simple recursive definition. Let a(i3/Y) denote the result of substituting an occurrence of f3 for every occurrence of y, where a is any DR-theoretic structure. Also defme a discourse referent argument for a condition to be any discourse referent occurring in the condition. DEFINITION: (FDRS): Any DRS is an FDRS. If'l' is a DRS condition in an FDRS K, then K(P/Iif) is an FDRS, and if'l' has a discourse referent argument x E UK, then K(P(x)/Iif) is also an FDRS. Ifx EUK and K is an FDRS, then K' = . (iii) If 6 occurs in K but not in an atomic condition: K[x/Ii] = < UK, {'l'[xI6]: 'l' E ConK}>, where: (a) 'l'[xlli] = 'l'(xI6) if'l' is atomic; (b) 'l'[xlli] = Q(K,[xI6], K 2 [xI6]) if'l' is a condition of the form Q(K" K 2 ) and Q is DRS operator or quantifier

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relation. DEFINITION: TO is a partial DRS (PADRS) iff K is an FDRS or a PRDRS and either: (i) K has one predicative DRS variable, Q, u is a designated discourse referent EUK U (UK' < K(UK')), Il a discourse referent or dr variable argument for Q, and TO = A.Q K[u/Ill; or (ii) K has two predicative DRS variables, P and Q, u is a designated discourse referent, and 8 a discourse referent or dr variable argument for P and Q and TO = A.PA.Q K[u/Ill ; or (iii) K has two predicative DRS variables, P and Q without any discourse referent arguments and TO = A.PA.Q K; or (iv) K has one predicative DRS variable P without any discourse referent arguments and TO = A.P K. Further, if TO is a partial DRS then so is A.x7t. In order to derme conversion, I define the substitution of a predicative DRS for a predicative DRS variable. Recall the definition of DRS update or DR-theoretic union K U K'. This obviously extends to FDRSs. Now for the substitution operation. In the following definition suppose that K is an FDRS, u e UK is a discourse referent, K I is an FDRS and P a predicative DRS variable occurring in a condition '¥ E ConKDEFINITION: Suppose'¥ is an atomic condition. Then, if'¥ = P(u), Subst('¥, K', P) = UK', Subst('¥, K', P) = K, otherwise. Suppose'¥ is a condition of the form Kl ~ K 2 . Subst('¥, K', P) = K(Subst(K" K', P) ... Subst(K" K', P)/ '1'). Suppose'¥ is a condition of the form ---.K,. Then Subst('¥, K', P) = KhSubst(K" K', P)/ '¥). Subst(K, K', P) = I,l [Subst('¥, K', P): '¥ E ConK}.

With the substitution operation defined. we are now ready to define DRS-

conversion precisely_ There are two cases: DEFINITION: (DRS-Conversion) (I) Suppose that A.P K, E PADRS with a desiguated discourse referent u, A.P K,A.a, ... A.a.K, E PRDRS U PADRS, a, is a discourse referent variable, and for i j aj is either a discourse referent or predicative DRS variable. Then: Conv(A.PK" A.a, ... A.a.(K" a,) = A.a, ... A.ai_lA.ai+I ... A.a.K, [PI! K,[u/a,ll, where: K[P II K, '} is an FDRS just like K except that: (a) Con K(P II K} = ConSubst(K, K', Pl·

*'

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101

(b) UK{P II K'} = USubst(K, K, Pl· (II) Suppose that A.P K, E PADRS, with no designated discourse referent and A.a, ... A.a.K, E PRDRS U PADRS. Then: Conv(A.PK" A.X, ... A.x.(K,) = A.a, ... A. a.K, [P II K,} The DRS conversion of an n+ I place predicative DRS with a partial DRS with just one predicative DRS parameter yields an n-place .predicative DRS. The DRS conversion of an n+ I place predicative DRS with a parnol DRS WIth two predicatlve DRS variables yields an I1+ I-place partial DRS. DRS conversion generalizes a form of the law of (3 conversion for the higher order A.-calculus, translating predicative DRS variables as second order variables and predicative DRSs as A-terms in an obvious way. Part of the DRS construction procedure is to specify the linking rules, which specify which syntactic structures under the DRS translation will introduce discourse referents for which argument positions in predicative DRSs derived from other constituents. The linkiog rules determine, in the definition above for a given partial DRS and predicative DRS, which argument place (occupied by the variable -",,)is to be fIlled by the discourse referent introduced by the partial DRS, if there is any. For the simple fragment defined so far, configurationally dermed notions of subject and object will suffice to detennine which noun phrase translation contributes w~iCh discourse referent to which argument place in a given predicative DRS. Thus, 10 a sentence like Every boy loves a horse. the linking rules would say that the "subject argument place" of the translation of love is to be filled in with the desiguated discourse referent introduced by the translation of every boy, while the "object argument place" of the translation of love is to be fIlled in with the discourse referent introduced by the translation of a horse. More complicated syntactic structures will require a more elaborate conception of linking rules, as we will see in chapter 4. With these linking rules, the definition of conversion allows us to put predicative and partial DRSs together in an order-free way; we are able to specify any logically consistent possible scoping of noun phrases from a given syntactic structure. Similarly, the conversion routine specifies which predicative DRS variable is to be replaced by the predicative DRS. But in practice we will not need this flexibility; the partial DRS derived from D or I always combmes first with the translation of the structure that is adjoined to D or I. To effect this I will simply exploit the linear order of predicative DRS variable abstracts, converting the outennost fIrst. Because the DRS conversion procedure allows us in effect to get several different DRSs from the same syntactic structure, it cannot produce a strongly compositional semantics in the rule to rule sense. Conversion is more than just function application. 56 If we wish to recover a strong form of compositionality for the mapping from syntax (and perhaps other sources) to meanings, then we must place

F<}"& .

,-~----

----------

)r

i·:

i

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constraints on the conversion process. For instance, the position of an NP or operator introducing expression in the syntactic tree might determine its order of application. Using a theory of syntax with quantifier raising and the configurational constraint on the order of application, we could then have a strong form of compositionality in which every syntactic structure produced a unique DRS up to anaphora resolution. The DRS conversion procedure enables us to put together partial and predicative DRSs in a bottom up, order free fashion to artive at a DRS for a sentence Sj. This DRS must now be integrated into the result of DRS construction for the discourse up to Sj. 11ris uses the DRS update or DR-theoretic union operation. It is very simple and has already been introduced. The final stage in constructing a DRS completes the incomplete conditions--resolving the anaphoric equations. Formally. anaphora resolution is a complex function from incomplete DRSs to DRSs that fills in the anaphoric equations. This function exploits syntax, the DR-theoretic semantic structures, world knowledge, and the discourse structure of the text to yield an answer; thus the full meaning of a DRS does not compositionally depend just on the meaning of its parts (unless one wants to think of pronouns as having a very complex meaning) but also on a number of contextual factors. I now tum to the semantics of the construction algorithm and the process of DRS conversion. Let M be a standard DRS model. An extended DRS model 'M = <M, E>. E is a type structure built up in the following way. Let DR be the collection of all discourse referents and 1"the set of all partial functions f: DR - DM--DM being the domain of M. DR and 'f are primitive types of E. E contains four complex types: to, t" t2, and t3. to is defined recursively as follows: 'fS to, and if (~ - '/) S to, then «DR X~) - '/) S to. to is the type of a predicative DRS.57 t, the type of a unary partial DRS and it is very simple: t, = (to - to). Two place partial DRSs have the type t2 = (to - (to - to)). The general semantic interpretation of Conversion, !Convl, is a functional of the type t3 = Un E [0, l}{ (tn+! X DR- (to 't n)}. Because of the way conversion is defined and semantically interpreted, the conversion. for instance, of a unary partial DRS with a designated discourse referent and an n+ I-ary predicative DRS will yield an n-ary predicative DRS; conversion of a one place partial DRS without designated discourse referent and n+ I-ary predicative DRS will yield an n+ I-ary predicative DRS. Now I give the semantics of partial and predicative DRSs for this frajLment in a fixed, extended DRS model. The denotation of a predicative DRS Ax, ... A",K relative to an embedding function g, lAx, ... Ax. Klg, is a function of type to:

conversion. Then for a partial DRS = APAQ «x), {P(x), Q(x)}> the appropriate denotation would be:

102

!Ax, ... AX. Klg = f: (DR)n - /O('/) such that: (VR E DRn) f(R) = {h 1 [h, K[R/x" ... , x,]gM & h '2 K[R/~]) g}. Suppose G is an n+ I-ary predicative DRS denotation. When a discourse referent x replaces one of the A-abstracted discourse referent variables of G, a family of n-ary predicative DRS denotations results--one for- each argument in G which x may fill. I will denote the result G{x} Which argument x will fill is specified by DRS

1Ig is a function E : to - (to - to), such that if G" G 2 are m+ I and n+ I-ary predicative DRS denotations, then E(G" G 2): DRn+m - /O('/) s. tho VR E DRn+m E(G" G 2)(R) = {f E 'f13h E U(G, {x))(R) & 3h' E U(G 2{x))(R) & (h Uh') U g =f}. The denotation of the partially filled in partial DRS that is the translation of a proper name a--i.e., where = A.P <{x}, {named(a, x), P(x) }>--is a function from a discourse referent and a predicative DRS denotation to a set of embedding functions. 1Ig is a function P: to ~ to, such that if G,is a n+l-ary predicative DRS denotation, then p(G,): DRn - /O('/) S. tho VR E DRn p(G,)(R) = (fE 'fl fE U(Gtlx))(R)(g~f&E InamedIM)· We must assign a denotation to a partial DRS like that introduced by eve!}' that takes its complex logical structure into account. We do not want this denotation to pick out a set of embedding functions relative to a choice of predicative DRS denotations Q,and Q2 and a background embedding function embedding functions that are so large that they assign values to discourse referents that are not in the domain ofK or introduced in Q, or Q2. This could mess up the content of our DRtheoretic structures. So I shall use rnin(f) such that !p(£) to mean that f is a minimal function that has the property!p. Formally, min(f) & = APAQ <{), {«x), {P(x» "*<{], {Q(x)} >} > relative to a function k: 1IIc is a function A : to - (to - to), such that if G" G2 are m+ I and n+ I-ary predicative DRS denotations, then A(G" G,): DRn+m - /O('/) S. tho VR E DRn+m A(G" G 2)(R) = {f E 'f 1 min(f) such that k S f & (Vg 2 f) (31 E U(Gtlx))(R) & I U f = g)- (3h '2 g) (3j E U(G(x})(R)) such that jUg = h)}. The other operators of the first order fragment are straightforward. For negation-where = AP <{), {~P}>, we have: 1Ik is a function N: to - to, such that if G' is an n-ary predicative DRS denotation, then N(G'): DRn - /O('/) S. tho \fR E DRn N(G')(R) = {f E 'f: min(f) such that g I: f & -.3k '2 f k E G'(R)}.

The semantics for the negative determiner no is quite straightforward given what I have said about negation and other determiners. I leave the detalls to the reader. The interpretation of the DRS conditional is very similar to that for the universal

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105

quantifier. If cl> = APAQ<¢, {p ... Q}>,

1cI>l g is a function D: 'to -+ 'to. such that if G 1• O2 are m and n-ary predicative DRS denotations, then D(Glo G,): DRn+m - p('f) s. tho Vi! E DRn G(Glo G,)(i!) = {f E 1'1 min(f) such that k S f & (\fg 2 f) (31 E G,(i!) & I U f = g)- (3h 2 g) (3j EG(i!) such thatj U g = h)}.

The other cases of conversion are similar and left as an exercise to spell out. Let's look at a particular example of how we generate the right sort of embedding functions. Consider Every boy kisses a girl. Let us first get the denotation of the noun phrase a girl. Converting lal with Igirll, we get a partial DRS denotation which is a function from n-ary predicative DRSs D and n-tuples of discourse referents i! such that

?ur translation for the inflection node does not force us to countenance new types partIal DRSs or interpretations. For the general quantifier relations, we have a more complex but general clause. Let cl> be a partial DRS of the following form where

la girll(D, i!) = {g E 1'1 3h E IAPAQ<{U}, {P(u), Q(u)}>I(IAx <{}, {girl(x)} >1[ulil(D{ u} )(i!))}. = {g E rl3h E k{u}, {girl(u)}>1 & 3h' E UD{u}(i!) & hUh'

<{ I, {P (x)



= g}. Q(x)}>

icl>i;, is a function Q : ~o - (~o - ~o), such that if Glo G, are m+ I ary and n+ l-ary predicative DRS denotations, then Q(Glo G,): DRn+m - p('f) S. tho Vi! E DRn+m Q(G lo G,)(i!) = {f E 1'1 min(f) such that k S f & 3g 2 f 3h 2 f <{g(x): (31 E U(Gdx})(i!) & I U f = g)}, {h(x): (3m E U(Gdx})(i!)) (3j E U(G,{x})(i!)) such thatj U fU m = hI> E [
A~K, is to weed out from l'all those embedding functions except those that pro~erly

embed K WIth tbe property variables instantiated to AuK, and A~K,. More formally, DRS converSIOn amounts to the operation of applying a partial DRS denotation to a pr.ed~cat~ve DRS denotation in the right arguments. Thus, my semantics is ehmmallve, unlike that of Groenendijk and Stokhofs (1990) semantics for their dynamic logic. While this semantics is not that of ftrst order logic since the semantic values of sentences are sets of embedding functions, it is no more complex than theirs. Let us examine conversion in more detail. The general semantic interpretation of Conversion, IConvl, is a function of type ~2' If f is a n+ l-ary function from discourse referents to a set of embedding functions, then f[ulil is the n-ary function that results from assigning u to the i-th argument place of f. Now let A be an n+ 1ary predicative DRS denotation and B a 1- place partial DRS with designated discourse referent u. Then ~Conv(B, A, x;lg = the predicative DRS denotation G: DR" - rsuch that for all i! E DR", G(i!)={fE rifE

B(A[uli])(~)&gSfI.

Suppose that C is the denotation of a two place partial DRS designated discourse referent u. Then IConv(C, A, x;lg = the partial DRS denotation G: such that for any m+l-ary predicative DRS denotation D and for all i! E DRn+m G(D, i!) = {f E 1'1 f E U(C(A[uli]))(D{u}) & g Sf}. '

Now iAxAY <{}, {kiss(x, y) }>I = f: DR2 - P('f) such that Vx,y f(x, y) = {g I [g, <{x, y}, {kiss(x, y)} >1 & dom(g) = {x, Y} }. Combining the two we get, IAxkiss a girl (x)1 = the function f: DR - P (1J such that Vx f(x) = {g E 1': g E la girll(1 Awkiss(x, w)I, w)} = {g E rl3h E k{ u}, {girl(u)}>1 & 3h' E IAxAw kiss(x, w)l[u/wll (x) & hUh' = g} = {g E 1'1 g E k{u}, {girl(u), kiss(x, u)}> I} = {g E 1'1 [g, <{u}, {girl(u), kiss(x, u)}>]}. Now we calculate levery boyi(lmiss a girl(x)I). The result is the following, correct set of embedding functions M: M = {f E 1'1 min(f) & (\fg 2 f) (31 E IAzboy(z)l(v)& I U f = g)(3h 2 g) (3j E IAxkiss a girl(x)1 (v) & jUg = h)} = {f E 1'1 min(f) & (\fg 2 f) (31 E k{v}, {boy(v)}>i& I U f = g)- (3h 2 g) (3j E k{u}, {girl(u), kiss(v, u)i}>&j U g = h)} = {f E 1'1 min(f) & (Vg 2 f) ([g, <{v}, {boy(v)}>l- (3h 2 g) ([h, <{u}, {girl(u), kiss(v, u) }>l. This gives us the right set embedding functions as the content of the DRS K for every boy kisses a girl. Each function in M is a proper embedding of K, but these are just the minimal such functions, and in this case there is only one--the null function. Thus, K is true iff (Vg) ([g, <{v}, {boy(v)}>l- (3h 2g) ([h, <{u}, {girl(u), kiss(v, u)}>l, which is what is desired. A final component of DRS conversion is when one adds one DRS to another, using the DRS update function. The idea of piecing together embedding functions for K and K' and requiring that the result be an embedding function ensures that an embedding function for the whole does not inadvertently piece together with a function in IK'lgM a "large" function from IKlgM, which assigns to a discourse

106

CHAPTER TWO

A CRASH COURSE IN DRT

107

referent v ~ UK but v E UK' the wrong sort of value. IDRS-update(K, K')I g = {f E 1'13h E IKlgM &3k E 1K'lgM &f =h Uk}.

One can check to see that the construction procedure gives us the right results: given denotations for the basic predicative DRSs and the partial DRS, the semantics of DRS conversion yields the appropriate set of embedding functions for the resulting DRS. We now can write down and straightforwardly prove a compositionality theorem. Let lail"", I~jl"" be the semantic denotations of a i and ~j as specified above in an extended model 'M = <M, E>. THEOREM: Suppose ~ is an n+ 1 place predicative DRS. Then if a IS a partial DRS, then IConvl""(IexI"", I~I"", Ui) = IConv(a, ~, ui)I"". COROLLARY: Suppose a DRS K has been fonned by converting together n partial DRSs a" ... ,a. and m predicative DRSs~" ... , ~m. Then: IConvl""(la,I"", (. " , IConvl""(Icx.I"", I~,I"", z",),1~21), ".),I~mi"", Z,) = {f E 1'",,: [f, K]M}. The proof of this theorem is a long-winded but straightforward induction on the

complexity of the conversion process. We still have to consider the semantics of anaphora resolution. Anaphora resolution falls outside the scope of the compositional theory of meaning. The discourse context, together with world knowledge, is needed to find the appropriate

antecedents for anaphoric pronouns. Thus, the meaning of a sentence containing a pronoun is not simply a function of the content of the pronoun, which simply introduces a denotation for the pronoun, and of the content of the other constituents. Accordingly, it seems best to treat the unresolved conditions of the fonn z = ? as empty; that is, they do not put any constraints on the proper embeddings for the DRSs containing them. Then, the semantic effect of the process of anaphora resolution is straightforward: it is a function from sets of embedding functions to a subset of those embedding functions. If IKlg is the set of functions properly embedding Kin M relative to some embedding function g and z = ? is a condition of K and z = y is a condition of K' (K. after anaphora resolution), then IKl g = {f E 1'1 f E IKlg & fez) = f(y)}. Every function in IKig is assured of aSSigning a value to y, given the way the process of anaphora resolution was defined (on K).

ISee Kamp all:d Rohrer (forthcomi~), for a detailed treatment of tense in French. Precursors to that

may be found m Kamp (1979, 19816) and Kamp and Rohrer (1983). Kamp 0981a) contains an early

4Heim (1982) was the ftrst of these. See also Groenendijk and Stokhof (1990). SOne reason for this perhaps is that fannal semanticists working in the tradition of linguistics have tried to elaborate a 1tcom~tence model" of knowledge of £!1ean~ng, which tends ~o ignore the li":k between meaning and use. Dummett ~d phtlosopher~ Iollowmg. hun have bee!1 particularly forcefu~ 1P addressing the latter i~sue. D~mmett.s concern~ 3f.1Se from rus attempt to mterpret Wlttgenstems comments on meaning m the PhilosophIcal InvestIgations. 6See also Zeevat (1989). Zeevat gives a reformulation of DRT with som~ different notations. In essence it follows the bottom up C~)fistruction pr<;K=ed!Jfe already developed Slnce Frey (1985) .. Zeevat does not. however, give a sem~tics for the .ieXlcalltems and then denv:e the sf!lndard meanmg of a DRS (a set of embedding funcnons, as we wIll see below) from the meanmgs of its parts. 7To see what a DRS with a disjunctive structure would look like, consider: (1) Mary likes John or M;iry likes Fred. This Yields the following DRS:

(Kl )

x,V Mary(x) John(y) like(x, y)

x', y'

v

Mary(x') Fred(y') like(x', y')

(Kl) confers the truth conditions one would e~peft it has a pro~r embedding just in case eith~r there are obiects conelated with x and y such that all of the conditiOns m the DRS on the left hand Side of v are satiSfied or there are objects correlated with x' and y' such that all of the conditions in the DRS on the right hand side are satisfied. 8For details on X' theory, see for example Radford (1979). The DRS cO!1str.uction pr9Cedure is q1)ite robust. Parsing implementations based on LFG and GPSG currently furnish mputs to unplementanons of the DRS construction procedure. 9nte original idea of a bottom UP: construction W"QCedure for DRSs beginning with LPG f-structure.s as inputs was described in Frey (1985). Reyle (1985), and Klein (1989). For a report of some extensions and an implementation thereof see Wad3. and Asher (1986) and Asher and Wad~ (1989). Many other implementations in the US and in Europe now employ this procedure, e.g., Klem and fohnson (1986) and various systems at IBM Germany, University of Stuttgart, MCC and the University of Texas and the University of Georgia. IGro supply the right arguments in the right argument places we need to appeal to the argument structure of the predicates that is taken from the lexicon. This is especially true in the treatment of scope ambiguities. 111 will think of the semantic content of predicative DRSs extensionally for this simple fragment here and identify them with sets of embedding functions. 12por a discussion of this see Heim (1982). 13There is a well-known difficulty with this division between i!1defmites and other quantificap~nal detenniners. This comes from the way indefi!1ites work witllln t)1e scope of complex conditIons introduced by ev~. The DRT construction predicts that a sentence like Every man who owns a donkey beats it. . . .. implies that ~very man beats every. donkey h~ own~. But many have won:'-e4 abouF thi~ predicnon, and similar predictions that surface wnh detennmers like most. These predictIOns give nse to what ~as been kriown as the "proportion problem." Another difficulty comes in accounting for conditionals like If I have a dime m my pocket, fU put it in the meter. Len Schubert and Jeff Pelletier argue that this sentence does not have the straightforward universal reading. But it is not clear that these examples constitute decisive counterexamples to DRT. In particular we have yet to understand the way lexical constraints and world knowledge as well as various cOmmunicative principles may constrain or eliminate buth conditional readings. 14rhis is an example of a "donkey sentence," a proper treatment of which was a principal motivation

for the development ofDRT. See Kamp (1981), Helffi (1982).

fonnulation of th.e rules for a fragment wi~ the conditional, universal quantifier, and indefinites. The present fonnulanon of the DRS constructlOn procedure reflects the bOttom up translation procedure suggested by Frey (1985) and implemented and extended in Wada and Asher (1986) and Asher and

15r assume that relative clauses like those in (S.b) are quantificational islands, in the sense accepted by syntactitians. Thus, a noun phrase inside a relative clause cannot have scope outside the clause.

2See Wada and Asher (1986) for example. 3sy this tenn I will mean to cover Heim (1982) and the various works of Kamp.

18See May's (1985) QR rule, for instance. 19For details see Wad. and Asher (1986) and Gadbois (1987).

Waaa (1989).

'

IlSpor details see Wada and Asher (1986). 17See Reinhart (1983) for a discussion. 2D-rhe syntactic literature, especially in Chomskian frameworks, is replete with studies of such

CHAP'IERTWO

108

A CRASH COURSE IN DRT

conilgurationaI constraints. An especially classic essay and very good introduction to the subject is Reinhardt (1983). For an indication of how to integrate syntactic constraints in the DRS anaphora

resolution modufe. see Asher and Wada (1989). 21pox (1984. (1987) contains a detailed treatment of the effects of Mann & Thompson's (987) theory of discourse sbUcture on the processing of individual anaphoric pronouns. Dahlgren (1989) contains a swnmary and review of the approaches including an early version of my own. 22These cues include the gt1U11matical po§ition within the sentence of the NP antecedent introducing the discourse referent, the number of times the discourse referent has been identified with other discourse referents anaphorically. and when the discourse referent was introduced into the discourse. See Asher and Wada (1989). Also see the discussion of local discourse structure by Joshi. Grosz. and Weinstein (1986). 23When we expand the syntactic fragment in the next section. it may also have scope over 1'. where IP is the maximal projection of inflection and corresponds to the S category here 24 Some DRT fragments include a disjunction operator. The one in this book does not Disjunction also may take as arguments any pa:ll: of predicative DRSs or partial DRSs1 as in complex determiners like two or three or In noun phrase disjunctions. These nonsentential disjunctions require the use of typeshifting operators. but these cause no more than a mechanical difficulty. See tfie Appendix to cb-apter 10. 25The problem concerning conditions introduced by proper names is familiar from discussions concerrung the scope of descriptions and modal operators in the philosophical literature concerned with Kripke's work on modality and names. For a review see Salmon (1986). 26 Irene Heim (1982) develope,d the familiarity theory of definite within the DR theoretic framework. For further details on how familiarity affects belief contexts, see Asher (1986). 27Barwise and Perry (1978) distinguish between a "value-free" interpretation of a defmite description and a "value-loaded" mterpretation of a definite description. Someth~g like this distinction (tfiough there are important differences) was noted earlier by Donnellan (19bO). The redundancy in (4} is avoided by supposing that the agent processes the definite according to a "referential" strategy that employs at the revel of discourse referents something like the value-loading strategy of interpretation in Barwise and Perry (1983). The princiuaI contribution that the DR-theoretic approach makes to singular terms is to combine in a fruitful way the distinction between nove1/familiar long employed by discourse theorists with more familiar distinctions of scope. The analySis of proper names Within DR-theory offers an illustration of this. 28The idea behind this implementation is due to I. Heim (1982) and her treatment of the familiarity theory of definiteness. 29There are uses of definite descriptions that don't meet either one of the cases I have just sketched. These could be treated as introducing a quantificationaI relation with a Russellian reading. 30A good introduction to some of these issues can be found in Partee (1984). 31 In English there seem to be three largely independent parameters used to encode temporal and ~tual infonnation--tense, as]Je:Ct and modality. See O~ (1989) for an elaboration of ibis claim. Tense is usually encoded morpfiologically on the verb With the past afftx -ed or with the present tense conjugation of verbs. Aspectual information is conveyed by tlie perfective use of the auxiliary have (e.g.• John has eaten) or by the progressive fonn of the vern (Jdhn is crossing the street). "Purely ~~r.?~" modals in English are will. Some English auxiliaries combine these parameters; (or instance. ~: (1989) argues that would is a combinatJ.on of a past tense marker and a modal. 3 Some have argued that "basic" categories like I themselves have a structure. See Pollock (1988) for some intriguing arguments about possible repercussions of a particular structure for the inflection node. 33I will only treat I as introducing one event discourse referent; I will not here go into a detailed examination of the way tense and as~t might work in DRT. For details on tense inrrench see Kamp and Rohrer (1981, forthcoming). Smith (1991) contains a study of aspect 34See for instance the analysis of the present perfect or the pluperfect in Ogihara (1988). which Kamp and Reyle (199+) take over. 35We would have two choices for the translation ofl, Option B or C given graphically below:

0C. .

A.PA. (

~ P(e) )
e

(~) ~

On options B or C, the inflection node would introduce a unctor mat when gIven the appropriate arguments returns the semantic value of the whole sentence. This would be a Tunction from partial DRSs and predicative DRSs and returning a DRS. The trans1ation of I would thus have a different semantic type from either that of a partial DRS or a uredicative DRS. Option B. however, nets us no new semantic flexibility over and aoove option A, the simple translation for I in the text; so given a

109

choice between A and B, we might as well stic.k wi!h the simpler transl~tion in option A.. Option C allows us to have an event discourse referent With WIde scope over the discourse referents mtroduced by the subject NP. but at the cost o~ an additional and useless subDRS that cannot be mterpreted. But see below for some reasons why A IS preferable to C. 36Bras (1990) and Kamp and Reyle (199+) give an overview of the rule~ of ten~ for Frepch and English res~tively. For a discussion of the iiependence of these anaphonc equations on dISCOurse relations, see Eberle (1990. 1991). 37See Lascarides and Asher (1991) for a discussion. . 38For details see Partee (1984), Kamp and Rohrer (forthcoming). For a more recent and computational . . treatment of a large French fragment. see Bras (1990). . 39 A Davidonian treatment of adverbial 'Qhrases as predicates of ~vents fllJ.1S mto some severe ob?tacles, there are adverbs that just don't in any plausible sense tran~late mto predicate~ of events. ConSider for instance the sentence Mary colored It purple. The adverbIal purple IS vefY, difficult to analyze as an event modifier. In the face of such examples•. we !Dust revise our analysIs. Let us call a Cresswell ad'unct any adverbial phrase whose translation IS a VP-operatqr of .the form A.P n(p(e. u]) (see Cresswell 1985). Cresswell and Davidsonian adjuncts are comp~t1ble, m that w~ can countenance a DRS construction procedure th.at use? both f!ansl~tions. W~ might translate adjuncts as C.resswel} ad" uncts by default. Davidsoman adjuncts. 10 which adVerbIal phrases are. treated as ~~3;tes 0 ev~nts appear upon further analysis. This ap'proach wquld aJlows ~s to avol(~ a standar cralnocdlSm gf adverbs as VP operators. The cnticism arises in connec~lO!l WIth the mterpretation of tempo a v~r s and tense Temporal adverbs like yesterday, in two day s tIme as VP ~to~ mu.st take.a scope v~s a vis the scope of the tempor.al operator PAST. This generate~ difficultIe~ !n getting ~e nght interpretation for sentences like John went home yesterdt!y.•.or m two days time, John WIll have fmished the examination (see Dowty (1979»). The poSSibilIty tha~ so~e adverbs are C~essw~U adjuncts avoids this difficulty. Temporal adverbs wquld pe paradigm Instance.s. of Davldsoruan ad uncts and so would not have to take scope positions VIS a VIS other temporal condi~o~s. .. 4~hrases like the leg in the adverbial PP appear tq be ellip~cal fun~tional descnptlOI?~--hldm&. a hidden argument place that is detennined by the lexlc.al m~mg of kick and the preposition. I will . forego here. however. any systematic attempt to deal With this J?OOblem. 41 In reference to the poo,sibilities discussed in footnote 35, optIons A, B or C here makes no difference to DRS construction m this case. . ' 42This is actually way too simple. See for instance Kamp and Rohrer (forthcommg). 'J!le mechanism of temporal reference though can be ignored here since it IS not really gennane to my tOPlC. 43 Again options A. B, C (see footnote 35) for the translation of I seem to make no ~fference here. 44Unless restricted the construction procedure also allows every boy to have w14e scope over the event discourse referent. Under the approach to scope disc,-!ssed .in the prevIo.us c~a~ter, !he contribution of the NP every boy woul4 combine in DRS conversIon With the translation ate entire f. This would result in an unproblematic DRS. . . 450n option C (see footnote 35) for translating I, this reading appears to be Ifl1posslble. So such sentences are an argument in favor of option A. 46 Again this militates against option C for translating 1. . . , 47Van Eyck (1985) gives one treatment of plurals in DRT along generalized quan~er lines. Root (1986) and Roberts (1987) also exploit DRT lor dealing with certain problems of plurality. . 481 will ignore here plural NPs that are. fonn~ from conjuncti9ns of singular NPs. Thes&>m)troduce complicatIOns that are not germane to tillS project For a diSCUSSIOn see Kamp and Reyle (I +. 49For a discussion of these prob~ems see Frey 3;nd Kamp (to appear) and Kamp and Reyle (199+). , . The problem arises very clearly With NP conJunctIon.. 50The one exception to this statement will concern sentences like fewer t?J.an two of Johns 1f;Fdf enjoyed themselves. But at least they had a good time. Some people find tins statement accepta e. f so. it appears that plural discourse referents may refer to atoms. .. . 51 In the DRS below. I don't give a full reconstruction ~f th~ definite NP. JWill assume a thea}:. of definite descriptions in which the uniqueness presupPOsition IS somehow satisfied by the context or . details on this see"Kamp and Reyle (199+). 52collective predicates like dispersed go very badly with NPs with many: *Many students dispersed. See Kamp and Reyle (199+) for a discussion. . ' . 53We need to ~ppeal to .~p'habetic variaI!ts here to aVOid problems With the DRT analogue of vanable clashes. Here IS the deflOltIOn of abstraction: Let Ko be a DRS containing a condition of the fann Z =? .and a conditio!, of the fon:n Kl .Q K 2, where n is a two place operator introduced by a plural or smgular determmer. Then If I; E UK 2 • and it is a presuppqsition or an implicature of ~l n K2 that ~ere '!Ie some I;s such that all tiie conditions in K2 ~ KJ are satisfiea. then if K3 IS an alphabetIc ~anant of K20 L I; K3 denotes a .. . d ced group ~at milY repla~ ? in th~ q:mdi~on Z = ? in anaphqra re~lubqn.. Abstraction IS qll1te a restncted pnnclple; It can only be used m conJuncbon Wlth conditions 101£0 u

110

CHAPTER TWO CRAI'fER THREE

by 4e~rminers: .As ~tated it also rules out ,!b;straction on a condition introduced by a downward ~ntai.ling quantifier lIke no, for suc~ ~ quantifier carries ne!ther the appropriate presup}J9sition or Imrhcature. ~ote also Om! the condition Kl n K2 must be m CooK as weD as the condition Z =?

IriS also predl~ts that certain sums are O?t pos~ible. For a discussion see Kamp and Reyle (199+). It would suffice to adopt a comprehensIOn mom that generalizes the e-path axiom above' 55 \jelE <.E<w,t1> Ve2 E ~W,t2>'" \len E E<w,tn» 3e' E E<w,t n> tel C e' & ... & en'c e' , Asher

(19~6,

ATTITUDES AND ATTITUDE DESCRIPTIONS

1987) defines. an embedding for a DRS directly. But these efforts contain some

errors. Here IS a co~ted ve!"Slon. One must as~ume that DRSs occur always in a particular context. No PRS ever oc:curs ill two different DR-theoretIc contexts, although infinitely many of its alphabetic vanants .occur m all sorts of DR-theoretic contexts. This is actually a byproduct of the DRS construChOn. De~e .(alternativelY):an ~~bedding f ofK in M at <w,t> as follows: (1) k~ a map from mdivldual diScourse referents in UK into D<w,t> if there is no K' such that K:S; (ti) Dom(f).2 UK & f is a function from individual discourse referents in D<w I> if there is a K' such that K:s; K'.

The rest of

the definition proceeds as in the text

UK- > K (UK- ) into •-

•

~6~ne c~ design a pure function application version of conversion, bu.t the conversion routine as e me~ WIll tum out to have advantages. The cost, I conjecture. of replacmg conversion with such an

~~~b~n 'wl:'ould be to make already c
This IS differen~ from the usual cumed de~lhOn of types. because Conversion may take any element of an n-tuple of discourse referents as one of Its arguments.

In the analysis of abstract entities, propositions requires careful consideration. This chapter presents the results of previous research in DRT on attitudes and attitude reports that bears on the analysis of propositions in natural language metaphysics. 1 My analysis of abstract objects in subsequent chapters starts from the view of \ propositions as I have portrayed them in my work on the attitude. This view differs from the usual approaches to propositions in the philosophical literature in several ways. First, it implies that the id~!ltity~9itions of propositions are radically context dependent. Because of this, traditional puzzles about belief like those proposed by Frege ana by Kripke (1979) receive a novel solution. Further, this context sensitivity suggests that the traditional search for one criterion of identity for propositions in terms of 'sets of possible worlds as in Montague (1968) or in terms of alphabetic variants of particular logical forms as in Fodor (1975), or in terms of structured states of affairs as in Barwise and Perry (1983), Soames (1987), and Salmon (1986) is deeply misguided. Second, while the analysis of attitudes and propositions requires postulating that mental states are structured and have contents, we need not postulate propositions as independent, abstract entities themselves. Attitude talk does not commit us to Platonism, contrary to what Bealer (1982) and many others have suggested. Third, DRT integrates and makes precise within a truth conditional framework some of the ideas of conceptual role theories of meaning (Field 1972). DRT thus combines advantages of what are often seen as incompatible approaches. Fourth. the extension of the DRS construction procedure to attitudes introduces concepts and concept discourse referents into the semantics. The discussion of concepts will also figure in my discussion of abstract entities and anaphora. Finally, the work on attitudes introduces machinery to develop a more sophisticated notion of update meaning in the dynamic interpretation of attitude reports than what was presented in chapter two, or in Kamp (1981), Heim (1982), and Groenendijk and Stokhof (1987). It is just this sort of machinery that will be needed in the development of an account of discourse structure. The dynamic theory of attitude interpretation follows a dynamic theory of attitude fOImation.

1. ATTITUDES AND ATTITUDE FORMATION DRT offers a highly contextual theory of attitudes and attitude ascriptions. 2 The context in which attitudes and attitude ascriptions are to be evaluated includes other attitudes of the agent. For a person's attitudes are typically connected in a variety of 111

-.-._._-_.

1If!IT----------------------~--r-··

112

CHAPTER THREE

ATTITUDES AND ATTITUDE DESCRIPTIONS

"

113

%

ways to other mental states, and it is this that accounts fundamentally for the contextual nature of attitudes, attitude ascriptions, and ultimately propositions. DRT's account of attitudes arises out of a certain view of how attitudes are fonned in response to verbal information. Consider (I) and its DRS (KI): (I)

Judge Gisell sentenced Colonel North to jail. (KI) D,V,n,e,x

named(v, 'Gisell') named(u, 'Colonel North') e
Objects, but may also involve relations of evidence and deduction. DDRSs may have external anchors. (Kl) is an example. (KI)

e', VI, UI, Xl named(v I, 'Gisell') KZ: named(u I, 'Colonel North') KI:judge(vI) marine(u I) e'-presides-over(v j, XI) of(ul, XI) trial(x I)

beliefCKI) beliefCKz)

e- sentence(v, u)

tore, x) jail(x) . {, J A simple thesis concerning belief formation is that in accepting (I), the agent forms a belief characterized by the DRS for (I). According to DRT, the same structures that represent the infonnation that a recipient recovers from a discourse also serve to characterize the subject matter of an agent's attitudes, or attitude Objects. A crucial aspect of acceptance is how the new belief is interpreted relative to, and coordinated with, antecedently acquired beliefs about the same subject matter. If our beliefs are false, the characters and objects they are about may not exist. And since false beliefs have the same phenomenological character as true beliefs,3 the individuals and objects constitutive of attitude Objects must be conceptual, not real. 4 A belief about familiar subject matter and familiar conceptual individuals, when incorporated into the agent's antecedent beliefs, shares with them one or more common conceptual individuals as constituents. From the perspective of DRT, this way of thinking about attitudes invites us to identify discourse referents with conceptual individuals. This suggestion implies that DRSs that characterize beliefs about the same conceptual individual must share at least one discourse referent. For example. assume that the agent who accepts (1) has various beliefs about Colonel North and the Iran-Contra investigation (e.g., North shredded documents, North lied to Congress about the arms for hostages deal with Iran), but that not among them is the belief that North is sentenced to jail. Suppose also that the agent knows that Judge Gisell presided over North's trial. Then in interpreting this new infonnation, the new belief must have the same conceptual individual constituents as the old beliefs about North and Gisell. We need some way of talking about collections of attitudes or portions of an agent's total cognitive state. I will do this by means of a delineated DRS (DDRS)--a structure composed of three parts. These are: (i) a set of DRSs or delineated DRSs (each one characterizing some Object of the agent's attitudes), (ii) a set of discourse referents ~ommon to these DRSs (the delineated DRS's universe), and (iii) a set of conditions on those DRSs.s These conditions deterurine the type of attitude of attitude

(KI) represents some of our hypothetical agent's beliefs about North. (KI) depicts graphically the three components of a delineated DRS. The top portion is the universe of the delineated DRS. The two portions of the delineated DRS in (KI), labeled K, and K" comprise the second part consisting of component DRSs. The third part, lowest in the diagram, states that K, and K, are both beliefs. (KI) also has external anchors for Gisell and North. Suppose that an agent with a portion of a delineated DRS such as that in (KI) accepts (I). This should lead first to an incorporation of the DRS for (1) with the material in (KI) to form a new delineated DRS (K1.a). The discourse referents declared in the universe of the DRS for (1) will now be declared in the universe of (Kl.a). In accepting (I), for example, the agent comes to believe that there is an event of the sentencing; the discourse referent for the event will be declared in the universe of (K1.a) and will represent the existential commitment. A complication arises in treating the conditions introduced by definite noun phrases (see section 2.5). The conditions introduced by definites should typically be deleted from a DRS as it is transformed into an attitude Object because they do not contribute to the list of conditions in DRS describing the subject matter of a belief but rather serve to make the right internal connections between the new belief and the background beliefs. An acceptance of (I), then, should lead to a delineated DRS In which the new belief shares discourse referents with the two portions in (KI). (K I a) vt. e', Ut. Xt. e, X2, v, U

named(v" 'Gisell') K . named(u" 'Ollie North') K,: e - sentence(v, u) ,. marine(u,) K , : judge(vI) tore, x,) e'-presides-over(v 1. Xl) jail(x,) of(u" x,) U=Ul trial(X,) v =Vl beliefCK,) {
beliefCK,)

>, J

beliefCK,) {, J

ATlTIUDES AND ATTITUDE DESCRIPTIONS

The DDRS (K1.a) represents the relevant portion of the agent's mental state that is affected by the acceptance of the new information in (I). The disconrse referents representing North and Gisell in the DRS for (1) have been identified with the ones that represent North and Gisell in the agent's delineated DRS in (KI). Note that not all the conditions introduced by the definite NPs are deleted. These conditions correlate a discourse referent with the linguistic item and are needed when we look for the right discourse referent to identify in establishing internal connections for a new belief. But these conditions remain in the delineated DRS directly attached only to the disconrse referent introduced by the agent's first encounter with the defmite NP. Belief formation is thus a function, according to DRT, from delineated DRSs to delineated DRSs. I will call this fUl:!on updatjpg. A precise statement of rules for updating of delineated DRSs is tricky. We disconrse referent identification 10 cannot a1 ways correctly maintain that two discourse referents introduced by occurrences of the same name or definite description, for instance, stand proxy for the same individual; different people may have the same name. Thus, the rule for identifying discourse referents so introduced must be a default rule, with a proviso that such an identification should be made only where the agent has no compelling reason to doubt that the same person is being referred to. The same goes for the assumption that discourse referents introduced by different Dames stand proxy for different individuals. Updating is the key to the story about content on the DR-theoretic contextual theory of belief. The content of a person's belief should be understood in terms of how the belief changes the antecedently given cognitive state of the agent. The updating of the delineated DRS depicting the relevant portion of the agent's cognitive state shows how accepting new infonnation generates a new belief, and how the new belief changes the agent's cognitive state. By using delineated DRSs and the mechanisms of DRT, we can represent and analyze the connections between the new belief, represented by K 3 , and other portions of the cognitive state. These connections are built up in a systematic way. There are two sorts of connections that a delineated DRS like (Kl.a) exhibits. The fIrst sort consists of "external" connections between attitudes in the cognitive state and objects in the agent's environment. These are represented by the external anchor of the delineated DRS, which pairs discourse referents that are constituents of attitude Objects with objects that exist in the domain of the full model. The second sort consists of "internal" connections between attitudes in the cognitive state. These occur when different attitude Objects are about the same conceptual individual" Disconrse referents in delineated DRSs serve to link to beliefs, or even attifudes ofUifferent types, together; such linked attitudes are be about the-same conceptual individual. I call such links for a given attitude Object intf'l'JJ!l anchors. These two types of connections are independent and potentially incompatibleJ The incompatibilities are of interest, for they are central to many puzzles about belief-for instance, Kripke's (1979) famous puzzle concerning Pierre. 8 Kripke's puzzle is about a Frenchman, Pierre, who as a child grows up looking at picture books of

taken

liS

London and forms the belief that London is pretty. Suddenly, he is whisked away to London and ends up in a seedy part of the city where he is confined for the rest of his days. He forms the belief that London is ugly. The process of belief formation in both cases proceeds nonnally. But because Pierre fails to make the connection between the city named 'Londres' of his childhood pictnrebooks and his current place of residence, he ends up associating two different discourse referents with London-one for the city he knew as a French child from pictnre books and one for the London slum that he currently lives in. While both disconrse referents are externally anchored to London, the sets of the property ascriptions Pierre ends up associating with the two discourse referents are incompatible with each other. Each set of associated conditions, however, is by itself perfectly consistent. Thus, although Pierre does have a set of beliefs about London that cannot possibly ever be all jointly true, no amount of introspection will enable him to discover his difficulty. A DRT theory of belief has no trouble describing Pierre's predicament. Neither would a number of representational theories of belief. But DRT diverges from other theories in that what an agent believes must be interpreted relative to background mental states. This leads to a sophisticated analysis and explanation of Kripke's puzzle. Other representational theories merely postulate a difference in belief without explaining how Pierre could have come to such a predicament.9 In answer to Kripke's question, "What does Pierre believe?" DRT answers that what Pierre believes can be made plain only when one looks at the whole of the delineated DRS depicting the relevant portion of his total cognitive state. An agent's beliefs and other attitudes are thus not a set of discrete and independent propositional atoms but rather a complex of interrelated structures built up through a complicated process of belief fonnation and revision. This is an extension of the DRT approach to sentence interpretation as a function from contexts to contexts. The view also has important consequences for attitude ascription interpretation. One could also interpret Kripke's question about Pierre to be "Which attitude reports in English are true of Pierre?" We will see how DRT answers this question in the next section.

2. ATTITUDES, OPERATORS, AND PREDICATES

An interpreter of a belief report must perform a complex task. First, he must process the belief report--say it is of the form K believes that p. Second, he must integrate the result with what he antecedently believes. Third, he must integrate the DRS constructed from the clause p into his representation of what he believes the agent already believes. So in dealing with a recipient's processing of an attitude report, we must countenance at least two delineated DRSs--the delineated DRS depicting the total cognitive state of the recipient, and the delineated DRS the recipient has for the agent. These delineated DRSs are constructed and updated with material from the belief report by means of three stages of processing (stages I, II, III below). I will build up this complex structure step by step. First, let us look at the structure of a basic attitude report. Suppose a speaker S tells a recipient R:

r-----------------~.-~-~

116 (2)

CHAPTER THREE Nicholas believes that the meltdown at Chemobyl has ended.

The syntax of such a belief report involves a verb whose complement is an S'. This S' introduces a subDRS characterizing the Object of a belief of the agent, a component of the agent's total cognitive state, for which I will introduce a discourse referent of a special type. The S' introduces a partial DRS that resembles the partial DRS introduced by a proper name. That is not so surprising; that clauses function similarly to names, because they are names for propositions! A straightforward approach to the translation of a that clause is to build it compositionally from the translations of the complementizer and the embedded clause. That yields a partial DRS with an argument both for the semantic contribution of the embedded clause and for the predicative DRS that results from the translation of the attitude verb--viz.,

Notice that the partial DRS above has two different types of variables--the ordinary predicative DRS variable for the translation of the verb and a different type of variable for the contribution of the embedded clause, which will serve as an argument to the predicative DRS. The embedded clause should in extensional contexts give rise to a DRS, which is a trivial instance of a predicative DRS. On the other hand, it is customary in many theories of attitudes to distinguish between the ordinary contribution of a clause in extensional contexts and its contribution in intensional contexts. I follow this custom here. This leads to a distinction between predicates of DRSs and DRS operators. DRS operators are familiar from the previous chapter. =* is a DRS operator and its semantics are defined relative to the proper embeddings of the DRSs that are its ~guments. Another such operator is --, or the modal operator D. The important difference between DRS operators and predicates of DRSs is with respect to their semanti:s. The semantics for an operator like negation is given in terms of the proper embeddings of the DRS that is its argument. A condition of the form -,K is satisfied relative to an embedding function f and indices w, t just in case there is no extension g of f such that g properly embeds K at <w, 1>. A condition of the form OK is satisfied relative to f, w, t just in case for all possible worlds w' there is an extension g of f such that g properly embeds K at w', t. Predicates of DRSs, on the other hand, take DRSs as arguments referentially. The descriptive conditions introduced by attitude verbs are predicates of DRSs.1 o Their satisfaction conditions will exploit the sttnctural properties of DR-theoretic objects, as well as the functions these objects specIfy under the correctness definition in the model theory. Thus, over and above the usual predicative DRS variables, whose interpretation ranges over predicative DRS denotations, we need variables whose interpretation will range over predicative DRSs themselves. TEe DR-.!!>eor~li£'y~g.!J.!];UheJll1'.elves are ..E3;!heoretic count~!l?..'I!!'UQJ're.gean"nollons..of.rere.ence-and.~~nse. DR'Ss;-ffiUs, can serve as oOfeCts of attitude verbs and hence help to chara~t~rize at least one notion of

ATTITUDES AND ATTITUDE DESCRIPTIONS

117

proposition. The distinction between predicates of DRSs and DRS operators is reflected in the translation of the complementizer above with the introduction of a new variable K of a type that ranges over DR-theoretic structures. The notion of a predicate of DRSs complicates the basic and the extended model theory of chapter two. First, DR-theoretic structures themselves must now be counted as elements of the models. There is also a question about the logical type of these structures; are they first order or second order objects? I will take variables ranging over DRSs as entities to be a kind of individual, and so the definition of partial DRSs and predicative DRSs of the previous chapter will remain intact But the decisions here are delicate; one could have done things differently. Further, as Thomason (l980b) observed, the decision to have attitude predicates take sttnctured objects like DRSs leads to paradoxes similar to the Liar when attitudes are taken to be closed under nontrivial modal principles. Similar assumptions will become unavoidable after expanding the DRT fragment in the next few chapters. I will discuss these issues in chapter 10. Finally, the semantic contributions of DR-theoretic structures in general must not only be phrased in terms of constraints on embedding functions but must also refer to some aspect of the structure of K itself. A noteworthy feature of the partial DRS introduced by the complementizer is that no discourse referents for the propositional argument are introduced. It will tum out that proposition type discourse referents may occupy the same argument position in the translation of an attitude verb as the subDRS contributed by an embedded clause. But there is no need to introduce discourse referents when translating the that clause. A subDRS as an argument to a predicate of DRSs is rather like a constant or a complex term if it involves discourse referents that are not declared in its universe; the model theoretic interpretation of predicates of DRSs implies that a subDRS as .an ~ument denotes a designated object jn the model. Since a subDRS is not a diS ..c..0.. u..rse ref.erent, .it.c..QU.stants-for--abstract is not assigned a value under.an. y denote e.m.b.ed.di.n.g.fu.n . c•. tl.·.O . n. 1;lJJU,J~ r ((n') <: c~~s~~~~t~gJh.~TI-:LaS. .objects, they.. the same object in the ~J(' ~ mo~el_.r.e.garill"s.,-pL.theDRSjnwhichthe)'.were."eclared and what embeddin function was being considered We don't need to introduc~'discourse;-referents for thatclaUStfrtofsemlffiucreasoiis~ Further, such discourse referents are not needed to account for scope ambiguities or quantificational dependencies; subDRSs do not have any. Finally, subDRSs are already recognizable constituents of DRSs, should we wish to identify discourse referents with them anaphorically. Thus, discourse referents introduced by that clauses appear otiose. Because I will allow quantification over the DRS arguments of attitudinal relations, we must also countenance discourse referents which will range over DRSs. I will call these discourse referents proposition discourse referents. The letters 'p', 'q', 'r', etc., stand for proposition discourse referents. These discourse referents are of a different type from either event or individual discourse referents. Where p is a proposition discourse referent, K a DRS, and a an attitude verb, then, a(x, p), a(x, K), are conditions. With these preliminaries out of the way, we can write down a first attempt at the processing of (2). By combining the DRS from the embedded S together with the '- -

ATTIWDES AND ATTIWDE DESCRIPTIONS

CHAPTER THREE

118

partial DRS for the complementizer and proceeding as in chapter 2, (K2.a) results.

(K2.a)

x,s named(x,'Nicholas') s-believe(x, e3. v, e4 meltdown(e3) named(v, 'Chernobyl')

e3 atv e4-end(e3) e4<now {<x, NIcholas>, }

119

cognitive state, however. To this end, I will adopt a representation of internal anchors sitnilar to the quasi-external anchors of Asher (1987). These function like external anchors with respect to the interpretation of the discourse referents declared in the nested delineated DRS, but their values are determined by the assignments to the discourse referents in the superordinate delineated DRS. Internal anchors are part of the cognitive state of the recipient and are represented in the diagram below by pairs of the fonn «(t" I3».13 Now since we must represent between both the agent's and the recipient's cognitive states and we must distinguish between beliefs of the agent and beliefs of the interpreter; we will label beliefs within DDRSs with conditions of the form believe(x, K), which tell us who the believer is. The interpreter refers to himself with the discourse referent i. (K2 b)

The first stage of processing of (2) yields the DRS above. The condition, believe(x, K), where K is a DRS, should say something like this: K describes a portion of the tolal cognitive state of x and this portion is a belief. But then this first stage of processing (stage I) is not by itself an adequate representation of what Nicholas believes. It fails to capture any of the connections that this belief has with other components of the agent's cognitive state which S was trying to convey,I1

S1> S2, s'o. s'" S'2' s, ell Vl> x" Ul> X,K

e2. V2, U2

K:=

3. INTERPRETING ATTIWDE ASCRIPTIONS Let us now fill in the interpretation of (2). Suppose that the agent Nicholas has certain background beliefs about Chernobyl--namely, that it is in Ukraine and it was a

dangerous accident--which the recipient R knows about and represents in his depiction of the agent's cognitive state. Let's suppose the speaker S believes that R has this information and is trying to convey Nicholas's belief that the meltdown has ended. Note that on this background story, R and the agent Nicholas are both familiar with the denotations of the dermite noun phrases that occur in the complement of belief report in (2). Moreover, the conceptual object that stands proxy for Chernobyl for R is an object that R believes Nicholas is familiar with. At least R has every reason to suppose that this is so, and so R's delineated DRS for Nicholas's cognitive state should make this evident. A commonality of reference between R and Nicholas should be indicated. 12 Establishing and indicating a commonality of reference is the main task of the second stage of interpretation of an attitude report; here the recipient integrates the new information with what he already believes about the subject matter. In the second stage of processing of (2), R integrates the new information with what he knows about Chernobyl and the surrounding events. Key to Stage II is the processing of definite NPs. The processing of the dermite NPs in the report forces R first to coordinate the interpretation of the discourse referents they introduce with the appropriate discourse referents standing proxy for the same entities in his total cognitive state. What does this coordination mean over and above a constraint on the embedding functions? Presumably we don't want to impute a necessary awareness of such internal anchors to the agent. We want these links to be part of the recipient's

v, inu, Ukraine(u,) named(vJ, 'Chemobyl) (other conditions about Chemobyl)

named(x" 'Nicholas') fother conditions about Nicholas) cognitive state (x I.K )

K,

K2

V2 in U2 e2 atv2 meltdown(e2) Ukraine(u2), named(v2, Chemobyl) accident(e2) dangerous(e2) K,

K\' s,-believe(x" K,')

I

I s-believe (x , K:

s2-believe(x" K 2')

{«elt e2»' «VI, V2»} s'o-believe(i, K 1)

e, atv, meltdown(e, ) accident(e,) dangerous(e ,)

s' ,-believe(i, K 2)

K\

e3. v, e' ) meltdown(e3) named(v, 'Chemobyl') e3 at v e' end(e,) e'<now

{«e3,e,», «v, v,»} s'2-believe(i, K 3 )

s' 2 -believe(i, K')

{<Xlo NIcholas>, , , } For reasons of space, I have been forced to put the labels for the various components of the main delineated DRS wherever I could. One can delete some of the information appropriate to constructing internal anchors at Stage II once it has served its purpose--viz. the condition named (x, 'Nicholas'). I cannot yet delete all such information, however. For although the connections between the new infonnation and R's background beliefs have been made, the belief being reported must, to receive a proper evaluation, be integrated with the agent's background beliefs of which the recipient is aware. This happens at stage III of the processing. Stage III, depicted in (K2.c) below, integrates the information contained within the

120

CHAPTER lliREE

A ITITUDES AND AITITUDE DESCRIPTIONS

complement of the belief report with the recipient's representation of the agent's total

total cognitive state. The belief report (2) is true in the context in which it is utterred if and only if the interpreter in the context is able to construct by means of the rules a faithful representation of the agent's cognitive state. The truth conditions of a belief report thus depend upon the interpreter's beliefs about the agent's total cognitive state. The truth conditions for a belief report must be stated relative to a contextually specified delineated DRS K representing the recipient's information. This is DRT's distinctive, context-sensitive approach to attitude reports. Stating the truth conditions for belief reports with some precision requires the following notions. Let us suppose for the minute that content is defined, as is traditional, via the set of indices or world-time pairs; thus, the content of a DRS K is the set of world-time pairs at which K has a proper embedding. A DRS K is at least as detenninate as a DRS K' just in case the content of K is a subset of the content of K'. I will say that a beliefreport of the form a believes that q> is true at w relative to a given context that includes K just in case the processing of the report yields an augmented delineated DRS K' which we may write as K+ K and the component of K + Kip that is derived from the complement of the report (Kip) approximates the content and structure of some component K* of a's total cognitive state K at w.

cognitive state. When definite NPs occur in then- belief contexts, a presupposition of familiarity extends to the agent in the following sense. In using a defInite NP within a belief context, the speaker is implying that the agent has some familiarity with what R and S take to be the NP's denotation. Names and definites of all kinds presuppose a definite element built into the belief context. Of course the agent may be taken to be.

wrong about the familiarity conditions for the object of the conversation. So the recipient of a report containing a definite NP

a should, according to the principle of

definite reference identification, identify the discourse referent introduced by ex with some discourse referent already declared in the universe of the delineated DRS representing what the recipient already knows about the agent's beliefs. These already declared discourse referents serve to connect the new belief to antecedent beliefs.I4 The same goes for discourse referents introduced by noun phrases with wide scope over the belief context but which playa role in the conditions of the subDRS describing the belief. SJ, SZ. S3. s'o, s'"

s'z.

elo

VI>

Xl, Ul> X,K

narned(x" 'Nicholas') other conditions aoout Nicholas) cognitive state (Xl> K)

f

ez,

K:=

v, inUI Ukraine(u\) named(v" Chemobyl') (other conditions about Chemobyl)

vz, uz, e', e3

ez at Vz Vz in Uz meltdown(e,) Ukraine(u,l named(v" Chemobyl') aCcident(ee dangerous ez)

Ki

e3 =e, e' end(e,) e'<now e3 atv 2 v 2 = v,

K,

K, K' srbelieve(xl, K,') sz-believe(xl> K z') s3-be1ieve(x" K') {«v" vz». «el, ez». <
K\

el atvl meltdown(e\) aCCident(e~

dangerous el)

K,

s'l-believe(i, K z)

s'z-believe(i, K3) (<Xi> NIcholas>, Chernobyl>, ,
(i) (ti)

121

the content of K* is at least as deterntinate as that of K,p, there is a function f from K+ Kip into the universe of K such that for any discourse referent x (of any type) in Kip' (a) the content of the DRS containing just those conditions of K* involving f(x) as an argument is at least as detenninate as the content of the DRS containing just those conditions of Kip involving x as an argument; (b) if x occurs as an argument of some other portion K'I' of K + Kip' f(x) occurs as an argument to conditions in some other portion K** of K such that the content of K** is at least as detenninate as that of K",.

To go back to our example (2), let us suppose that the relevant portion of the agent's cognitive state is as depicted in the delineated DRS K included within the component K\ of (K2.c), and suppose that we are interpreting (2). Then the role of K* in the definition of the satisfaction conditions is played by the rightmost component of K. On this assumption for the internally anchored discourse referent e3, K z ' would play the role of K** and for V2 K\' would play the role ofK**. The adequacy of the last part of the satisfaction definition for belief reports depends upon what portions exist or may be assumed to exist in delineated DRSs. One way of carving out portions is by looking at the discourse referent involved. Distinguishable conceptual individuals are those whose sets of property ascriptions are distinct. I will assume that for two discourse referents representing distinguishable conceptual individuals in a given delineated DRS K, there will be some portion of K in which one discourse referent occurs without the other, IS In view of parts (ii.a-b) of the satisfaction definition for belief reports, any two distinguishable conceptual individuals x, y occurring within a constructed belief state

122

CHAPTER TIlREE

ATIITUDES AND ATTITUDE DESCRIPTIONS

K must be mapped onto distinct discourse referents in the agent's real DDRS, unless K contains the equation x = y. This still leaves open the question of what happens to the mapping n between the constmcted cognitive state representation K and the real cognitive state K in cases where the two conceptual individuals, though distinct, are qualitatively indistinguishable. Suppose that this holds for some agent f(u) in a world w in a model 'M. We can show that n still will be I-Ion those equivalence classes. [x] of discourse referents in K, where [x] = {y E UK: 'M FK, w, f Kbelieve(u, x =

defended,l7 For in this example, the putative belief that you do not have enough money to pay for your meal plays no role whatever in your behavior at the restaurant You only become aware of your unfortunate situation when you get the check! Such problems arise because of the traditional notion of content underlying the satisfaction definition above, which identifies content with a set of possible worlds. This notion of content is unsatisfactory. A satisfactory notion of content for cognitive states and their descriptions takes these contents to have a logical structure. This logical stmcture should reflect the intuitive, logical stmcture of our beliefs. Sets of possible worlds do not reflect the logical stmcture of our beliefs and as such they fail to give us the appropriate notion of content On the other hand, contents are not simply bits of syntax--sentences in the langnage of thought either. As the possible worlds notion of content suggests, contents are possibly partial views of the way the world might be. We must combine both this notion of logical structure and the extralinguistic view of content. One notion of structured content and one solution to the problem of logical equivalence extends the structure of cognitive states already discussed to the conceptual level. This is the approach I have pursued here and elsewhere.1 8 I introduce discourse referents for concepts. I then exploit their internal and external connections as I did those of individual discourse referents in the satisfaction definition for attitude conditions. To motivate the introduction of concept discourse referents, consider a conceptual analogne to Pierre's predicament. Imagine that Peter, a New York City kid, has read several books about the English countryside prior to going there for a bicycle tour. In descriptions of the moors, he has read i about a certain kind of bush, gorse, with pretty yellow flowers. He forms a belief that gorse is pretty. Now suppose that Peter does not get to England until October (when I suppose that gorse is not in bloom). While bicycling along a slippery road, he falls into a thorny, undistinguished looking bush and gets scratched rather badly. He forms the belief that the sort of bush he has just fallen into has about as much merit as poison ivy. Explaining his misfortune to a doctor, he describes the green spiky bush and asks what it is. The doctor replies by saying, Db that's furze that you fell into. Furze and gorse are identical types of bushes, but nothing in Peter's cognitive state would lead him to suspect this. The parallels between Peter and Pierre suggest an analysis of Peter's doxastic situation along the lines of that of Pierre's. Peter does not identify the two concepts of furze and gorse, just as Pierre fails to identify the place he lives in with the city he read about as a child. In fact Peter believes,

y)J.'6

A special case of the internal connections between attitude Objects arises with

quantifications into attitude contexts. Quantifying in occurs when a quantifier outside the scope of a belief context binds a valiable within the belief context. The fact that an attitude predicate takes a DRS itself as an argnment leads naturally to questions about quantifying into an attitude context. In DRT, quantifying in is reflected in a DRS Kin which an attitude ascription taking a DRS K' as an argument occurs and a discourse referent x is declared in UK that also occurs within a condition of K'. The contribution to the interpretation of K' of the noun phrase that introduces x is purely structural; it contributes a discourse referent and some familiarity presuppositions to the content of the belief Object being described. These familiarity conditions will force x to have an internal connection to some antecedently given y in the representation of the agent's cognitive state.

4. CONCEPTS AND ATTITUDES Despite the machinery so far, the theory of attitudes and attitude reports is still seriously incomplete. For while the theory has a representational flavor, it fails to block the dubious inferences based on substitution of logical equivalents within belief contexts. This substitution of logical equivalents within attitude contexts is known as the puzzle of logical equivalence. But it is precisely this ability to block such inferences that makes representational theories of belief attractive in the first place! To see just how dubious such inferences are, suppose that you are at a restaurant in Austin, Texas, and about to order some Mexican food. Suppose also that you believe that you have $5.00 in your pocket and so you order the fajitas and an iced tea. You order because you have the belief that you have enough money to pay for the meal. You also believe, having just looked at the menu, that the fajitas cost $4.00, an iced tea $.60, and that there's a 10% sales tax on the total. But your joint belief in all these things together with your belief that the total price of your meal is the sum of the prices of the individual items ordered plus 10% of the total is logically equivalent to the belief that you do not have enough money to pay for the meal. It seems to me disastrous for a theory of belief to predict that if you have the one joint belief, you have the other. This prediction is obviously bad if the model of belief is one which counts as beliefs those attitude Objects of which the agent is consciously aware. But the prediction, at least in this particular case, is equally bad, I believe, if beliefs are constmed functionally as dispositions to behavior, a view that Stalnaker has forcefully

(3)

123

gorse is not furze.

But this failure to identify the two concepts is not the fault of Peter's logical powers; he lacks certain empirical and linguistic information. Let's now take a closer look at properties and concept discourse referents. I will identify a property with an intension, a function from worlds to sets of individuals. Natural kind terms, common nouns, and perhaps also verbs and at least some adjectives function similarly to proper names; they introduce concept discourse

CHAPTER THREE

ATTITUDES AND ATTITUDE DESCRIPTIONS

referents when processed and they generate similar familiarity presuppositions, 19 The discourse referents they introduce are concept discourse referents, discourse referents that stand proxy for properties. Like individual discourse referents, concept discourse referents may be constituents in more than one attitude Object. Concept discourse referents also typically enter into relations with linguistic items; where a is a general term and c the concept it evokes in an agent, 'named (c, a)' might be one sort of condition (presumably there would be others) applying to the concept discourse referent in the agent's total cognitive state. Finally, some concept discourse referents, viz., those introduced by natural kind terms, may have their content detennined by relations external to the agent's cognitive states; that is, concept discourse referents may be elements of an external anchor.2o On the other hand, concept discourse referents apply to individual discourse referents. just as predicates are applied in ordinary DRT to individual discourse referents, With concept discourse referents, it is easy to describe Peter's predicament. For Peter as for Pierre, internal and external connections are in conflict, as is witnessed by the delineated DRS (K3), Notice that the logical functors and relations like named are not replaced by concept discourse referents; the innate conceptual apparatus of the cognitive agent includes the logical operators and the relation that ties linguistic expressions to concepts.

processing of the report yields an augmented delineated DRS K', Call the component of K' that is derived from q> K
124

K3

Clo Cz. C3, X,

nm(ch 'gorse') CI(X) c,(x) KI believe (K 1)

Y

nm(c" 'furze,) c,(y) ~ c,(y) K, belief (K 2 )

K,

nm(c" 'pretty')

K'

Cl '¢:. Cz

belief (K3)

belief (i, K')

{, }21 Given the information available to him, Peter rightly distinguishes between CI and c, or the concepts of gorse and furze; one concept applies to an object that is pretty, while the other applies to an object that is not pretty, To get an adequate account of Peter's predicament, the theory of belief reports must be sensitive to the internal connections and, more generally. the internal role of the concepts constitutive of the agent's belief Object. Crucial to understanding Peter's predicament in (K3) are the arguments x and y of the concept discourse referents, as well as the indirect connections x and y provide to other concept discourse referents of which they are arguments. The internal role of a concept discourse referent includes a specification of which conceptual objects fall under the concept--i.e., which discourse referents the concept discourse referent is applied to. To capture these requirements, I extend the definition of the function I defined on individual discourse referents that I used earlier to determine the truth conditions of belief reports to concept discourse referents, Suppose that the report a believes that

i

I'

(I)

(ll)

125

(as before) the content ofKI is at least as determinate as that ofK,p, there is a function f from the universe of K' into the universe of K.22 such that for any discourse referent x (of any type) in K,p, (a) the content of the DRS containing justthose conditions of Kl involving f(x) as an argument is at least as detenninate as the content of the DRS containing just those conditions of K

.. " u, as arguments in K~ then I(x) has JUl> .. " JU, as arguments in K 1 and (iii) lis a restricted isomorphic embedding (see appendix chapter 10) ofK~ in Kl> defined recursively on the logical structure ofK~,

The final characterization of an attitude Object is thus the structural description of a DRS as a set of discourse referents and a set of conditions paired together with its traditional content. At least some of the conditions are structured and built up out of concept discourse referents, conditions on those discourse referents, and logical operators (or other predicates that are taken to be part of the logical structure of the DRS),23 The structure of the DRS is essential in characterizing beliefs; for it is the connections that discourse referents of the DRS have to the environment and to other DRSs characterizing portions of the agent's cognitive state that determine the belief Object's content. 24 The definition above takes account of this structure with the notion of a restricted isomorphic embedding defined in the Appendix to chapter 10, This more complex truth definition takes into account the structure of conditions needed to address Peter's predicament as well as the puzzle of logical equivalence, Suppose now that Peter believes the inanity that the kind furze is self-identical or that furze is furze but that otherwise his mental state is as depicted in (K3), Why does Peter not believe that gorse is furze on my view? To make the report true, we would have to use the inane belief that furze is furze as our designated portion of his total cognitive state, We would then have to suppose a function Ii from the DDRS constructed from the report to the one characterizing the agent's cognitive state in the model such that the concept discourse referents c 1 and c 2 generated by the concept words furze and gorse in the report were mapped onto a single concept discourse referent, the one associated with the predicate furze in the real representation (call this c'), But if li(cI) = Ii(c,) = c', then given what we know about his encounters with

CHAPlER THREE

ATITIUDES AND ATTITUDE DESCRIPTIONS

gorse and furze, Ii cannot satisfy clauses ILb and ILc.ii; he does not associate the same properties with Cl and C2 and he does not attribute them to the same objects in the belief report. Substitution of logical equivalents will fail in general because of

clause II.c.in.

Truth predicates and attitudinal predicates also have similar logical complexities, to be discussed in chapter 10. So it seems that they should both be analyzed as predicates. Following Kratzer's (1981) analysis, one might view modals in DRT as somewhat intermediate between DDRS independent predicates like truth and the attitudinal

This truth definition provides the general framework for the analysis of all attitude verbs in DRT. The differences between verbs consist in how the structure and content of the target attitude Object relates to the structure and content of the DRS representing the attitude Object that is constructed from the report. Clause lI.c.iii, for

force and cause--might be DDRS independent but intensional. It would be a relatively easy exercise to adapt modal analyses of causatives within the DRT framework, but in these areas DRT seems to offer few new insights.

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127

predicates. Still other clausally complemented verbs --in particular causatives like

instance, may be quite complicated when attitudes other than belief are countenanced.

What is distinctive about DRT's view of attitudes and attitude reports and how this

Briefly, attitudes are grouped into a number of types. Certain attitudes, which I'll call projective attitudes, introduce operators on the DRSs that describe a portion of the mental state. These operators affect both the content of the attitude Object described and the homomorphic embedding conditions for the function f in clause lLc.iii.

affects the general analysis of propositions is that the semantics of attitude reports, and the attitudes themselves, are dependent upon the way the attitude being reported

Examples of projective attitudes are wanting or desiring, questioning, and free-choice permission; all of these "project" some reaction or intention on the part of the agent. The principal difference in the rules of DRS construction for projective attitude

reports occurs at stage I of interpretation. A report like

interacts with other elements of the interpreter's representation of the agent's cognitive s,tate. Thus, attitude reports must always be evaluated relative to a delineated DRS. In

situations where the interpreter has a hopelessly inaccurate representation of the agent's total cognitive state, many reports that might otherwise be adequate will turn out to give the wrong picture. So, belief reports may lead to the right picture in some circumstances (for some audiences) but not in others. In some cases, the delineated DRS supplied is radically defective to the extent that no report about a certain mental

(4)

John wonders whether Mary got the contract

state of the agent's would lead the recipient to construct a correct approximation of the "targeted" mental state. In such cases there is nothing the speaker can do except to try

would yield the following DRS for a stage I analysis:

to rebuild the relevant portions of the recipient'S delineated DRS so as to ensure a correct interpretation. 26 Thus, it is difficult (though perhaps not impossible) to

classify belief reports as true or false simpliciter, belief reports are true or false relative to a context that specifies what the recipient knows about the agent's cognitive state. The DR-theoretic approach is quite different from several competitors. There are

x, p, e named(x, 'John')

e-wonders(x, Q

e, v, w named(v, 'Mary') the contract(w) e-get(v,w)

e<now

{<x, John>, }

two sorts. One is Cresswell's (1985) structured meanings view, also proposed by Lewis (1972), on which a proposition (and an attitude Object) is to be modeled as or

identified with a sequence of intensions--one corresponding roughly to the meaning of each constituent of the sentence. Cresswell thus shares the DRT view that the

characterization of an attitude Object must both take account of its structure as well as its content traditionally construed. Cresswell's approach distinguishes between logically equivalent propositions like those expressed by the sentences in (6):

The operator Q is introduced by the WH element. A full interpretation of (15) requires as before the two additional levels of processing. I omit the details. 25 At the other end of the spectrum of complexity lie non-attitudinal propositional predicates like the modals and true. While the proper interpretation of attitude

predicates depends on a representation of the agent's total cognitive state, clearly a predicate like true does not depend on any such representations; ideally it depends only on what happens at the world of evaluation. Truth is DDRS independent and extensional. Nevertheless, treating true as a predicate of DRSs makes it easy to analyze sentences like (5)

Everything Jom believes is true.

(6.a) (6.b)

The distance between the two lakes is 12 miles. The distance between the two lakes is 7 + 5 miles.

This is so because the structured intension for 12 miles differs from that for 7+5 miles. There are alternatives to Cresswell's that also differ from DRT--theories of first order propositions like Bealer (1982) or Chierchia and Turner (1988), or higher order theories of propositions like that in Thomason (1980a). All of these views offer solutions to the problem of the substitutability of logical equivalents within attitude contexts by taking propositions to be highly structured objects.

Missing in all of these competitor treatments is the context sensitive interpretation

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ATfITUDES AND ATfITUDE DESCRWTIONS

of attitudes. In order to accommodate the Pierre and Peter puzzles. it seems that all of these theories must treat primitive concept terms and names as definite descriptions. This means that they must reject well-entrenched theories of direct reference. Further. which definite descriptions these names and concept terms are abbreviations of must

delineated DRSs, given that we start from a context in which nothing is assumed about either Joni's or Chachi's mental states, or a context in which we make the same assumptions for both.28 This looks suspiciously like substitutional quantification to many, and indeed it is very closely related. DR-theoretic structures are, as characterizations of attitudes, predicates of mental states. They are not linguistic objects. But since DRSs are isomorphic to DRS inscriptions, it would appear that quantification over DRSs is simply quantification over DRS inscriptions. But then haven't we just elaborated a variant of the sentential view of belief--the view that sentences of some language of thought are the objects of the attitudes? If so, doesn't an argument like that developed by Church impugn this view? I believe not. In fact I will use this argument to highlight how the DR-theoretic treatment of belief and of propositions as objects of belief differs from the usual sentential approach. Church devised a particular argument to criticize Carnap's semantics for belief sentences on which sentences were the objects of belief. A certain refinement of Church's argument can be used as a general attack on representational theories of mind and semantics like the one proposed in this chapter. Church plausibly assumes that when a monolingual Gennan speaker sincerely and knowingly asserts to himself Schnee ist weiss, a monolingual French speaker sincerely and knowingly asserts to himself La neige est blanche.and a monolingual English speaker sincerely and knowingly asserts Snow is white, this is good evidence that they all have the same belief. Suppose sentences are taken as objects of beliefs. A Carnapian might assume that each of the sentences above forms the object of a belief of the agent who asserted it. As Church remarked, this entails that these individuals do not have the same belief, which is counterintuitive. What all the sentences have in common, Church would have said, is that they express the same proposition. If beliefs are relations between agents and Churchean propositions, then this predicts that the three monolingual speakers above all have the same belief. Church's argument is a powerful argument against sentential theories of attitudes and offers at least a potential difficulty for the DR-theoretic view of the attitudes. DRSs are closely linked to sentences of natural languages, and indeed the DRS inscriptions that issue from the English to DRS translation program do not share all the same elements of the DRS inscriptions that issue from the Gennan to DRS translation or French to DRS translation. But to see whether the difficulty is real, we have to examine more closely the meanings of predicates of DRSs. I have analyzed predicates of DRSs into conditions similar to those introduced by proper names; a word like 'snow' introduces a concept discourse referent c and the condition named(c, 'snow'). DRS concepts are thus connected in a special way to their linguistic expressions. But the predicate constant 'named' denotes a basic primitive concept of humans; it is not a piece of language. It relates a linguistic tenn and a non-linguistic concept or conceptual individual. Both proper names and concept words contribute a truth conditional content to a discourse by supplying external anchors for the individual or concept discourse referents they introduce. External anchors for concepts are intensions, and these

depend on other facts about the agent's cognitive state, which these other theories

cannot account for since they don't have the right sort of context sensitivity. For some agents the belief that furze is a pretty bush is the belief that gorse is a pretty bush. The DRT account of attitude contexts is precisely designed to accommodate a theory of direct reference while also making sense of the context sensitive interpretation of attitudes. For the DR-theoretic account. the meaning of an expression should be the contribution that the expression makes under an interpretation to the semantic content and structure of the whole. In a dynamic setting the structure of a condition with an altemation is important for the way the rest of the text is to be processed. It may make a difference to the processing of an anaphoric pronoun. If that is the case then it seems reasonable to think of or as contributing not just the truth conditional content of a famlllar operator, but a particular structure as well. That structure plays an important role in the cognitive life of the agent--especially in his reasoning; the content of that structure also plays an important role: it detennines whether that reasoning is correct. Both are needed for an account of agents.

5. ATTITUDES, PROPOSITIONS, AND REPRESENTATIONS DRT's analysis of attitudes has important implications for a general theory of propositions although DRT itself does not actually say what a proposition is. But DRT does imply that if propositions were to be identified with Objects of attitudes, capturing unifonnities of structure as well as content, then they would have to be thought of as having a complex structure, articulated within DRT in terms of concept discourse referents, individual discourse referents and logical predicates. But in fact my account of attitudes and attitude reports does not commit us to the existence of propositions as distinct objects at all. Rather it conunits us to the idea that mental states have both a content and a complex structure described in tenns of DDRSs. Consider, for instance, the propositional quantification in (7): (7)

Joni believes everything that Chachi believes.

Suppose that K, is the delineated DRS for Chachi and K2 the delineated DRS for Joni. (7) implies that there is a 1-1 function f from UK, into UK, such that for every constituent K < K, there is an alphabetic variant constituent t(K) < K 2 • This would guarantee that Joni believes every proposition that Chachi believes. We can get this interpretation of the quantification in (7), simply by quantifying over the proposition discourse referents in the first stage of interpretation of (7) and by assuming that such discourse referents map onto DRSs in the model under embedding functions. 27 The rules of DRS construction and delineated DRS updating will then build the same

ATITfUDES AND ATITIUDE DESCRIPTIONS intensions are part of the sphere of socially detennined meanings, in which individual speakers participate by using the language. How to spell out this socially detennined meaning is an open question. I shall assume that an answer compatible with a conceptualist outlook on abstract entities is possible. As we saw in connection with belief reports, however, the internal connections among discourse referents also are important in describing a person's cognitive state. These internal connections. or internal anchors, must be taken into account in detennining what an agent believes. 29 They help detennine the structure of the mental state whose content and structure we are trying to capture by making attitude attributions. Sometimes the fit between the agent's state and what the recipient constructs is not altogether exact, but adequate attitude interpretation aims for as close a fit as possible. The upshot of this discussion is that while DRSs aren't linguistic objects, they do have linguistic elements in them according to the DRS construction procedure as outlined. The question that Church's argument raises is, How can we say that two monolingual speakers of different languages have the same beliefs? The external and internal anchors that help to analyze puzzles ahout belief yield an appropriate response to Church's argument. Let us fIrst look at the case of a monolingual speaker of a foreign language, Pierre, whose beliefs are reported by a monolingual English speaker, Peter. In this simple case, matters become already quite complicated. Let us suppose that Pierre sincerely and reflectively asserts (8)

La neige est blanche,

and that Peter reports to a recipient Sam, who is a French and English speaker and who is aware that Pierre is a nonnal, competent, monolingual French speaker. (9)

Pierre believes that snow is white.

(9) should come out true on our theory. Sam will interpret Peter's report against what he knows of Pierre's background cognitive state. Knowing that Pierre is a competent, monolingual French speaker, Sam might use the appropriate translation of snow in French, neige, as a constituent of a condition, named(ct', 'neige), in a portion of the delineated DRS K that for Sam represents Pierre's cognitive state. The condition, named(cI', 'neige'), says that Pierre has a concept CI", which is named by the tenn neige. Similarly, for Pierre's concept of whiteness. In interpreting the attitude report, Sam must find for Cl ", the discourse referent introduced by the occurrence of snow in (9), an appropriate internal anchor. Assuming that Pierre is a competent speaker, Sam will link C1" with C1' in K. When updating K with the subDRS derived from the complement clause of (9), Sam will delete conditions like named(ci ", 'snow') and named (C2 ", 'white') and insert the appropriate internal anchors, as the principles of attitude report interpretation require. But in following the procedures for attitude interpretation, Sam has already anchored Cl ", the concept discourse referent introduced by snow in (9), to the concept discourse referent C1 that for him represents snow--similarly again for the concept of whiteness. Presumably

131

too, Sam will internally anchor Pierre's concepts of snow and whiteness to his own concepts of snow and whiteness. In so doing, Sam will come up with a faithful representation of Pierre's cognitive state, which the pri~ciples of attitude re~ort interpretation of this chapter will assign, given the assumptIOns, a proper embedding. Thus, (9) comes out true as desired: c10 C2, x named(c [, 'snow') named(c" 'white') Pierre(x) x's cognitive state!l()

CJ',C2',Ct",C2" named(ct', 'neige') named(c" 'blanche')

K

u K9:

C1 "(u)

Cl"=Ct'

...

c,"(u) C2" =C2' I

believe(x, K) believe(x, K9) «Ch CI"», «C2, C2"» «Cit cl '», «C2, C2 '» In interpreting (9), Sam has done something that my earlier account of delineated DRS construction did not mention. Sam uses a translation manual to detennine the appropriate internal anchors. Good translation manuals correlate words whose predicates of DRSs have the closest intension or the closest functional role across the speakers of a given language community,30 The translation manual helps Sam correlate Ct with c 1 ' --his concept of snow with Pierre's concept. In determining appropriate internal anchors for concept discourse referents, the interpreter chooses the concept discourse referent already declared in the delineated DRS that plays the closest functional role to the concept discourse referent representing the concept for the interpreter. By doing this he ensures that the internal roles of Cl and c 1 ' are, if not identical, as close or closer than any other two roles.31 This is what is required to give a faithful representation of an agent's cognitive state. An interpreter of a belief report should exploit all of the tools available to situate the report within the appropriate context of interpretation for the particular agent (or group of agents). By using a translation manual in interpreting the belief report about an agent who is a monolingual speaker of a foreign language, the interpreter is merely exploiting a tool essential to getting the interpretive context right. Suppose now that Sam does not know what Pierre's linguistic capacities are. He may assume a cautious interpretation. and so internally link the concept discourse referent CI" with whatever discourse referent CI' occurs in his representation of Pierre's cognitive state K that represents the concept of snow. We should note that C1' will only represent snow if in this delineated DRS K for Pierre, c l' has an internal anchor c I, the discourse referent the concept of snow for Sam --which represents the concept of snow in the delineated DRS K of Sam's cognitive state. Sam may not specify what the linguistic tenn associated with c I' is in K; that is, K may not contain

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CHAPTER TIIREE

a portion in which the condition named(cl', a) occurs. Or it may contain a generalization of this condition--with an existential quantification over the name position; that is,., Sam may just say that Pierre links whatever the appropriate translation of 'snow' in Pierre's home language with c 1. In either case, however, he will get the faithful representation and (9) will come out true. What is crucial to the correct interpretation of the report in this case is: (i) that the concept of snow for Pierre play the appropriate functional role in the total cognitive state to that of snow for Sam, and (li) that any external connections between the concept of snow for Pierre and the environment also approximate as closely as possible those connections between Sam's concept of snow and his environment. Matters become really interesting when Sam knows that Pierre has certain idiosyncratic features about his language use--Le., when he knows that Pierre is not a normal monolingual French speaker--at least not normal in ways relevant to the interpretation of (8). (Here is where the interplay between socially detennined and individual content becomes very important.) Let's suppose that Sam knows (though Peter does not) that Pierre has a rather idiosyncratic use of the word neige. By neige, Pierre means heroin. Sam will exploit this knowledge to get a rather different interpretation of Peter's statement. Though Peter may not have a faithful representation of what Pierre believe, Sam may, in virtue of his "insider information" about Pierre's linguistic idiosyncrasies. Once again, Sam is exploiting the relevant tools to build a faithful representation. Before he used a translation manual for the two languages; now he uses his knowledge about Pierre's idiolect. Once again it is important to notice that the "proposition" to which Pierre is related in his belief that he would express as (8) is one whose content and structure are defined at least in part by its many connections with other components of Pierre's cognitive state. This affects how we should understand reports involving quantification over objects of attitudes or agents. When we have quantification over DRSs as in the translation of (10),

(10)

Peter believes something that Pierre believes,

we must understand (10) as a quantification over some DRS that can be added both to a DDRS faithfully representing a portion of Peter's cognitive state and to a DDRS faithfully representing a portion of Pierre's cognitive state so as to produce two DDRSs faithfully representing possibly more inclusive portions of the respective agents' cognitive states.3 2 Suppose now that we find a witness for the existentially quantified variable in (10). The replacement of the propositional variable by a DRS is only the beginning of the interpretive task, as outlined in the procedure of delineated DRS construction. We must now reinterpret that DRS, using the conditions with the predicate named to give the DRS its appropriate internal connections. This implies that a sentence like (10) may be true without its being the case that both Pierre and Peter share all the same internal connections or, indeed, have cognitive states that are mirror images of each other. So, in particular, Pierre and Peter may share a belief in the sense that (10) is true, even if Pierre and Peter are both monolingual speakers.

-~t-~,c",j"

"

ATIITUDES AND ATIITUDE DESCRIPTIONS

'lj

133

DRT thus does not succumb to Church's argument. The distinction between the DRT view and the sentential view of attitude objects is that the relation between a DRS and the attimde it describes is very much more complicated than that supposed by the sentential view. Church's argument fails against DRT because of the complexity of this interpretive task. Since DRT does not claim to offer a reduction of truth conditional content to some DR-theoretic notion, an appeal to translation manuals, which involves a tacit appeal to the concept of meaning, may be accommodated without circularity. Translation manuals, which pair words with the same or similar truth conditional intensions, are a legitimate device that can be used in attitude ascription interpretation, in particular in detennining the appropriate internal anchors for concepts. If we wanted to reconstruct Churchean propositions, we could have appealed to the appropriate sort of equivalence classes of DR-theoretic structures under predicate of DRSs translations and alphabetic variance. Simply defining propositions using the equivalence classes defined by alphabetic variance would not suffice, as our example shows. The discussion of (8) and (9), however, also reveals that such reconstructions of propositions are otiose. Further, the reconstruction misses the point about contextual interpretation. We can get the desired prediction that Pierre and Peter can have the same belief even though they are both monolingual speakers, without supposing there are such common, mind independent entities as fine-grained propositions toward which they both bear the attitude of belief. We can quantify over DRSs alone and get the correct truth conditions for (10) and for more customary sentences like (11), (11)

Everyone believes that snow is white,

without implying that the same DRS (or the same object) with the same internal connections is a constituent in all those mental states. Indeed if that were what was meant by (11), such statements would never be true. Indeed quantification over DRSs alone, which are not at all good candidates for the post of DR -theoretic counterpart to propositions, is the most sensible approach in this framework to the problem of representing quantification over attitude Objects and over propositions generally. The moral is that natural language attitude ascriptions don't really require propositional quantification. The philosopher's propositions are an abstraction, a construction unnecessary for the purpose of doing natorallanguage semantics, and in particular the semantics of the attitudes. Apparent reference to such entities in natural language stems from an uncritical look at natural language syntax and evaporates upon closer analysis. Thus, the construction procedure and analysis of propositional quantification and reference to propositions reveals that we do not have to countenance propositions after all. What philosophers have called propositions are various ways of classifying the contents of mental states. In some cases a very fine-grained notion of proposition emerges from our descriptions of cognitive states, as in our discussion of puzzles like

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those besetting Pierre and Peter. In other cases, and especially in the case of animals like dogs, a much cruder notion is called for. The beliefs of a dog or even a small child ought to be reported according to different criteria than those I have been proposing for adult humans. The concepts of a dog or a small child may not be connected to any linguistic tokens. The interpretive task is now even more complex. In such cases there is no question of using a translation manual to get the right internal connections; the agents don't speak any language at all. Our guide to getting the right internal connections for the concept discourse referents introduced in the processing of a report about a belief of such an agent must look at rough, functional equivalences. Again let's consider an example. Let's suppose that my dog, Demi, sees me pick up my leash and put on my running shorts and shoes. She gets very excited and acts as though she believes that she and I are going for a run together. On the basis of this behavior, I say to my wife, Sheila,

interpretation for dogs, we avoid attributing to them beliefs in tautologies or logically equivalent beliefs that may be logically very complex. If that structural constraint does not hold, for instance, then it would follow that if Demi believes that we are going for a run, she also believes that we are going for a run and that the axiom of choice is equivalent to the Hahn-Banach theorem. A semantic theory ought to avoid such conclusions. Having looked at how one might interpret a belief report about a dog, what lessons have we learned about propositions? The "propositions" that a dog entertains might be much more roughly or coarsely individuated, in the sense that a great deal many more reports might generate DRSs faithfully describing the dog's belief state. This is because the semantic constraints generated by internal anchoring are so much weaker in this case. A dog's belief state in general has much less structure than an adult human's. Further, the basic concepts are not tied to linguistic expressions. so a whole level of complexity is eliminated. The choice of internal anchors for the representation of a doggy belief is guided only by rough functional role equivalents. The proposition that a dog is related to when it believes something is again an abstraction over and above the DRSs used to describe the contents and structure of mental states. For dogs, however, the relevant propositional objects of belief may be modeled by different equivalence classes than those used to isolate the propositions appropriate to adult human agents. The individuation of propositions at the level of natural language metaphysics is thus highly context-sensitive and interest-relative. Against this perspective the debate between possible worlds theorists, Neo-Russellians and Fregeans concerning the "true nature" of objects of belief or propositions seems misguided. Many direct reference theorists have argued that their theory of structured proposition is the appropriate one. Possible worlds theorists champion an even cruder notion of proposition, while Neo-Fregeans concentrate on fine-grained theories of propositions. Their debate misses the point; propositions are abstractions of bits of contents and structures of cognitive states (which DR-theoretic structures attempt to model); these abstractions don't have set identity criteria outside of a particular context of interpretation. Sometimes, crude propositions would have sufficed; at other times. only extremely fine-grained context sensitive ones may do. In light of these investigations into the nature of attitudes and attitude reports, it is tempting to conclude that propositions are really abstractions and ways of classifying agents' mental states. In chapter 10, I shall argue that at the level of real metaphysics, the propositions of natural language metaphysics may be reduced to the DR-theoretic constructs and as such are byproducts of human infonnation processing.

(12)

i I

Demi believes that she and I are going for a run.

Sheila interprets this relative to what she knows about Demi's cognitive state and relative to her own state. In so doing, for instance, she finds an internal anchor for the concept of running in her representation of Demi's cognitive state K.. Let's call this doggy concept of running Cd. As part of her interpretation of (12), however, Sheila also links Cd with the concept of running Cs of her own cognitive state. There is a question about how to specify that internal connection. So far we have treated this connection as a matter of identity. But perhaps the relation should be. one simply of correlation; Demi's discrimination of concepts in view of her cognitive capacities are perforce much cruder than Sheila's--so the two concepts should be distinguished. But what would the truth conditional import of this correlation between discourse referents be? It might be something like this: the intension of Cs determined by its role in Sheila's cognitive state is closer to the intension of Cd as detennined by its role in Demi's cognitive state than the intension of any other concept discourse referent in Demi's cognitive state. This semantic interpretation of the link imposed by the demands of internal anchoring will not support any deterininate way of constructing internal anchors for such elaborate conceptual discriminations as those of Pierre and Peter in chapter two, in which there are two distinct concepts with the same intension. But note that such examples are very difficult to construct for dogs or small children; only the connections between language and concepts or individuals appears to generate such puzzles. We still want to distinguish logical structures of beliefs for dogs, and thus keep the general outline of our semantics for attitudes. Doggy beliefs, however, may only have a very simple logical structure; they are most likely described by atomic DRSs only. Dogs probably don't reason much if at all--they don't exhibit behavioral signs that would indicate that they have disjunctive or negated beliefs (what could those signs be other than verbal behavior?), though they may have existential beliefs--viz. wanting attention from someone. If we keep the structural constraints on belief

l35

6. CONCLUSIONS This chapter finishes the presentation begun in chapter 2 of research in DRT that is the necessary ground work for the semantics of abstract entities. We have now introduced a semantics within the DR-theoretic framework for abstract objects

136

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CHAP1ER THREE

including quantification over propositions. The task of the next two chapters is to expand the foundations for the semantics of abstract entities described in this chapter and to examine a wider range of abstract entity denoting constructions. 1 Kamp (1985,1990), Asher (1986.1987.1989), Zeevat (1986). A related view is that of Stalnaker

&1987). For developments of this view see Kamp (1985, 1990), Asher (l986. 1987, 1989). 30therwise, we could tell they were false and it would be irrational to continue to have these beliefs. 4Por a discussion of conceptual individuals, their philosOphical heritage and AI applications, see

I: II! I: .

Rappaport (1988). SHow the objects of attitudes are to be individuated is a complicated matter--the question may have no elegant solution. For a discussion see Asher (1986). 6As we shall see later, the use of the same concepts will also generate such internal connections. 7 Par a discussion of various types of incompatibility, see Asher (1989). 8 The topic has been discussed at some length within this framework in Asher (1986) and Kamp 11985). 9S ta lnaker (1987) has also advocated a contextual theory of belief. His notion of context, however, is much less structured than that postulated by DRT. lOMy approach here differs from one I have pursued elsewhere (Asher (1986, 1987, 1989). While the model theory of the fOffiler approach was more elegant, a problem arises with respect to the anaphoric data. In those earlier works, PI, pz, etc. were menial state discourse referents and· were mapoed onto total cognitive states of agents, represented in the theory as delineated DRSs. But then shoula be able to refer to an agent's total cognitive state with an anaphoric pronoun. But this is not the case. To remove this proDIem, it seems to me now best not to have discourse referents for total cognitive states. Otherwise, however, much carries over from the earlier papers. 11 I have also brushed over certain issues here that are crucial in the recipient's inte:g>retation of the belief report. The condition named(v, 'Chemobyl') within the conditions of the DRS characterizing the discourse referent p in Stage I indicates that the recipient assumes that the agent associates the name 'Chernobyl' with some conceptual individual, but thlS assumption may be questioned in some cases. For discussion see Asher (l9!:16). 12These observations introduce a default rule of discourse referent identification: if the universe of a delineated DRS K' contains a discourse referent x introduced by a defmite NP and K' is nested within another delineated DRS K and UK contains a discourse referent y introduced by the same NP, then x and y ought to be mapped to the same object by an embeddin,&: function. This is similar to another default rule--namely, if the universe of a delineated DRS K for an agent A contains a discourse referent x introduced by a definite NP and another attitude!epQlt about A contains an occurrence of the same defmite NP, then the discourse referent introduced by the new occurrence should be identified with x. There are well-known exceptions to this rule. These examples merit discussion, but they seem rarasitic upon the customary uses of NPs. I shall ignore these examples here. 3Rainer Btuerle suggested this notation to me. 14Certain rules are needed to handle those cases where the context specifies no or an empty delineated DRS for the agent whose beliefs are being interpreted. For details see Asher (1986). 15por more details on this problem, though with different tenninology, see Asher (1986). 16More precisely, suppose that (i) 'M ~K w f Kbelieve(u, g>(x y»), (li) x =F y and (iii) 'M w f Kbelieve(u x =J'), where Kcp is the DRS formed from cpo SupPose (iv) agent u believes the irivial identity x ='x. By (i) there is a function n: UK+ Kc:p ->- UK, where K is the cognitive state off(u) that meets all the constraints defined above. Assume n(x) = n(y). By (iv), there is a condition in K+ K

"K

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ATTITUDES AND ATIITUDE DESCRIPTIONS

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I

__________________________________________________

I

fix) "f(y)· 23The details of such an account would have to address in detail what concept-type discourse referents are to be introduced in the \,rocessing of a discourse. Does each word introduce a concept discourse referent? Cresswell (1985 has indicated that such assumptions may be too simple. Whlch concepts are introduced in a sentence depends not only on the words involved but on its topic-comment and focus structure as well. 24Por a detailed defense of this view see Asher (1986, 1989). 25por some details see the next chapter. But for a fun discussion of the truth conditions of reports like (15) see Asher (1987). 26This is known colloquially as supplying a "background story," and it is a favorite pastime of philosophers who discuss difficult examples about belief. 27 Notice that (7) does not contribute any new material with which to update the recipient's representation of elther Joni's or Chachi's cognitive state. The statement will thus be evaluated in effect relative to what the recipient already believes about Joni's and Chachi's mental states. 28To be sure statements like (7) are not usually meant literally; there is a certain amount of "slop" in what counts as having the same belief. In the DRT account, however, there are many places in which we could relax the account of truth conditions to account for the sloppy use of sentences like (7). We could alter the relation between the DRS derived from the complement of a report and its relation to the portion of the cognitive state the reporter wishes to report on. Alternatively, we could alter our aefinition of what counts as the same delineated DRS or the same DRS. 29The internal connections between discourse referents, in combination with inference represent the use to which the agent puts the conditions and the structures in which they figure. Par an account of these internal connections in teffilS of a probabilistic notion of functional role, see Asher (1988). 30Note that the functional role of an expression may be at variance with its intension, if the intension is taken to be fixed by something like a "paradigm sample" as in Putnam's or Kripke's work. 31We need to make precise some measure of closeness of content. But there are many metrics that one might define on indices to get an appropriate notion. I will not pursue that topic here. 3~That. is, they will be more inclusive if the original DDRSs do not already contain a witness verifying this claim.

I

SENTENTIAL NOMINALS

139

CHAPTER FOUR nominals and semantically correlated sentences. The theory §hgJJJd predict the synonymy of the a-b pairs in (1) - (4) while avoiding that prediction for the pair in (5) and (2.c-d).

THE SEMANTIC REPRESENTATION FOR SENTENTIAL NOMINALS

In chapter 1, I introduced several tasks for any linguistically sensitive, semantic theory abstract entities. One was to provide a semantics of the variety of construcnons that make up the class of sentential nominals, by which I mean all those

0:

~:~~~[~~~7~~~~~:~j~!!y~~;:~;~~~e~~;~~_t:j~~~~~~~~~~~~~ ~n~ ~~runds

and POSS-ing gerunds), that clauses, for infinitival phrases, naked mfIm~ve p~ases and noun phrases involving a variety of common nouns that may combme WIth that clauses or gerund phrases. The class of common nouns itself divides into three: nouns that are nominalizations of some propositional attitude verb, nouns that are nominalizations of other complemented verbs, and nouns that are not nominalizations of any verb. This chapter and the next develop a semantics for sentential nominals using the DRT framework. My semantics for nominals follows the characteristic two level analysis of DRT--one relevant to DRS construction and the other relevant to DRS interpretation. The next two chapters elaborate the construction procedures and DRtheoretic structures for sentential nominals and their constituents. Because of the complexity of the construction procedure for nominals, I will concentrate on sentence interpretation. Questions of discourse interpretation will come in chapter 7, where an account that integrates DRT semantics and discourse structure, and which is much ~ore sophisticated than the multi sentential interpretation of chapter two, will be mtro~~ced. In chapter 10, I describe the truth conditional interpretation of these condillons and structures and discuss some of the logical difficulties that they introduce. Th~ construction procedure for sentential nominals is complicated, because the syntactIc structure of some of the nominals, in particular the gerunds, is unclear. I will spend the first part of this chapter laying out my syntactic assumptions and their semantic consequences. I will then turn to a DRS construction procedure for event l denoting nominals--derived nominals and the so called of-ing gerunds and some 1abstract nominals-- that clauses and infmitivals. Chapter five will investigate the more problematic POSS-ing and ACC-ing nominals and return to look at the problems , described in this chapter. Before getting started with the analysis, let us first investigate three problems that a semantics for sentential nominals should solve. First Problem: The Semantic Correlation between Nominals and Sentences. A first criterion of adequacy for a semantics is to get right the relations between

I

138

(1.a) (1.b)

The army's destruction of the city was bloody. The army destroyed the city. It was bloody.

(2.a) (2.b)

Fred's shooting of Bill led to his imprisonment. Fred shot Bill, and that led to his imprisonment.

(2.c) (2.d)

Bill's hitting of that policeman will land him in prison. Bill hit that policeman. It will land him in prison.

(3.a) (3.b)

John's hitting Bill caused Bill to yell. John hit Bill. That caused Bill to yell.

(4.a) (4.b)

John sprinting past Bill was a welcome sight. John sprinted past Bill. It was a welcome sight.

(5.a) (5.b)

Mary doubted that John was unhappy. John was unhappy. Mary doubted that.

",,"1l.'"):

In de~igning the appropriate DRS construction procedure to account for these data, we Will also perforce make other predictions concerning other anaphoric data, such as anaphoric reference to indefinite NPs occurring within the context of sentential nominals. This will test the adequacy of our constructions. Capturing this anaphoric data is a principal reason to use the framework of DRT. Second Problem: Spectra of Nouniness and World Immanence. Derived nominal and gerund constructions exhibit a varied range of syntactic forms and a correlated range among their semantic denotations. Ross, Quirk, and others have spoken of a spectrum of "nouniness." Derived nominal constructions are true nominals like noun \ phrase~; they m~~ CO?tain detei1tiInerS:"l)e plUraTIZe'(f.'ai1cfmaytike'ii"djectival, but not ) adverbIal, modIfIcatIOn. At the other end of the spectrum of nouniness are that clauses; they do not take determiners, cannot be pluralized and may take adverbial, but not adjectival, modification. In the middle are various gerund constructions. Some gerund constructions may come with deteIDiiii:ers;-oiliers-prohibri"iiiem~'Some gerund constructions take adjectival modification only, while others take adverbial modification only in English. In languages like German and Italian, both adjectival and adverbial modifications together are allowed on some infinitival constructions which makes them fall in the middle of the scale of nouniness. The nouniness of ~ nominal also affects the argument structure it inherits from the verb from which it derives.. The argument structure of very "nouny" result nominals may drift 1 ~
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CHAPTER FOUR

SENTENTIAL NOMINALS

that of the verb from which they are derived. The syntactic spectrum of nouniness correlates with t~e spec~rum of wOrl.d immanence among the semantic denotations of sentential nonunals. I mtroduced thIS spectrum in chapter 1. Here I dwell on it at greater length. In chapter 1, we employed three different tests to find ontological distinctions--Vendler's container argument, quantification and anaphora, and the logical structure of the .~om~ins of typ.e~ of entities. All the tests distinguished between purely abstract entItles like pr'2Positions at one end of the spectrum and eventualities at the other. Most of the tests upheld finer distinctions between various-types of pure abstract entities--for instance, bet~~J,-!_~jec.!!-y~~p!9.n9j.i.tiQ!!§'J!D.\;l_PJll:e..PL~p.o.sitions--as :-v~l: as between various types of eventualities--accom'plishmen.ts,~~.?;~v:"?:7Ets,'_.~~!l.":!!~,~~~,,~2_~~~~s: They also for the most part distinguisheaoerween purely aostract objects, eventualItIes, and entities intermediately placed on the spectrum of world immanence--e.g., facts, possibilities, and situations. There emerg~ n~ simple correspondence be~ween t~pe of sentential nominal and type of semantic object. But there were some mterestIng generalizations. Infinitivals appear to denote only projectiv~ pro~ositi~ns. Si~arly, some gerund phrases and derived nominals are quite restncted m therr denotatIOns. ( POSS-ing and ACC-ing gerund p~~ses deno~e facts or possibilities, and in certain \ circumstances perhaps eventualitIes. Of-mg gerunq.L~p"~_l!!:...!(L.~en~nly e~alities. Derived result nominals may only denote a concrete physical obje~t.as in the product of his labor, or a physically visible or verifiable res~lt of some act~vlty or process as in the city's destruction. As Vendler (1967) pomted out, den.v.ed I process nominal constructions may denote eventualities but also more abstra~t entities \ like facts or possibilities. That clauses typically denote purely abstract objects, but they appear indifferent as to which type of abstract object--they may denote facts, propositions, possibilities, etc. These observations raise questions that an analysis of nominals must answer. How do w~~~em~9"§']'.Qtations? What is the relation betwee~ syntactic form, DRS structures and the typology of natural la~guage metaphysics? Should and if so how can we integrate an account of the different semantic denotations with an account of the syntactic spectrum of nouniness? Yl,hy do the POSS-ing constructions and that clauses have the flexibility to denote ( different types of abstract entities, whereas others like derived nominal phrases, and \ ACC-ing gerund phrases do not? Further, an analysis of nominals should assign the appropriate logical structure to the domain of events, st~tes, facts, etc., that ~hey denote, and it should make evident the observed connectIOns between the vanous ( distinct types--for instance the connections ~tween facts and ev~n:~~lities, facts and situations, situations and events, and propOsItionS, facts, and possIbilities. Third Problem: Nominals and Event Negation. Some derived nominals and all ( the gerund forms can incorporate some form of negation.

These nominals introduce the problem of event neS!!!.i2.n. Given the DRT approach to verb interpretation of chapter 2, the sentence corresponding to (6.a)--the train did not amve--generates the following DRS.

140

If'-b(pj.s

(6.a) (6.b) (6.c)

I

The non arrival of the train John's not kissing Mary Fred not seeing Mary

-,

x,e train(x) e-arrive(x)

It will be true just in case there is no event of the train's arriving. But then what does the gerund construction in (6.a) denote? The role of negation with nominals is peculiar. I will examine the details in chapter 5 and argue for a combined syntactic and semantic solution to the problem of event negation: the place of negation in the syntactic structure and the general translation from syntax to DRT forces the negated nominal to denote a fact, not an eventuality.

1. SYNTACTIC AND SEMANTIC ASSUMPTIONS AND BASIC PRINCIPLES With the goals of the analysis sketched, I now layout its basic assumptions. The DRS construction procedure, introduced in chapters 2 and 3, translates the lexical items and follows the structure imposed by the syntax "from the bottom up" to put these translations together into a DRS for a sentence. The complex syntax of nominals requires more syntactic assumptions. Although chapters 2 and 3 used only a "plain vanilla syntax," I will assume in what follows the framework of Chomsky's Government and Binding theory; it is the syntactic framework in which the most f sophisticated work on the syntax of nominals and nominalization has been done.

1.1 Assumptions about Syntax and the Syntax -Semantics Interface Already in chapter 2, I adopted X' theory as the basic grammatical framework. X' theory stipulates the following. Let X, Y, and Z be any categories. Then

XP -> ZPX' X' -> X YP I assume seven basic categories: D (determiner), N (noun), P (preposition), M (Modifier--either adjective or adverb), V (verb), I (inflection) and C (complement). In chapter 2, however, D was not assumed to have the structure of an X' category. In this chapter, each basic category has the structure of an X' category. This assumption leads to the so called DP analysis. Abney (1986, 1987) has put forward some interesting syntactic arguments for a parallel treatment of inflection and

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CHAPTER FOUR

detenniners. Abney's work, as well as that of others on the DP analysis,2 is essential

r for the study of gerunds, whose syn~ Abney discusses in de~il. Like the inflection position I, the detenniner is the locatIOn of agreement features In the noun phrase, and like I it is a head of a maximal projection. The maximal projection of I is IP (standing for S); the maximal projection of D is DP. The inflectional elements in I .tak~ a projection of V as complement, while the inflectional elements in D take a proJectlon of N as complement. The agreement features in I detennine the tense and number markings on the verb, while the agreement features in D detennine the genitive case marking on the subject of the noun phrase that is in specifier position in the DP.. In following Abney's analysis, I will also argue that the agreement features aSSIgn accusative case to the subject of ACC- ing accusatives. Now for several assumptions conceming nominals and nominalization. Lexicalist Hypothesis: Following Chomsky's (1970) general "lexicalist" hypothesis, I assume that in the lexicon are nominalization affixes -ing and -ion and rules for attaching such affixes to verbal stems like destroy, kill, and the like. Affixes like -ion or -ing are deverbalizing elements that take a verbal lexical item into. a nominal one. That is, they carry a +n, -v pair of features into a -n, +v feature parr. This is a lexical transformation. To deal with ACC-ing and POSS-ing gerunds, however, I will use a form of affix hopping, on which the -ing affix takes a wider scope at surface structure than their phonological form implies} But it is only of the sort that is required in any case to deal with the movement of the tense features from I onto the verb, and so is not something out of the ordinary. Argument Structure. Linguists use the terms argument structure ~d ~guments in different ways.4 Syntacticians use the notion of argument often to IndIcate what semanticists would call an argument place--for instance, the subject or agent argument place. Every noun or verb yields a DRS predicate u~der the semantic o:anslation (encoded in a lexicon); an argument place of the predicate, and by extensIOn of the noun or verb is indicated by a lambda abstracted discourse referent variable. Semanticists ~ould understand that such an argument place could be filled by a wide variety of arguments--semantic arguments are simply discourse referents supplied during the construction process. Syntactic arguments, typically of lexical elements like instances of verbs or nouns, are those syntactic constituents, typically noun phrases or nominals, that introduce such discourse referents to fill the sem~tic argument places. A further complication is that argument places may be la?eled ~ a variety of ways. One way syntacticians have labeled argument places (e.g., In LeXICal Functional Grammar) is by using the traditional grammatical functions subject, object, indirect object, etc. Another way is to use the semi-syntactic, semi-semantic notion of "thematic roles" or a-roles that come from work in Government and Binding Theory-Agent, Patient, Theme, Goal, etc. Argument structures have typically been defined . to be sets of labeled argument places.s The notion of argument structure is indeed relevant at several levels of analYSIS-lexical, syntactic, and semantic. So one should have a variety of labels for argument places--hence possibly a number of argument structures. 6 ~er, there.§hQJJldjle linking rules that detennine th~,~p!.~P.rt~r~,f9J}JJ..\':.GtiQJ1s...b.e,tweeu.a,rgument places and ..,"""'....",,,.•.,,.,...,..,,.,.,.,•....-,,.... ,,-->",..-..,..,,'''''"' "

.....'"

-' ~

~

SENTENTIAL NOMINALS

143

potential syntactic argumen~~~~!ll~_t~~u:ee;. these maY.be defined by correlating variOus labelings of argument places. These linking rule§-WIll correlate conceptual or "lexical-semantic" labels (on which selectionai restrictions are defined) with the semisyntactic labels given by theta roles and in tum correlate these with the fully syntactic notions of subject, object, indirect object, etc. While I could make do with argument structures defined using either grammatical functions or a roles, I will assume the existence of an appropriate set of linking"Ftlles that will allow me to use grammatical function terminology or theta role terminology to specify the right semantic arguments for the semantic translation of a verb or verbal nominal. It is convenient to be able to use both a roles and grammatical functions. Locality. Given this notion of argument structure, we need principles concerning how these argument positions may be filled. The linking rules between syntax, lexicon. and semantics tell us the details. But the linking rules themselves obey a more general constraint, which I call the locality principle. Inspired by Fukui (1986), we might require that an argument place of the semantic translation of a V or N /3 may be filled by a discourse referent x only if x is introduced by a D or I within the minimal CFC of /3, where:

/3 for a is the minimal DP or IP that

DEFINITION: The minimal complete functional complex (minimal CFC)

common noun or verb 'Y in a syntactic tree dominates /3.

't

Thus, if a PP occurs as part of a DP in which a verbal nominal occurs, the PP may furnish an argument in the structure, not otherwise. As Grimshaw (1990) and others have observed, however, a verbal nominal may contain syntactic argument positions that are not realized at phonological form. In this case syntacticians have spoken of "optional arguments." In the tenninology I have just tried to make precise, this means that argument places may optionally have syntactical arguments. This is quite different from saying that argument place~ do not need to be filled semantically; not filling an argument place at the semantlc level drastically changes the semantic type of the object. A predicate with an unfilled argument position denotes a property, while a predicate with all argument positions filled denotes a "saturated" object--like an eventuality, a fact or a proposition. An argument of a nominal may be syntactically optional and nevertheless semantically required, if the context requires that the nominal denote a saturated entity. To deal with this possibility, I propose the following revised locality principle, or (RLP). Suppose that the argument positions of some predicate a are syntactically unfilled within the complete functional complex /3 of a, but that the selectional restrictions of a predicate on /3 dictate that /3 introduce a discourse referent of saturated type. The revised locality principle allows us to fill these positions. I assume with Grimshaw (1991) that argument positions of verbs and nouns are labeled optional or not optional in the lexicon and that a nominalizing affix may change the status of an argument position from required to optional. Typically, lexical nominalizing affixes have this function .

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CHAPTER FOUR

DEFINITION: The DRS-component of a partial or predicative DRS of the form

Aa.1> .. , Aa. n K is K.

13 of the semantic translation v of a V or N a in a syntactic tree 't may be filled by a discourse referent x only if either: (i) x is introduced by a D or I within the minimal CFC y for a; or (ii) 13 is optional and selectional restrictions on y require that 13 be filled. x must then be declared in the universe of the DRS K in which v is a condition. (B) If 13 remains unfilled, then the minimal DRS-component K' in the translation of y containing v is converted to a predicative DRS AuK' and u fills 13.

DEFINITION: Revised Locality Principle (RLP). (A) An argument place

(RLP) is a complex semantic principle. 7 It exploits selectional restrictions for property or saturated abstract entity readings. By part (A), (RLP) will supply discourse referents so as to saturate a nominal when the predicate to which it contributes a semantic argument allows that the argument is a saturated entity. But when the predicate licenses a property reading of the argument, (RLP) will contribute a property by part (B), or more properly speaking a predicative DRS, to the process of DRS construction. In the case of a nominal with a verbal root, the predicative DRS will contain the conditions derived from the verb and all the verb's arguments realized within the minimal CFC. I shall give some examples of this when I analyze of-ing gerunds. A [mal assumption concerning argument structure arises from the observation that some nominals have the same argument structure as their associated verbs, while others do not. Roeper (1988, 1989) distinguishes between argument structure preserving affixes and non-preserving affixes. I will follow the spirit of this view, modifying the letter: the appropriate difference seems to be between argument transforming affixes (-A affixes) and argument preserving affixes (+A affixes). The linking rules will determine how the argument structure for a given constituent a is to be filled with syntactic and semantic arguments. The one constraint in view of the revised locality principle on these linking rules is that the syntactic arguments must all lie within the minimal CFC containing a.

1.2. Additional Semantic Principles and the Effects of the DP Analysis on DRS Construction

The DP analysis and principles like (RLP) that relate to the argument structure of nominals and how these arguments are to be filled form the principal new assumptions of this chapter about syntax and the syntax-semantics interface. These assumptions will affect the DRS construction procedure. But most of the basic apparatus that we need for constructing DRSs for nominals is already in place. The

SENTENTIAL NOMINALS

145

DRS construction procedure already distinguishes between various types of objects by assigning distinct types of discourse referents for various sorts of eventualities, concepts, propositions, concrete individuals and groups. I will broaden this list of distinct types here by supposing that there are in addition abstract discourse referents, k 1 , k 2 • There are also more specific types of abstract entity discourse referents: fact discourse referents, fl> f 2, ... , possibility discourse referents pOI> P02, ... , pure proposition discourse referents, p, Ph P2 ... , as well as projective proposition discourse referents of various kinds. Type information will be defined by means of conditions on discourse referents; So a condition of the form cp(k) is equivalent to cp(x) & abstract(x). The distinct letters serve only as abbreviations for these extra conditions. Sometimes, more than one condition is needed to encode the type information. For instance, a condition of the form cp(f) is equivalent to cp(k) & fact(k) & charf(k); cp(po) is equivalent to cp(k) & possibility(k) & charf(k). The condition fact(k) introduces factive presuppositions that must be processed in DRS construction, while possibility(k) tells us that k must map onto a DRS and signals a distinct type at the level of natural language metaphysics. Charf(k) is a special predicate to be discussed below. The different letters T, 'pI for these defined types will serve as abbreviations for such extra conditions. Another trait of the construction procedure is that while a true noun phrase must introduce a discourse referent as an argument of the matrix verb of its clause, some non -"DP-like" abstract object denoting expressions like that clauses do not introduce discourse referents but DR-theoretic structures as arguments. Already a feature of the construction procedure and its interpretation in the previous chapter, we will see much more of this here. The roster of DRT predicates must also expand to accommodate the semantics of sentential nominals. Some of the logical operations introduced in chapter 2 in the formalization of the DRS construction procedure and its interpretation now will be adopted as part of the language of DRS conditions. Included are the symbols for the logical operations of discourse referent abstraction A and functional application O. The fragment also includes the predicate: '",,'. It denotes the characterization relation, which takes as arguments a discourse referent of some abstract type and a subDRS or a predicative DRS; I write x "" K when the DRS K characterizes x. I will make key use of the "characterization" predicate in this chapter and following ones. There are in fact several "characterization" relations--one for each type of abstract object. I will distinguish them by introducing a condition charrO or charpO to indicate that the characterization relation denoted is the one appropriate for facts or for propositions respectively. CharfO further constrains the conditions for a proper embedding of a DRS Ko in which it occurs; charf(k) is satisfied in M relative to w, t, f iff for any DRS Kh if E [""DM, then f(k) is a DRS intensionally equivalent to K 1 • CharpO, the characterization relation for propositions, is interpreted more strictly: charp(k) is satisfied in a DRS model M relative to w, t, f iff for any DRS Kh if E [""DM, then f(k) is a DRS identical with K up to the discourse referents introduced in UK--i.e., f(k) is an alphabetic variant of K where the variance differs only in what is declared in UK and Uf(k).8 This definition of course

146

SENTENTIAL NOMINALS

implies that DR-theoretic structures like DRSs, and now also predicative DRSs, are elements of the domain of the model, but this assumption already underlies the discussion of attitudes in chapter 3. Details of the model theory come in chapter 10. One new syntactic assumption, the DP analysis, significantly affects DRS construction. The DP analysis supports the similar way in which the construction procedure interprets I and D. Both inflectional elements and determiners will introduce discourse referents whose type will be determined by the predicates assigned to this discourse referent. This parallelism plays an important role in my interpretation of sentential nominals. In order to understand the semantics of sentential nominals--particularly derived and gerund nominals, we must give a semantics for the DP in specifier position that makes general sense in the grammar. Its translation should at least resemble if not be identical to the normal translation of the DP. But it also supplies an argument to the head common noun of the dominating DP, and my semantics will reflect this. This argument may have a quite different function depending on the type of the head noun. Consider for instance a derived nominal like

Following the treatment of defmites in chapter 2, I assume that the context or meaning of the nominal and the process of anaphora resolution supply the definiteness or maximality effect and so the partial DRS it yields will be identical to the one for a. The conclusion that there are such null determiners follows from the assumptions of the syntactic analysis. Null determiners are needed to assign case to the nominal subject in constructions with DPs in specifier positions, in which no other determiners occur. But another interesting fact is that other, lexically realized determiners realized in the D slot are incompatible with a DP in specifier position:

(7.a)

John's honesty.

The DP in specifier position in (7) denotes the bearer of the property of being honest. This is a quite different relation from that borne by the DP in specifier position to the head noun in a noun phrase like (7.b)

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CHAPTER FOUR

*The army's the destruction of the city. *John's most moves. *The friend's no claim. *A man's all dreams. *The army's a destruction of the city.

One might think that this does not apply to all determiners. At least some lexically overt determiners, including all the cardinality determiners, appear to go with DPs in specifier position: (9.a)

(9.b) (9.c) (9.d)

John's every move. A man's many dreams. Cantor's uncountably many sets. Everyone's three wishes.

John's mother.

The DP in specifier position will have a uniform translation in the DRS construction procedure; the difference in meaning will depend upon the N' which is the head of the DP, its argument structure, and the linking rules. The head determiner of a DP assigns the possessive case to the DP in possessive case, should the latter exist. Often, however, as in (1.a) - (S.a) or the examples in (7), there is no lexically expressed determiner unless it is the's. But this ending, as well as the his in his kissing her, more plausibly mark the possessive case. 9 If it is a case marking, then according to the DP analysis there must be a head determiner of the whole DP which assigns case to the DP in specifier position. Since there is no lexically expressed determiner in the DP, I infer the existence of a null determiner in the D slot. What sort of determiner should this be, however? One thing to notice is that the noun phrase (7.c)

(S.a) (S.b) (S.c) (S.d) (S.e)

John's friends

denotes the group of all of John's friends. A DP containing a DP in specifier position thus appears to have an existential force and a maximality effect as part of its meaning. The appropriate sort of null determiner in the D slot then should be a definite determiner similar in translation to the. I'll call it sthe for silent the.

But note that each one of the determiners in (9) may be read as a measure expression --hence, as a modifier of the set introduced by the N'. There is no measure reading for the or a; it must always introduce a partial DRS structure and be treated like a full determiner. My hypothesis, which accounts for this data, is that only null determiners assign case to the specifier slot of the DP. Since the determiners in (9) are used as measure expressions, we may consistently assume that in these examples, it is the presence of the null determiner that assigns case.1O The assumption of a null determiner is also essential, however, to interpretation. By assuming a null determiner, we can give a DP with possessive case its normal semantic analysis. The semantics of the entire noun phrase is built up in a compositional way. The presence of such a determiner in constructions with DPs in specifier position is essential to DRS interpretation. If possessives are present and contribute one argument to the head common noun, typically the head has an obligatorily labeled argument position, which must be filled by a discourse referent introduced by a determiner. I will assume that the lexically unrealized determiner sthe occupies the D position whenever there is no overt determiner. The assumption of a null determiner is not completely novel. ll But so far as I know, mine is the first semantics of nominals that makes use of it. Another complexity concerning the interpretation of possessive modifiers of DPs is the relation between the quantificational force of the null determiner and the

CHAPTER FOUR

SENTENTIAL NOMINALS

possessive modifier DP. By having the order of application follow the syntactic analysis, the quantifier that results from translating the DP in specifier position has wide scope over the quantifier formed from combining the null determiner with the head of the main DP. An example of Hans Kamp's, however, shows that there are examples in which it appears that the generalized quantifier formed from the null determiner and the head noun may take wide scope:

thus provide the desired syntactic correlate. 13 There is, however, in the case of quantifier scopes within a DP an additional, empirical constraint.

(ll.a) Martin Luther King voiced every good man's dream. This dream has liberty and justice for all people, not just those with money or a light skin.

This constraint seems supported by the contrast between (ll.b) and (ll.a), where the wide scope reading of the generalized quantifier formed from sthe and the head noun is not possible:

148

In (ll.a) the context forces a wide scope for the embedded quantifier. The bottom up DRS construction procedure accommodates such an example, because it yields different scope readings for noun phrases, when one varies the order in which the partial DRSs introduced are applied to a predicative DRS with multiple argument places.l 2 Nothing prevents converting the partial DRSs with the predicative DRSs in a DP translation in a different order from that suggested by the syntactic structure. In particular, by first applying the partial DRS derived from every good man to the predicative DRS derived from dream, we get the following interpretable structure:

AX

x

CCJAI ~

w

I

Idream(y, x)1

Applying the partial DRS below derived from sthe to the structure above yields the partial DRS for the whole nominal (the second figure below):

APAQ l--_x_ _ _

1

P(x) Q(x)

AQ I

x

I

CCJA' I ~Wldream(y,x)1 Q[x]

One would like, in the interests of a stronger form of compositionality, a syntactic correlate to the DRS construction procedure's flexibility for handling (l1.a). The closeness of the syntactic analysis of DP with that of IP suggests that a syntactically plausible theory of scope assignment that allows the elements of I (such as negation) to have wider scope over the DP in specifier position of an IP will also allow the embedded D to have wide scope over the DP in the specifier position of a DP and

149

CONS1RAINT ON QUANTIFIER MOVEMENT IN DPS: The head D of a complex DP a cannot have wide scope over the DP ~ in the specifier position of a when ~ introduces a negation.

(ll.b) No good person's dream envisions torture of the innocent. In conclusion, the DP analysis, together with the assumption that there are null determiners filling in the D position when no overt determiner is present, accounts for possessive constructions in general and in particular for their use in conjunction with derived nominals and gerund phrases. The principles of syntactic construction and semantic interpretation of DPs are perfectly general, but a key feature of my analysis of gerund phrases and derived nominal phrases is to exploit the analysis of DPs proposed here. The assumption of null determiners together with (RLP) and the semantic effects of the DP analysis allow us to distinguish grammatically between abstract entity and eventuality denoting nominals. Roughly, the presence of an inflection node within the nominal, together with its proposed semantic interpretation, will determine whether a nominal must introduce an abstract object into the discourse. Given the presence of an inflection node within a construction, (RLP) and the semantic translation of the DP analysis will ensure that the construction denotes an abstract object. Although as we shall see there is little hope for establishing a general correspondence between particular syntactic constructions and particular types of abstract entities and eventualities in natural language metaphysics, a grammatical distinction corresponding to the general division between abstract entities and eventualities nevertheless exists. This reflects the strong differences in the syntactic distribution of abstract and eventuality referring expressions, practices of anaphoric reference, and semantic intuitions about the nature of these entities. Armed with an expanded DRS language, the DP analysis, the constraint on quantifier movement in DPs and (RLP), I now tum to the details of the DRS construction procedure for the nominals. I will begin with the syntactically straightforward and proceed to the problematic constructions.

2. DERIVED NOMINALS Derived nominals can form sentential nominals, in the sense that their content is the same as that of a sentence. The army's destruction of the city, for instance,

SENTENTIAL NOMINALS introduces an event in which the anny destroyed the city; thus, the sentence, the anny

I destroyed the city, makes same semantic contribution to a discourse as the nominal in (l.a) and (l.b): (l.a) (l.b)

The anny's destruction of the city was bloody. The anny destroyed the city. It was bloody.

2.1 The Distinction between Process and Result Nominals Derived nominals need not only refer to processes. They can also refer to particular objects: (12.a) Franklin's favorite invention was the printing press. Lebeaux (1986), Abney (1987) and Grimshaw (1990), as well as others, distinguish between "process" and "result" nominals. (1.a) contains a process nominal denoting the process or event of ;cIty'S destruction, while (12.a) and even (I.c) are so called result nominals. (I.c)

151

between (La) and (I.c) is between argument preserving and argumen.!Jransf9.!!1!!nK nominals; thus, the term result nominal should be replaced by argument transforming (I.c) and (12.a-b) introduce another semantic argument place in the translation of the nominal--an argument place such that anything filling it must be related causally to the event satisfying the event argument of the corresponding \ process nominal. The noun phrases filling the semantic argument places of the translations of the nominals in (12.a) and (12.b) appear to obey the same linking rules as they do in the process reading of (1.a).14 The only difference is that in the case of result nominals, (RLP) fills in the event argument place, while in the case of process nominals, it is the head determiner. The basic distinction between process and result nominals is thus a semantic one. It is reflected in the features relevant to argument structure. Both process and result nominals are V nominalizations. Process nominals~.§~~_~!h~_¥_gyX!)~!l~!DI..£t.!JI,e,..Qf the verb; they have the feature (+A), which alloWS the argument structure of the verb topercolate up the tree. Result nominals do not preserve the argument structure of the verb; they have the feature (-A), which indicates that the argument structure of the root has been in some way transformed. 15 There is thus very little difference between the two syntactic structures for (1.a) and (1.c).

'nominal.

Tree for (1.a)

Tree for (1.c)

IP

IP

The destruction remained for all to see.

There is clearly a difference between the denotation of the nominals in (1.a), and (1.c) and (12.a). The first thing to observe is that result nominals do not denote resulting states of a process. If result states, like other states, exist only if their actors exist, then one might think that the destruction of the city fails to denote anything at all if it must denote a state. After all, the city exists no longer. MUC~?~~plll:~~}>l?I~__l!.nd intuitiv.e is the thesis that (l.c) refers to theeffec.t§,Qtllix_Qs:sJruc.tion. What are effects?->Theyare-typ{caily not's'tates-6utifiings"iiiat result from an event that is a change of state. In the case of a city's destruction, they might consist of piles of rubble, burned out buildings, and the like. Importantly, effects do not fill an argument t place of the verb destroy; they are the causal byproduct of the events that satisfy the event argument place of the verb. (12.a) refers also to an effect of some inventing process. But effects are only one sort of denotation for result nominals. Consider for instance the use of translation in (12.b). (12.b) Fitzgerald's translation of the Iliad is a masterpiece (over 300 pages long, weighs more than 3 pounds, took ten years to complete). The nominal may refer to either the abstract object--the translation, a collection of English sentences or its physical realization in a particular edition, as well as the process of translation. A certain flexibility is needed in determining what a derived nominal construction contributes to the meaning of the clause in which it occurs. The real distinction

/~

A

/~A) the anny's

D' (+A) was bloody

~ D

~+A)

MP

~l'

N' (+A)

A L

N'(+A)

~(+A) of the city I destruction (+A)

DP (-A)

/ D

I

the

~'(-A) ""

~

remained for all to see NP (-A)

A

MP

N' (-A)

I N(-A)

I

destruction (-A)

The syntactic anl!!Y.~_tL@:~i!,dYJ!l~~the !iKQ!;~q!£!!2ns. Since there is no VP in the nominaIization, no adverbial modification of the nominal is possible. Since an NP is part of the nominal, adjectival modification for derived nominals is predicted [ to be possible.

152

CHAPTER FOUR

SENTENTIAL NOMINALS

2.2 Process Nominals

We must combine (K.l) with the head of the DP and the translation of the possessive. Now the DP analysis does some work. The DP in specifier position, the army, is assigned case (the possessive). So according to the DP analysis, there must then be a head determiner of the whole DP which assigns case. There is no lexically expressed determiner in the DP. My analysis postulates the existence of a null determiner in the D slot, sthe; and I claim that only the null determiner can assign possessive case to DPs in specifier position. The semantic translation for sthe is just the partial DRS for the determiner a; the use of the defInite determiner implies that there is a unique or at least most salient event of the destruction of x by y in the context. The discourse referent that this partial DRS introduces fills the event argument place of the nominal, when the translation of sthe in D combines with the head N' translation.

Let us now tum to the semantics of process nominals. The hypothesis that (1.a) is a nominalization in which the argument structure of the verb is preserved implies that subject and objects are required if the verb is transitive. The translation of the derived nominal in (1.a) will be the predicative DRS,

AV Ae AU e -destroy (u, v) We must now combine this translation of the nominal with the rest of the nominal phrase. But how are the various argument places filled? This is th~U~~K.2f the r l~J~.riik~. Forrurargument preserving eventuiillty-no!ii.illaIs;oar;ooimportant liriling rule is that the discourse referent introduced by the head determiner must go into the event argument place. PPs typically realize object and indirect object arguments of derived nominals as in the gift of a math problem to Alexis. According to (RLP), these PPs must fall within the minimal CFC containing gift. The semantic contribution of the prepositions here is simply to help guide the conversion process to insert the right argument in the right argument position. If a nominalization subcategorizes for an object and indirect object, then a prepositional phrase headed by of typically contains the direct object, while a prepositional phrase headed by to typically contains the indirect object. The rules for the fIlling of the subject argument place are more complex. But at least it seems to be the case that if an of PP is present in the nominal, then if the nominal contains also a possessive modifIer, the translation of the latter fIlls the subject argument place. 16 Now let us apply these rules to (1.a). First note that the syntactic structure of the nominal tells us that the city may go in for one of the arguments of the verb, since the affix to the nominal passes the verb's argument structure up the tree to the minimal CFC containing the prepositional phrase. In this case the translation of the city furnishes the direct object or Theme argument for AXAeAY e-destroy(y, x).17 The translation of the city is the following partial DRS--assuming the DRT analysis of definites, on which the uniqueness presuppositions of a definite are somehow satisfIed in the context.

AU AQ

e, x city(x) e-destroy( u, x) Q(e)

One of the argument places of the translation of the N' is still unfIlled. It will be filled by the discourse referent introduced by the translation of the embedded DP with possessive case. According to our linking rules, this DP is a DP in DP nominal subject position; it should contribute a semantic argument to the subject argument place of the property or relation that is the translation of the head noun, not to the matrix verb. The translation of the army's is:

AQ

y army(y) Q(y)

The partial DRS just constructed from sthe destruction of the city is a property for the partial DRS from the annyto combine with, yielding the partial DRS:

AQ

Combining the predicative DRS and partial DRS with the process of DRS conversion defined in chapter 2, we get the following predicative DRS (K.l): Ae AU

153

x,e, y army(y) city(x) e-destroy(y, x) Q(e)

This structure now combines in the usual way with the translation of the verb phrase to get the following DRS for all of (1.a).

x city(x) e -destroy(u, x)

L

~------~~~~~~--~-~~-~~~----~-----,----.--.~--------------------

154

CHAPTER FOUR

SENTENTIAL NOMINALS

x,e,y,n

Such argument positions are labeled optional, if it is possible for them not to be realized at phonological form. {BLP) in~~.l!~~~.~.2i~~o.!!rS_~r~[~~m..illt.~t~!1.Ql?jJQ!LI!l argu!!l~I,lt.Q9.~j!iQn, if this does not conflict with the type restrictions of the predicates mwhich the semantic contribution of the nominal figures as an argument. Finally, derived nominals may have their direct object realized by the DP in specifier position. Consider, for instance,

army(y) city(x) e-destroy(y, x) bloody(e) e
(15)

This example shows how the linking rules, the DP analysis and the assumption of a null determiner are essential in the construction of a DRS translation for a nominal. The assumption .of a null determiner is also essential in giving the DP with possessive case marking its normal semantic analysis and the semantics of the entire noun phrase in a compositional way. The DRS for (1.a) is essentially an alphabetic variant of the DRS that would be derived for (1.b), and so I predict (1.a) and (1.b) to be semantically equivalent. Below is the DRS for (1.b) after the process of anaphora resolution has filled in the equation derived from it and after the temporal anaphora rules have added their conditions as described in chapter 2. Note that the predicates type the discourse referent introduced by the pronoun as an event predicate.

army(x) city(z) e-destroy(x, z) e
'Au 'AQ l--~e,,:-x~_--1 city(x) e-destroy( u , x) Q(e)

The subject Agent argument place of destroy is an optional argument place. (RLP) fills in the Agent argument place with a discourse referent x and so transforms the partial DRS derived so far into the following partial DRS.

Some process nominals do not come with a possessive modifier. In such cases the construction procedure will exploit the (RLP) assumption. The destruction of the city was bloody.

'AQ

In (13) destruction has the process reading in virtue of the predicate bloody, qut there ~ no l~icalJy',~5Qr.~§§~~.nQI11il1ill.~yJ)ject. Indeed we cannot on my analysi"s have a lexically expressed subject as a DP in possessive case together with the determiner the in a derived nominal or gerund phrase. The prediction that this must be so follows from our assumption that overt determiners in D do not assign case; only null , determiners do. But although there is no lexically expressed subject, there is evidence that sentences like (13) have a lexically unrealized SUbject, since it can be anaphorically bound as in (14). It is presumably the army that did the destroying.

x,e,y city(x) e-destroy(Y, x) Q(e)

The discourse referents introduced by (RLP) are similar to other discourse referents in that they inherit the quantificational force of the DRS structure in which they are introduced. In (13) the discourse referent x introduced into the Agent position just inherits the existential quantificational force of the DRS for the whole sentence:

I

(14)

Scipio's destruction

It appears that (15) only has the reading where Scipio is in fact the object argument of the nominalized verb. is Examples like (15) complicate our linking rules for derived ., nominals by adding an extra clause: if a nominal contains an activity verb nominalization, a Theme must be lexically realized if an Agent argument is already present. Thus, the DP in specifier position may sometimes furnish an object or Theme argument, depending on what other arguments are realized in the nominal phrase. Again the null determiner contributes the eventuality argument while (RLP) fills in the rest of the arguments. Let us see now how (RLP) interacts in these cases with the DRS construction procedure. Let us, for instance, construct the partial DRS for the nominal in (13) and (14) in two stages. We first get the following partial DRS in a manner similar to the construction procedure for (1.a) using the DP analysis, the linking rules, and the null determiner assumption:

x, z, n,e, e'

(13)

155

x,e, Y city(y) e-destroy(y, x) bloody(e)

The destruction of the city made the army very unpopUlar.

L

~--~~~~~~-~~=-=~~------P""--~-----~---------------------

156

CHAPTER FOUR

SENTENTIAL NOMINALS

Given our discussion of the correctness definition for such a DRS developed in chapter 2, my construction procedure furnishes the right results for (13). Here are some other examples showing how discourse referents introduced by (RLP) may inherit the quantificational force of the context determined by the DRS construction procedure. In (16.a), the discourse referent introduced by (RLP) assumes a universal force due to the quantificational force of never, which has scope over the subject noun phrase as well as the VP, and in (16.b) the discourse referent is bound by a generic operator.

e, x, z, u,e', n city(z) e-destroy(x , z) x =u army(ur--)_ _ _---, e'- make(

(16.a) The destruction of cities is never justified. (16.b) The destruction of wildlife typically occurs with uncontrolled development. The mechanisms of DRS construction appear to give the right predictions in both (16.a) and (16.b). Here is the DRS for (16.b), in which gen is a quantificational relation representing Krifka's (1988) generic quantifier. 19 I omit the temporal information here for simplicity. Again we use (RLP) to fill in optionally labeled argument places.

t

x,y,e wildIife(x) e-destroy(y, x)

e,

~

U,

v,e

I

unpopular(u~

-----157

I)

Curiously, discourse referents introduced by anaphoric pronouns cannot be linked in the process of anaphora resolution with discourse referents introduced by (RLP). Compare for instance,20 (17.a) Every failure of a man hurts him. (17.b) ??Every failure hurts him. where him in (17.b) is identified with the implicit subject of failure. I propose a general lexical realization constraint for propositional anaphora: discourse referents introduced by anaphoric pronouns must be anaphorically identified with discourse referents introduced by overt lexical elements. So no discourse referents introduced by (RLP) can be used in anaphora resolution.

lf

e'-occur(e) withee', e") e"-develop(u, v) uncontrolled(e") u=y

I have identified u and y above, since the agents of the destruction of the wildlife are understood to be also the agents of development. These examples show how (RLP) interacts with the principles of DRS construction. (RLP) also interacts with the process of anaphora resolution in an interesting way. The discourse referents introduced by (RLP) are similar to other discourse referents in that they may be linked anaphorically to discourse referents introduced by noun phrases other than anaphoric pronouns, like definite descriptions. (14) above is an example of this. This discourse would be uttered felicitously only in a context in which the discourse referent introduced by the defmite description the army would be anaphorically identified with some antecedently specified discourse referent. I will assume that unpopular yields a subDRS argument of make, in which the discourse referent introduced by the army figures as an argument of a condition. This will allow us to solve the anaphoric equation optionally introduced by (RLP) in the following way:

2.3

~esult~oIninals

On my analysis, result nominals are distinguished by the transformation of the argument structure of the verbal complex. This acknowledges the observation, made by Lebeaux and Abney, that !.~§l!I~.~'2..~~.~,!~,~!1~~!JfC:>__ ~~_~I!:!I~i9__drift. As for an explanation of this drift, the transformation depends on at least two semantic factors. The first is the ev~~ual!!l.!Y.£~J~1~~~5:~::~:LQy"t,!}~y_
The army's destruction of the city remained for all to see.

mr:I!'I1~1fi~T------15-8~~'='='-==~='--~--~~--~C~H-A-P-TE~R~F_O-U~R=~-~_'-----_ _ _ _~l·~·T_"-~---~--~~"~----

r ,

,

-

. :/:

i i

z,x,y,e e-destroy(y, x) effect(e, z) [remained for all to see(z)] From the lexical realization constraint for pronominal anaphora, I predict that only the effect of the destruction is available for anaphoric reference. Thus,

should strike the reader as rather ........odd. --~-",,-.~--

There is a particularly interesting argument transformation for derived norninals that chang~~.!?e type of their denotation from an eventuality,()En~i!!QiyJ
e -destroy (y, x ) effect ( e, z) Q(z) I assume that in the lexical transformation from destroy to destruction all the argument positions of the translation are labeled optional; that is, they need not be filled at the level of the syntax. Thus, we exploit (RLP) to fill these argument places in order to derive the following partial DRS for the nominal in (I.c). AQ

z, x, y,e e-destroy(y, x) effect(e, z) Q(z)

i Applying this partial DRS to the translation of the verb phrase yields the DRS. The

....

'

..

~.,~,~ ~"""

(19.a) The collapse of the Germans is a fact. (19.b) John informed Sue of Mary's departure. (19.c) A collapse of the stock market is a real possibility.

This combines with the translation of the determiner and yields the following partial DRS:

; :

'''';

2.4 Propositional and Fact Readings of Derived Nominals

I

AY AX Ae AQ f---_--=-z _ _----;

?IThe destruction remained for all to see. It had lasted for hours.

(I.c)

AYAZAXAe ~I_________~I

I

S-E-NT-ENT-I-A-L-N-O-M-IN-A-L-S---------15;---

square brackets indicate an incompletely processed condition.

Using the DRS construction procedure, I define argument transformations more precisely. Now suppose that the nominal is lexically derived from a verb
e -destroy(y ,x) effect( e, Z )

___

c~

•

The nominals in (19) !l~~~Jl.I£!X~~.9!!!-$s. To account for these, my analysis proposes a particular form of argument transformation and a particular argument transform. 22 The transform~es the derived nominal and adds .!!.!Ulf.$JU!!IW!..PJJl£!tXllL!!D abstract object that the-denvoonOri'llnannmnlpC113racterizing. I shall call it the abstract argument transforma'fioIi-:-Tfie affirtilltnnay function as an abstract argument transform. Graphically, we have Normal Translation AX!> ... , AX n , Ae r~----~

Abstract Argument Translation Ak, AXI'"'' AX n , Ae

i---::=====:::;-

1
The characterization predicate'" has already been introduced as part of the expanded DRT vocabulary of this chapter. k is a discourse referent variable of abstrasLQQiect type. The type information on discourse reIerelltsor-irrgument plaCeSTs7'arried by Coiiditions. Thus, when a discourse referent fills in the argument place indicated by k, it will be typed as an abstract entity discourse referent. In the linking rules for derived nominals, the head determiner will fill in the abstract entity argument place in the

_fh

~

.~",»

.~

CHAPTER FOUR

SENTENTIAL NOMINALS

argument transfonned translation. With this argument transfonnation and our other assumptions, we have ready-made a propositional reading of derived nominals. Let us work out the translation of (19.b). Assume t.lliU.Jllf.Q1Jn~_ill.K~.L~wq indivi~~~d a!~t as.~m~~. Thus its translation is:

following construction. The simple condition 'Mary(u)' is shorthand for the metalinguistic infonnation and external anchors, discussed in chapter 2, that names introduce.

160

'Af 'Ax 'Ay 'Ae

'Ae 'AQ [------'u::.!..,-"'k'--_ _--"1 Mary(u)

Ie - infonn (y, x, f )I

I

I

k"" \e-depart(u~

In order to convey the typing infonnation that one of its arguments is a fact, this predicative DRS must actually contain some extra conditions about that argument place. The condition charfO constrains the characterization relation, as noted in section 1. 'Az 'Ax 'Ay 'Ae

161

f---:-::----:----:---i

Q(k) An application of (RLP) now fills in the event argument-place not syntactically realized within the DP structure of the nominal. According to the definition, (RLP) must introduce a discourse referent e within the universe of the subDRS that characterizes the fact. This gives us the following partial DRS for the nominal:

e - infonn(y,x, z) char feZ ) fact(z)

'AQ

u, k Mary(u) I

We now need to specify how the nominal contributes a fact to the fact argument place of inform. Departure has the following nonnal translation on the left and abstract argument translation on the right (the predicate"" requires that the discourse being characterized is of abstract type, and I have used my abbreviation in choosing the variable k).

l

e

I

k"" e-depart(u)\ Q(k) This combines with the translation of the matrix verb to yield the DRS on the left, which we abbreviate as the one on the right using the conventions about fact discourse referents discussed in section 1:

'Ak 'Ae 'Ax

'Ae 'Ax e - depart(x )

e -depart(x )

I

Since Mary has possessive case, my syntactic assumptions imply that the nominal contains a null determiner as head, the familiar sthe. The linking rules for the abstract argument transfonnation of the nominal tell us that the discourse referent introduced by the detenniner must go into the abstract entity argument place, where the DRS constructed from the nominal will end up characterizing it. The predicative DRS above then combines with the partial DRS derived from sthe to yield this partial DRS: 'Ae 'Ax 'AQ

k

1--;1====~11 k "" Ie - depart(x )1 Q(k)

The declared discourse referent k is a generic abstract entity discourse referent. Continuing the conversion process, we combine the partial DRS for Mary to get the

v, w, u, e', f John(v) Sue(w) e'-infonn(v, w, t) Mary(u)

v, w, u, e',k John(v) Sue(w) e'-infonn(v, w, k) Mary(u)

I

k ""

l

e-depart(u)

char f (k)

e

I

e

I

f ""

e-depart(u)

fact(k)

Note that the discourse referent introduced by the determiner automatically inherits the type infonnation from the abstracted argument place in the predicative DRS. The truth conditions of the finished DRS are that John infonned Sue of the fact that Mary departed, and this is just what we want for the fact reading of (19.b). For it may be the case that Mary departed in a hurry, y~t(12,l?J.g2~.§.~not !!!!I1!Y..that Joh!l in~2.wed Su~.M...ruy!..h.uEie!L~el?arture.23 Conversely, if John infonned Sue of Mary's hurried departure, he must have infonned Sue that she departed hurriedly, not simply that she departed. Since the approach to abstract entity readings for derived nominals does not depend on the type of determiner but rather on the presence of an argument

J

~

__________

~~=-~c~

____

~

__

~=-~~~

______- - - -________

..

"~

~~----~----·----------------------------

CHAPTER FOUR

SENTENTIAL NOMINALS

transform, the nominals in (19.a) and (19.c) are predicted to have abstract entity readings.

matrix predicate is well knownrequires a pro~osition as an.argument. By the same general translation procedure'as that given for (l9.b), we come up with the following DRS for (20.a), except that the nominal refers to propositions rather than facts:

162

163

."L,-, .

v, S',p

2. 5 Remarks on Property Derived Nominals

John(v) We have so far considered derived nominals that come from or contain verbs and even verbal complexes. But t~~_.~~.!!!~.Q.!!'Q.mi,nals thatcomeJroIDJlQ.i!<£tLyes. From honest we get honesty; from good, goodness; and so on. One might also consider in the class of derived nominals, expressions like John's honesty, Sheila's goodness, etc. '~'""'~'''-'''='''''~''''''..-.,,~....- .•~.-.''''""'''''''''''''',.,"",'.-.- .... ~., •• ,,'.-.~"'''.~''''.~. I It would be rather astonishing if such nominals acted in a completely different manner \ from the sort of nominals we are considering. The analysis of derived nominals carries over to the nominalizations involving abstract nouns like honesty, goodness, and the like. Such nouns traditionally have been thought to pick out universals or properties. To the noun honesty should correspond something like the property AX honest(x). But honesty does not just denote this property, since sometimes the argument of the property may be filled in-e.g., by the denotation of a DP in possessive case as in (20.a-b). (20.a) John's honesty is well-known. (20.b) John's honesty l~ he realized he would never be caught cheating the customers. In (20.b2..!E~::s."g.Qll~§tx,£tYltQ!:~~~~,§.t~te ~le in (20.a) it denotes a proposition or some abstract object. The analysis of derived nominals, and in particular the use of the null determiner hypothesis and~~~!!!:.ac~,~~I!EJ~!!!~~!?~~!!?n, predict that I both an eventuality and a fact reading are possible for such nominals as in (20). The tra~~!"~?!!.'?~!l, __i!.!!,,p.E~9.!~a!!:y~ .P..R§,_~iJh,J.W.\Lar,g!JJ!l5;n1.,pla.c~s~.:a,_.s.@te argument place aI),d ~ipdividual arg!!~~tP!1!~e.

AS Au I

I

I s -honest(u ) I

Once again my syntactic assumptions imply that there must be a lexically null determiner to assign case to the DP in specifier position, John. The translation of sthe, together with the standard argument structure for honest, give this DRS for (20.b). u,s John(u) s-honest(u) [s lasted only until ...] The DRS for (20.a) indicates that the nominal has a propositional interpretation. The

l~ !

I

p""

s

I

l s-honest(v)J

s'-well-known(p)

3. OF-ING GERUND PHRASES AND BARE NOMINALS Of-ing gerund constructions or phrases are phrases like Fred's shooting of Bill and his loving of Mary. They contain gerunds like shooting as well as possessive and prepositIonal phrase modifiers. This form of gerund phrase is distinguished syntactically from two others--in particular the POSS-ing and ACC-ing gerund phrases to be discussed in the next chapter. The of-ing gerund combines well with determiners, accepts adjectival modifiers, and submits to pluralization (a shooting of Bill, many shootings of Bill, the violent shooting of Bill) but POSS-ing and ACCing gerund phrases do not (*a shooting Bill, *many shootings Bill, *Fred's violent shooting Bill). Of-ing gerunds also fail to have tense markers. These features distinguish of-ing gerund nominal constructions not only from other gerund nominals but also from the other abstract nominals like infinitivals and that clauses. Of-ing ) gerund phrases closel.Y.!~~~
3.1 Analysis of of-ing Gerund Phrases

The syntax of of-ing gerunds closely resembles that of derived process nominals. The affix -ing, like the affix -ion, has the lexical function of turning a verbal form into a nominal form. Some have argued that of-ing gerunds are deverbalizations of V', assuming again that PPs headed by of furnish internal arguments. 24 However, insertion of material between the PP and the gerund is fine and so casts doubt on the idea that the of phrase and the gerund form a constituent: (21.a) The unveiling by the President of his new budget was greeted with

164

CHAPTER FOUR

SENTENTIAL NOMINALS

guffaws by Congressmen from both sides of the aisle. (2l.b) The flogging by the guards of the prisoners was overlooked by the committee. I will assign the gerund phrase the same general syntactic structure as that for derived norninals.

I

165

rules for argument places in of-ing gerunds are quite sensitive to the 1 structure of the whole gerund phrase. Let us translate our earlier example (2.a) of an of-ing gerund phrase: Fred's deliberate shooting of Bill led to his imprisonment. We begin with almost the same syntactic structure for (2.a) as (l.a): (2.a)

DP

~

DP

DP

D'

~

A

Fred's

DA MP

N'

/~

A+ +A affix

I

n)

PP

V

The translation of the gerund will be a predicative DRS that is identical to the translation of the verb stem, and it will have the same argument structure. This argument structure is either preserved by the affix or altered according to one systematic pattern to yield a manner or event property reading for the nominal (see 22.b below).25 The argument structure percolates up the tree determining in conjunction with linking rules the semantic effects of various PPs that it Ccommands. The linking rules for of-ing gerund phrases are largely familiar with the following exception: when of-ing gerund phrases are argument preserving, the discourse referent contributed by the head determiner either fills in the eventuality argument place of the gerund or an argument place that is typed for a property. Ofing gerunds do not have saturated abstract entity readings. When an of-ing gerund has both a DP in specifier position and an of PP, then the possessive modifier furnishes the subject argument of the gerundized verb, while the of PP will yield an object or theme arguments. When no of PP is present, a DP in specifier position may contribute either a subject or an object argument: (22.a) John's shooting led to his death. (22.b) John's shooting was rather poor on the hunt last week.

I Without the presence of DPs in specifier positions, of PPs also may contribute either , a subject or an object argument: (23.a) John witnessed the spanking of Frank (contributes an object) (23.b) John applauded the elegant playing of the visiting team.

D'

~\

led to his imprisonment

N'

~ N(+A)

6

I

of Bill

destroying (+A) This postulated syntactic structure predicts the adjectival modification of of -ing gerunds. The DP in specifier position Fred yields on translation a partial DRS of a familiar sort. The discourse referent introduced by Fred fills in the subject argument place of the gerund's translation. The syntactic structure for (2.a) requires that the translation of the gerund have the same argument structure as the verb has--to wit:

A.y I.e A.xl---_ _ _-l e -shoot(x, y Once again the DP analysis and my syntactic assumptions entail that a lexically null determiner in head position assigns case to the DP Fred's. After combining the DP Bill's translation with the predicative DRS, we combine the result with the translation of the null determiner. This yields a partial DRS of the following form:

Ax A.Q

u, e e-shoot~ ,u)

Bill(u) Q(e)

This structure combines with the translation of the possessive noun phrase to yield the expected partial DRS.

------------------------,---

SENTENTIAL NOMINALS

A.Q

v,u,e Fred(v) e-shoot(v, u) Bill(u)

my syntactic analysis.

3.2 The Aspectual Force of -ing in Of-ing Gerunds

Q(e)

~ll t?is is farni!iar from the previous section on derived nominals. Once again the predic~tIve DRS dictates that the type of the discourse referent introduced by the null determmer must be an event. It is now a routine matter to combine this structure with

the VP to get a DRS for (2.a): v, U, e, Z, x, e', n

Fred(v) e-shoot(v, u) Bill(u) z's imprisonment(x) z=u e'-lead to(e, x) e'
A surprising feature of of-ing gerund constructions is that on an event reading of a gerund construction, the nominalizing affix makes an aspectual and semantic contribution to the information content of the nominal. This calls for a new assumption about the interpretation of -ing. -ing', the interpretation of[-ingD, is a partial function on eventuality types into event types: if cp is an event type E, then [ingD(cp) is an activity type, if an activity type naturally correlated with E (like the activity involved in crossing a street) exists; otherwise, [-ingD(cp) is undefined. 27 Also [-ingD determines a linking rule: the head of the nominal construction (this is a D in of-ing gerunds and an I, as we shall see, in POSS-ing and ACC-ing gerunds) must fill in the activity argument place. There are two consequences of this interpretation of [-ingD. First, it implies that of-ing gerunds must denote eventualities. Second, it predicts that s~6 coiTIpTeXes1liYnot1laVeoT-mg ~ruiial'orms, sil-ice states have'weli~defmed, correiiiie!d~~ti~iti~s:' i~' th;"p~~wes~r;e"il{ood,ringD. "",,,,,,,',",,, seems to have a similar effect. 2 State types do not combine with the progressive form; nor does [-ingD combine with a state type in the of-ing gerund construction.

ao-ii"ot

--.-"-'.,~'"'""""""""'""",','"".""-

L

The. construction procedure yields essentially the same DRS for (2.a) as for our earlIer (2.b) repeated here: Fred shot Bill, and that led to his imprisonment. The theory thus predicts an equivalence in meaning of (2.a) and (2.b). The DRS construction procedure for of-ing gerunds is almost identical to that for derived, event nominals. The DRS for (2.b) differs from that for (2.a) only because of the anaphoric equation introduced by the pronoun and because of the tense coordination equation that will insist that the event of shooting is not after the event of lea~ing to. imprisonment. But tense coordination is important. The predicted eqUIvalence between (2.a) and (2.b) follows only because we have some lexical information about one event leading to another. Such events must have a definite temporal sequence; the one leading must precede the one which is brought about. (2.c),and (2.d), on the other hand, (2.c) (2.d)

Bill's hitting of that policeman will land him in prison. Bill hit that policeman. It will land him in prison.

are not synonymous, though (2.d) entails (2.c). The reason for this is clear, once we look at the .teI?poral info.nnation conveyed by each discourse. (2.d) is true only if the event of hIttmg the polIceman takes place earlier than the speech time on a DR~heoretic analysis of tense. 26 The analysis of the nominal (2.c), however, carries with It no temporal information. The nominal itself does not yield any information about when the event it introduces must take place. There is no temporal information about the.connecti?n between events that is grammatically expressed in of-ing gerunds or

denve~ normn~s. ~njs..contai.nedin..te.infl\f.£liQIl'"nQ"d~H~L!lJieme[lce. ~ut !!.~~~r.()f~~~_~9.~~~g1:iQnsnot(lerived.nominals"containinflectional,"elementIi~QP

167

"8"""'''''"·""~·'''"'"=·ww.'"'',

(24.a) ??John's knowing of calculus (24.b) ??John's loving of Mary '- b" L ~ (24.c) ??John's lacking of a car

e..~~( J/~ ~':.J \y.~'): "J

It is difficult to interpret these nominals; no process or activity is associated with the

state of knowledge or the state of love. This is not to saYJh~L~.9.!illQt reieuo.the states ~~~~_lan..1!!~g~!",».!!Ji!ls..~l!:(L()i",~jpg,ph!!l~,e~,,_"W!;.JJ~~.deriyeO.,Qominals. There is another interesting interaction between the aspectual force of [-ingD and the type of eventuality. When one applies [-ingD to telic eventuality types like achievements and accomplishments, one does not denote the completed event but rather a preparatory phase of it; the preparatory phase is the naturally correlated activity. The completion's existence is a default inference, which one can assume to exist unless this is inconsistent with information in the text. This lies at the heart of the so called imperfective paradox,29 but it also manifests itself wiih"noITiliia:rs:-'Une defallitimplication of an of-ing gerund that has an achievement or accomplishment denoting verbal complex and refer to the completion. But it is also important to notice that the reference to the completed event can also fail when the context warrants.(25.a) The launching of the space shuttle occurred at 10:40 a.m.

may"exploit'the

(25.b) The launching of the space shuttle was aborted because of a computer malfunction. ~ (25.c) John's crossing the street caused him to run into Jones. (25.d) John's crossing the street was cut short by his being run over by a truck. _ _ _ , __ ,.,'"'' .• .,_,r .~

~~._~

I

SENTENTIAL NOMINALS (25.e) Sheila's drinking of wine took place in the Weinstube Trauble. As we might also guess from studying the behavior of progressives--PROG(
I

3.3 Bare Gerunds and Nominals

,! Gerunds without modifiers or PPs, also known as bare gerund phrases, and the . similar bare derived nominals are difficult to analyze. But using (RLP) they tum out to be quite similar to "clothed" nominals. (26.a) Unsafe flying caused the aircraft to crash. (26.b) Unsafe flying is dangerous. (27) Des~?.!i~I!,"~~_~i~!S~. (26.a-b) have no lexically expressed arguments or determiners at all--hence the name \ of "bare gerund." Q.Q,_a:..b.)_artLexarnpl~s--.of-ot.Jng.,g.elluN,__.£2!1§!!:':l£t!,?tI~_"~nd not ~OS~:JEg Ot.b.1:C:iag,,~D.ID.d'&'.~.~y"&.!:<"'9t~th~ta9i«'£!i¥aLJ:no.difiC,i!timLpresent. The nominals in (26) have the same syntactic structure as normal of-ing constructions, while (27) has the same syntactic structure as a normal derived nominal. Bare gt{m!l.~~!.ill!§..hl!~~~~qmgs. (26.a) for instance may have an existential reading--i.e., someone's unsafe flying aircraft x caused x to crash.31 It max. ~2. ha~C#lm~.r~!!di»....g;__UllSafe,.ilying"typicAUy,_w..a::Ub.t<~gl:m~~Qf th~~ r aft9JasAS<1· (:?2.,g~2.1~7thav_~~~~,.2.'E!~~~}".~~~~~~.!!:~~~~:_ ,t!:P.!,~~,,~~ts of ( £ryin~~~.£~9~g,~!2?~,~~~"!~~~~!!stJ_~f,Q~!tt9.£,tiQR,,~e_,,wj5(~_~. But they may also have uJlly~[s.al.xeadings--e.g., all acts of destruction are wicked. A sentence like (28) has a~_r.~~ding. :

an:c

(28)

Extermination was the general's favorite method of quelling a discontented populace.

I Method identifies a way of acting or an event type, and presumably this forces

~

"

extennination to denote some sort of unsaturated abstract entity.

(26.a) has a straightforward translation with the help of (RLP). The Agent and Theme arguments ~rt]x-i!?g~l!!:~_QPtional. Accordingly, (RLP) fills in these"argiiffient places·o:filieo·semantlc translation of the gerund during the translation process, if the context permits the nominal to denote a saturated entity. I also assume that the lexically null determiner sthe exists in of-ing gerund constructions. This determiner introduces a discourse referent that fills in the event argument place of the translation , Ii

!i

j ,""',ill,l

'i l ! ill !I::,I

till!:

169

of flying. Without any specifier in nominal subject position and without any mOdal) operator, we predict the quantificational force of the DRS context to be existential in the DRS derived from (26.a), which gives us the right truth conditions for (26.a). This analysis also predicts that we can anaphorically refer to the unsafe flying event in ) '---,-..-- .. --, ----",'" subs~calI1IiS,course:-'-'-------'-'-----""'-

(29)

---"--.-.,"-~,-,,,--,-.~-------.---,-~-

Unsafe flying caused the aircraft to crash. It was a typical fighter jock ) stunt.

When specifiers occur in argument positions with gerunds or in the determiner position, the analysis predicts that the quantificational force of the DRS context will affect the interpretation of the sentential nominal. (30)

Every killing is an offense against God.

In (30) the truth conditional effect of the DRS construction procedure is a universal quantification over the discourse referents introduced by (RLP) in subject (Agent) and object (Patient) argument places as well as a universal quantification over the event introduced by killing. A proper treatment of (30) simply falls out of the 1 construction procedure together with a use of (RLP). Applying the partial DRS for every to killing gives us the following predicative DRS.

"Ax 'Ay 'AQ

--

~ -@ill

(RLP) fills in the rest of the argument places to give us the following partial DRS which yields intuitively the right truth conditions for (42.a).

u, e, v e-kill(u, v)

I

r====1

I - ~

..J

The generic reading of (26.b) is also easily represented if we assume with Krifka ( that a lexically unrealized, generic quantifier occupies the D position. Applying the partial DRS for the generic quantifier and using (RLP) on the translation of unsafe flying, we get:

AQ

x, y,e e-fly(x, y) , unsafe(e)


---------;1;-:;7-;:;:-O~==~~~~---':C::::H::-A:-::PTE:::::::::::-R-:F::-:::O::-U=R~~-----~---~-,t-r-'';''_''~--~"-~-----SE-NT-E-NT-IA-L-N-O-M-IN-A-L-S----------~~~-------

When combined with the predicative DRS for the VP of (26.b), the resulting DRS indicates that (26.b) is true just in case events of anyone's flying unsafely are typically dangerous. I As (28) indicates there are also property readings for bare nominals at least. How _' do we derive those? We must exploit an as yet unused condition in (RLP), Part (B). I The VP of (28) selects a concept as an argument; this concept is according to the VP identified with the general's favorite method. Concepts are abstract objects, and so the contribution of the subject DP in (28) must be a concept discourse referent characterized in some way by extennination. The nominal extennination like other nominals has an abstract argument translation whose abstract entity argument place is filled in by the discourse referent introduced by the lexically unrealized determiner, sthe, in the head position of the nominal. Since the predicate of the nominal takes a concept or property as an argument, there is a translation of the nominal on which (RLP) does not fill all the argument places of the nominal's translation. Let us look at the completely unsaturated reading. By part (B) of (RLP), if the argument places of the nominal are unfIlled, the A-operators and their arguments must be attached to the minimal DRS-component containing the translation of extennination. Part (B) of (RLP) in fact type shifts the denotation of the nominal, since the result of exploiting (RLP) characterizes the abstract argument place of the nominal's translation by an unsaturated structure and hence types that argument place as a property argument place. Consequently, we have the following partial DRS for the nominal in (28), in which the normal translation for extennination characterizes the discourse referent introduced by sthe. AP

J

This concludes my treatment of the nominals that can straightforwardly denote eventualities. The translation begins with a uniform syntax for all of-ing gerund constructions and treats bare gerunds, gerunds ~~~~~ifie~p~~.!ions, and gerunds with lexically expressed determiners in the head D position in a uniform way. Derived nomrriiifsnave-tworumosn:aen:ncrusyntacncstrUciiifes::a:rrfenn'in:,iiTy in the type of affixes used. Using (RLP), the linking rules, uniform interpretations of affixes, four types of argument transforms--the effect transform, the product transform, the manner transform, and the abstract argument transform--and the assumption of a null determiner sthe, the translation procedure makes sense of the diverse truth conditional readings and anaphoric properties of gerund and derived nominals in a compositional way. Of-ing g~~!l~_ap_~9:~EY~_~2.!!!i-.!1_~:Lp!!ra~~~_~~~~a.! ) }I:" ,€,~", a characteris.!ic ~blgYl!Y,QLQl~!1Y.:_~~!l~I!g~B2~!1,l!lS. They have a "chameleonic" character, in that they may denote different sorts of saturated abstract objects, eventuality types or eventualities.32

4. THAT CLAUSES The most straightforward type of pure abstract nominal construction is the that clause, syntactically an example of the CP category. Pure abstract nominals denote only abstract entities, not eventualities. That clauses may occur on their own, as subjects of predications, as complements to attitude verbs, and as elements in N CP constructions like the thought that Mary is wise. One desideratum for an analysis is) that that clauses be treated uniformly throughout these constructions, even though they have widely varying semantic interpretations.

c

c'"

AY Ae AX

--------1

[-I

Ie -extermination (x, y)

4.1 That Clauses Differ from DPs

P[c] Converting this partial DRS with the VP's translation, a DRS results that determines (28) to be true just in case the event type of exterminating is the general's favorite method. (RLP) thus yields an unsaturated, property reading when selectional restrictions require it. If an event nominal supplies an argument to an event predicate, however, then the property reading will be predicted to be unavailable, because one cannot apply an eventuality predicate to an abstract object. The typing restrictions on the discourse referent introduced by the nominal will not be satisfiable. My analysis of -ingpredicts that bare of-ing gerunds also have property readings. Speaker's judgments vary in this area, however. Some but not all find the examples in (31) fine, both of which would require a property reading of the nominal: (31.a) Vigorous walking is what Amanda likes to do. (31.b) Slow skiing in the bumps is what Paul likes to do.

That clauses that occur within propositional attitude contexts are already discussed in chapter 3. There they introduce subDRSs as arguments to attitude predicates. I argued that that clauses had a particular interpretation that distinguished them from ordinary DPs. In this section, I will continue with that approach. The decision to differentiate that clauses and DPs requires more discussion in this more general context; it also receives additional plausibility. That clauses do not have the same distribution or enter into the same constructions as DPs. In particular, the noun that clause construction is not an N DP construction or a DP DP construction. Suppose that that clauses were in fact just DPs. If that clauses were noun phrases, then the most plausible analysis of the the N that S construction would be that of Delacruz (1976), who treats the that clause like an appositive. But the appositive construction is symmetric, while clearly the noun that clause construction is not: (32.a) John, a friend, took me home last night. (32.b) A friend, John, took me home last night.

172

CHAPTER FOUR

(32.c) The thought that Fred is insane has crossed my mind. (32.d) *That Fred is insane, the thought, has crossed my mind. Further, the mark of a DP in DRT is that it introduces a discourse referent and a condition on that discourse referent. But that clauses may combine in the noun complement construction with NPs which themselves generate discourse referents of different and incompatible types. One may speak of the fact that Mary is wise, the possibility that Mary is wise, the thought that Mary is wise. The very same that ( clause may characterize a wide variety of abstract entities--thoughts, propositions, , facts, possibilities, and the like. If the typology of chapter 1 is right, then these different NPs give rise to different and incompatible types of discourse referents. That clauses put conditions on these discourse referents; they do not introduce yet another type of discourse referent to be identified with different incompatible types. This furnishes yet another argument for distinguishing that clauses from DPs. On my approach, a that clause introduces a DRS, not a discourse referent. , Nevertheless, this DRS has an ontological status. It may be anaphorically referred to, as we will see in chapter 6. It can also be quantified over or play the role of a constant in the following pattern of valid quantificational patterns of reasoning: John believes everything that Mary believes. Mary believes that Susan is smart. So John believes that Susan is smart.

SENTENTIAL NOMINALS

construction. These head nouns may be either nominals derived from various clausally complemented verbs--in particular attitude verbs, or abstract nouns like fact, truth, falsity, possibility, etc. I consider the attitudinal, derived nominals first. Derived nominals like belief, knowledge, doubt, claim, etc., as we have seen, have an argument structure. Consider for instance, (33.a) The belief that Mary had gotten an A on the test made John behave rudely toward her. (33.b) The knowledge that Sam was an idiot did not alter Mary's feelings toward him. (33.c) The proof that Fermat's last theorem was false made Susan famous. In (33.a-b), the attitude verbs have subjects. The subject of believe, the believer, is John in (33.a); the knower in (33.b) is Mary; the theorem prover in (33.c) is Susan-even the nominal proof appears to have a subject argument. None of the examples in (33) strike one intuitively as result nominals; they intuitively denote states, but not result states. So the argument structure of the verb should percolate up the tree. The syntactic analysis of such sentences follows that for derived nominals--the only difference being that the NP dominates a CPo Here is, for example, the syntactic structure for (33.a). IP

1~6

r

This argument has the form of a syllogism whose first premise quantifies over the structures introduced by that clauses. The second premise indicates that the structure introduced by the that clause serves as an instance of the antecedent of the first premise. I shall interpret such quantification referentially and assume that DRSs are objects in the domain of a DRT model and that quantifiers like everything may range over them. So it makes sense to think of DRSs as denoting entities in the model-themselves.

D'

~ NP

I the

Let us now look at some that clause constructions in more detail. The translation of that clauses is already familiar from chapter 3. They introduce partial DRSs of the following form: AKAP~

~ A more complex construction involving that clauses is the N CP construction. The way in which the subDRS introduced by the that clause is incorporated into a common noun phrase denotation depends on the type of head noun in the N CP

made John behave rudely toward her

I N' (+n, -v)

N~CP I

4.2 N'-CP Constructions

173

believe(+n, -v)

I

C'

~IP

I /~ that Mary had gotten an A on the test Given this syntactic structure for (33.a), the noun complement structure readily translates into a DRS structure. The CP will yield a partial DRS, where again the square brackets indicate that the conditions they enclose are not fully processed.

(S34)

AP

u,el

P(

)

Mary(u) [el- got an A. .. (u)] This now combines with the familiar translation of believe, filling the complement argument place of the condition to yield the following predicative DRS:

AS AX S - believe( X

) u,el Mary(u) [el- got an A. .. (u)]

The result is a familiar looking predicative DRS for the NP inside the DP. The translation of determiner the will supply one argument, (RLP) the other. The derived nominal is argument structure preserving, so the fills in the eventuality argument slot It is possible to anaphorically identify the discourse referent introduced under (RLP) with one introduced by a definite, and I do so here. With the translation of the VP and the choice of appropriate antecedent for the discourse referent introduced by (RLP), the following DRS for (33.a) results: s, x, v

x=v s-believe(x, f----=u,-,e:..!I_ _ _---j Mary(u) el- [got an A... (u)] John(v) [s made v behave rudely toward her] This translation gives the intuitively right truth conditions for (33.a); it implies that John has the belief and that it is his state of belief that has the causal efficacy. That the state rather than the proposition has causal efficacy is what is also wanted in view of the discussion of such sentences in chapter 1. An N' CP construction with an abstract noun as head is exemplified in (34):. (34)

175

SENTENTIAL NOMINALS

CHAPTER FOUR

174

The fact that Mary is wise reflects well on her teachers.

The most obvious syntactic construction rules would attach the CP to the N' in the following way:

~

D'

~

~e

A

reflects well on her teachers

I

lP

fact

~IP

~at

6

Mary is wise

Abstract nouns like fact, truth, etc., must have an optionally label~d characterization argument place, since they may take that clauses or other sentenu~ nominals that characterize abstract entities like facts or propositions. On thIS assumption, the translation of fact would introduce a characterization co~dition with one argument place for the discourse referent introduced by the detern~mer. and the other for the contribution of the complement if it exists. The contrlbutIOn of a complement of an abstract noun will be either a subDRS that characteri~es the discourse referent introduced by the determiner in noun complement construcuons or a discourse referent characterized itself by a DRS. Here is the general type of predicative DRS for abstract nouns:

e

Here k is an abstract entity discourse referent, while ranges over DR-theoretic structures or abstract discourse referents. 33 The head noun of N' CP constructions often dictates what type of abstract object is involved. Some nouns may ch~acteri~e the discourse referent as propositional; other nouns like fact subcategonze theIr discourse referent arguments to be of fact type. . Now we are ready to interpret (34). The N CP construction yields the followmg predicative DRS. The head noun fact has typed its discourse referent argument as factive. Once again, fis a fact discourse referent variable that is shorthand for type information encoded as conditions in the predicative DRS.34

----------------------------------

176

CHAPTER FOUR

AI

fact(f) u,

f""

SI

Mru:y(u) SI- wlse(u) This predicative DRS now combines with the translation of the determiner the to yield the following partial DRS, in which the discourse referent introduced by the determiner inherits the type restrictions in the predicative DRS.

SENTENTIAL NOMINALS

Since true and false take propositions as arguments, the nominals in (35) must denote propositions. The examples in (35) are instances of argument transforming nominals. The head determiner sthe in (35.b) simply fills in the proposition argument place of the nominal, and (RLP) fills in the state argument place. (35.a) is an example in which the argument structure of the nominal is transformed by means of a version of the abstract argument transform applied to abstract nouns and attitude verb nominals. This adds an optional characterization argument to the translation of belief:

AX AP Ax AS

r-------j

s - believe( x, p) p""K

f

c1aim(f)

f""

I

u, SI Mary(u) wise(u)

SI-

177

The complement fills in the characterization argument, and the head determiner sthe fills in the proposition argument place. On the other hand, the theory predicts that since of-ing gerund phrases are argument preserving unless they have property readings, they do not license such propositional readings.

Q(f) Conversion of the partial DRS above with the predicative DRS formed from the VP of (34) now produces a DRS that says that it is the fact itself, not some associated state as in (33.a), that reflects well on Mary's teachers.

i

!

f fact(f)

f""

U, SI

Mary(u) wise(u)

SI-

[reflects well on her teachers(f)] These seem to be the right truth conditions for (34). Using ideas about argument transformations from result nominals, (RLP) and a well-supported syntactic analysis of noun complement constructions, the construction procedure shows how a noun complement construction may in some cases, e.g. (33.a), contribute a state as an argument to the matrix verb and in other cases, e.g. (34), a fact or a proposition. The linking rules and argument transformations for derived nominals and of-ing gerunds prove themselves useful in connection with that clauses too. Derived nominals can have altered argument structures; attitudinal derived nominals may have a particular propositional reading on which the argument denoted by the nominal is the subDRS introduced by the that clause or simply by its propositional argument. Thus, it is felicitous to say: (35.a) John's belief that Mary will leave him is true. (35.b) All of John's beliefs are false.

J

(36.a) *John's uttering that Mary loves him is true. (36.b) ??Samantha believes every one of Mary's mutterings. How does my analysis of thatc1ause constructions fare on the desiderata? It does not predict the synonymy of (5.a) and (5.b), repeated below: (5.a) (5.b)

Mary doubted that John was unhappy. John was unhappy. Mary doubted that.

The analysis also predicts that noun complement constructions whose heads are abstract nouns like fact, proposition, or truth only take the as a determiner.3 5 (37.a) # A fact that Mary is wise (37.b) # Many truths that Mary is wise (37 .c) # Every fact that Mary is wise The reason why this behavior is predicted is that the that clause in the noun complement construction uniquely characterizes the abstract entity discourse referent that is the other argument of the abstract noun. Where the head noun of the noun complement construction has no other arguments except these, determiners other than the will be misleading at best--as in the case of (37.a) or (37.c), in which the use of the indefinite or every has the implicature that there are more than one proposition or fact. Plural determiners, on the other hand, presuppose that their NPs are plural and plural NPs must denote groups of more than one member; thus (37.b) is completely incoherent.

_,.---------~~~~=~--~-~~-~~~----------"~P~--~'--'-~-~---------------------

178

CHAPTER FOUR

SENTENTIAL NOMINALS

4.3 That Clause Constructions, Factive Presuppositions, and Individual Anaphora

referents introduced by the processing of the complement clause or nominal into a subordinate DRS be entered into the main DRS, or in as superordinate a DRS as is possible within the bounds of consistency in a further stage of processing. 36 The same copying rule should be used on the subDRSs that are derived from the processing of these nominals as is used on those derived from factive verb constructions. Similarly a subDRS that characterizes the argument of the predicate fact should also be treated with the copying rule. As an example of the treatment of factive presuppositions on nominals, consider (38.c). Here first is the DRS for (38.c) without the additional processing of the factive presupposition of know:

The DRT analysis of noun complement constructions also has certain implications for individual anaphora. This confirms the adequacy of our construction rules with some different data. Consider the following examples. (38.a) ?The mistaken belief that someonej had tried to climb the mountain in a blinding snowstorm stopped the mountaineers from trying to rescue himj. (38.b) The fact that a manj had tried to climb the mountain in a blinding snowstorm did not stop the mountaineers from trying to rescue himj. (38.c) The knowledge that some bOyj kissed her at the party didn't help Mary recognize himj in chemistry class the next day. (38.a) is predicted to be bad by DRT when the quantifier someone has narrow scope with respect to the belief context. Let us see why. I abbreviate the embedded DRS as kl and for simplicity I will not process the VP except for the pronoun; I will assume that the discourse referent for the pronoun is declared in the principal DRS. U,X,z,s false(kl) s-believe(U,1' - - - = x - - - - - - - - - , I ) person(x) [x try to climb the mountain ... ]

I

I

mountaineers(X) [s did not stop X from trying to rescue z] z=? U=X The intended discourse referent antecedent for z, x, is inaccessible to z and so the discourse is predicted to be bad. Syntactically and structurally, (38.b-c) appear to be similar to (38.a); but they are acceptable, while (38.a) is not. The crucial difference is that (38.b-c) involve factive predicates. An explanation of the anaphoric behavior in such examples depends on a treatment of factive presuppositions. Factive verbs like know and regret presuppose the truth of their complements. Nominalizations of factive verbs yield the same predicate of DRSs as the verbs and so should inherit the factive characteristics of the verbal forms with which they are associated. So the knowledge that cp, John's regret that cp and Mary's knowledge of the proposition that cp all presuppose cpo The abstract noun fact also presupposes the truth of its complement or argument; the semantics of fact dictate that the noun introduces a typing predicate, 'U:possibility(k) and a factive presupposition that the DRS characterizing the possibility is true. DRT builds these presuppositions into the construction rules for treating factive expressions by requiring that alphabetic variants of the conditions and discourse

179

u, x, s, Zl u=x s-know (u, I--_-'-v'-'z""--"e"-"w'-------J boy(v) e-kiss(v, z) z=u party(w) eatw [s did not help x recognize Zl ...] Mary(x) Zl =? This DRS does not provide a suitable antecedent discourse referent for z" the discourse referent introduced by the pronoun him. With the processing of the factive presupposition, however, an antecedent becomes available for the pronoun.

u=x s-know(u,

I--_v-,-,_z,,-e--,-,_w_-l

) boy(v) e-kiss(v, z) z=u party(w) eatw [s did not help x recocgnize Zl ... ] Mary(x) Zl =VI bOY(VI) el-kiss(v" Z2) Z2 = u Party(WI)

el atwI This treatment of factive presuppositions thus predicts that (38.b) and (38.c) are acceptable.

--------------------~""~--~-----""

180

CHAPTER FOUR

5. MORE ABSTRACf NOMINALS: INFINITIV ALS AND PROJECTIVE PROPOSITIONS Infinitival phrases are another instance of the category CP.37 Like that clauses, for infinitivals combine with NPs in the noun complement construction, or they may stand on their own as complements to various attitude verbs or in other contexts. But they do not combine with paradigmatically propositional contexts.

SENTENTIAL NOMINALS DP

DP~D'

Fr~

~NP

~N'

N~CP I desire

(39.a) Fred's desire for Frank to please Sam is encouraging. (39.b) For Frank to please Sam will be difficult. (39.c) *For Fred to shoot Bill is true (a fact, a claim I would not have made). When combined with particular verb nominalizations, for infinitivals appear to have the same semantic function as that clauses do; they characterize saturated, propositionlike entities. But infinitivals also differ in several important ways from that clauses. First, there are some well-known distributional differences between for infinitivals and that clauses as complements to attitude verbs; that clauses with indicative mood don't combine with equi verbs like want and desire, but for infinitival phrases do. On the other hand, forinfinitivals don't combine with propositional verbs like believe or predicates like is true, while that clauses of course do. An infinitival is felicitous as a complement in many contexts in which that clauses in subjunctive mood are felicitous. This limits infinitivals to complements of those attitude verbs which I have called projective attitude verbs (these include buletic, permission, intentional, and rogative verbs), complements of modal adjectives or adjectives morphologically derived from projective attitude verbs, and complements of NPs whose heads nominalize a projective attitude verb or modal adjective.

5.1 Analysis of Infinitivals

I follow the standard GB syntax for infinitivals. For infinitivals are an instance of the category CPo I will take to as part of the inflection node I; for is a complementizer, needed in English to be sure that the subject of the infinitival receives case. The infmitival in (39.a) thus has the following syntactic structure:

181

'-... C'

~

.........-c for

- IP

DP~I'

I

Frank

I-----------VP I

~

to please Sam

The semantic translation of this construction proceeds along the same lines as the one for that clauses; since the tree for (39.a) is structurally similar to the syntactic analysis of (33.a), the construction procedure should proceed similarly. The principal difference concerns the translation of the for infinitival itself. It is this:

A.P I~======;-I

I x,e, y I P (* Frank(x) ) Sam(y) e- please(x, y)

* is introduced by the forcomplementizer, and it carries the information that such a structure characterizes a projective proposition of some kind. As there are many sorts of projective propositions, the surrounding context, in particular the predicate introduced by the attitude verb, must determine exactly what sort of projective proposition is being characterized, just as the head noun an N'-CP construction with a that clause determines what sort of entity the that clause characterizes. In (39.a), for instance, the for infinitival characterizes a desire, as is made evident from the head noun of the noun complement construction. Thus, the head of the construction determines * to be a function from DRSs to objects of desire; I will denote this function with the symbol W. The semantic translation for the whole DP then is:

A.Q

u,s Fred(u) I) s-desire(u, W I x, e, y Frank(x) Sam(y) e- please(x, y) Q(s)

This translation predicts that (39.a) will be true just in case the state of Fred's desiring

182

183

CHAPTER FOUR

SENTENTIAL NOMINALS

Frank to please Sam is encouraging. These are intuitively the right truth conditions. It is not the abstract proposition that is encouraging, nor is it merely the fact that Fred and the projective proposition are related in some way. Rather it is the fact that Fred is in the state of desiring that projective proposition that is encouraging. In another context, the translation of the infinitival might differ. Consider, for instance,

analyses of infinitivals, but there is considerable evidence for the syntactic assumption. 40 Further, there are several arguments that indicate that forinfinitivals must be treated as a semantic as well as syntactic unit. First, for infinitivals can be quantified over as in (42.a) or anaphorically referred to as in (42.b). The semantic object quantified over in (42.a) is a complete proposition--it is the proposition identified by the that clause that Fred shoot Bill. The noun phrase that possibility has as antecedent the entire for infinitival, which also expresses a complete proposition.

(40)

Fred's permission for Frank to use his airplane did not extend to using it for drug running.

The syntactic structure of (40) is almost identical to that of (39.a), and the contribution of the CP to the interpretation of the subject noun phrase is identical to that given in the DRS above. But because the head of the subject DP is a nominalization of permit, a different projective proposition is determined. In (40) we have a projective proposition that is the object of attitudes of permission and prohibition. I denote such objects of permission and prohibition with a DRS and an operator P--P is also a function from DRSs to projective propositions. The contents of objects of attitudes of prohibition and permission differ from the contents of desires. A set of propositions WK is determined relative to a set of beliefs; each member of the set contains doxastically possible worlds and represents a most desirable realization of K. PK is a set of propositions determined relative to a set of prohibitions; each member of PK represents a permissible outcome in which K is realized. The projective semantics is useful in getting certain inference patterns validated here that are not valid for non-projective contexts. 38 The contribution of the infinitival nominal is to characterize outcomes, but such nominals do not fully specify the sort of outcomes being characterized. The examples discussed so far all have heads that are deverbalizations of projective attitude verbs. But there are also abstract nouns that are heads of the noun complement construction--for instance: (41)

The necessity for Fred to jump made him scared.

The analysis of (41) resembles that of (33). The CP in (41) has an almost identical syntactic structure to that of (34). The subject or theme argument place of make is filled by a projective proposition, which is characterized by a DRS K and an operator N. Like all projective propositions, N(K) determines a set of propositions. The content of N(K) is defined relative to the set of contextually admissible worlds, those that verify everything in the context. Then every proposition in N(K) represents a possible extension of the context in which K has a proper embedding. This makes (41) true at a world w and a context C just in case every possible extension of C verifies Fred's having to jump. If these extended contexts are identified with worlds, then we have a definition of alethic necessity,39 This semantic analysis of infmitivals follows closely the syntactic assumption that such constructions are instances of CPo There are alternative syntactic and semantic

(42.a) For Fred to shoot Bill is not something I desire. (42.b) John wanted for Mary to be chair, but that possibility scared Frank. This is evidence that a for infmitival gives us a complete semantic unit and a saturated object. The DRS construction procedure together with the CP syntactic analysis of infmitivals predicts this. As further evidence for this semantic unity, infinitivals take on the propositional character that this logical form would imply in some constructions like those involving attitude verbs. A sentence like it was necessary for Fred to jump is synonymous with it was necessary that Fred jump.41 Another example of such a construction occurs in John wants for Mary to be chair. This report is synonymous with John wants that Mary be chair, or John wants Mary to be chair. (42.a) also has a that clause paraphrase. It would appear that a for infinitival in such a context should introduce a proposition-like entity. A final argument for treating infinitivals as introducing saturated entities is this. My semantics for infinitivals implies that the noun phrase right after the occurrence of the complementizer for is within the scope of an intensional operator. This predicts that an indefinite like a or someone may very well have narrow scope and a de dicta reading in a sentence like (43.a) Fred wants to marry someone. Indefinites occurring in the infinitival appear to have the predicted scope ambiguities with respect to intensional operators. Fred may be happy with anyone who wants to marry him (the de dicta reading of 43.a), or Fred may want someone in particular to marry him (the de re reading of 43.a); the mechanisms for scope variation discussed in chapter two and earlier here account for these readings. Anaphoric examples, however, confirm that if the noun phrase follows the complementizer, only the de dicta interpretation is possible: (43.b) ?For someone to marry him is something Fred desperately wants. She is very pretty. (43.c) ?For a neighbori to own a pit bull is something we do not want. Nobody likes himi' The second sentence (43.c) has a strongly preferred de dicta reading, on which it

...."",...------~=~=~~-~-~~~~~-------.~--~. -~-----.------------

CHAPTER FOUR

SENTENTIAL NOMINALS

expresses a about our desires. On such a reading the discourse referent introduced by a neighbor is declared in the subDRS constructed from the infinitival. This discourse referent is inaccessible to the discourse referent introduced by the pronoun in the second sentence, and so (43.c) is predicted to be bad. I assume a syntactic constraint prevents the wide scope reading of the DP.42

include this information under the I node, where it would most naturally go, unless we adopt a non-standard view of I and VP ( on which the VP dominates elements of I). Further, the CP analysis makes our semantic translation easier by letting the I fill in the event argument place of the predicative DRS derived from the VP (or its nominalization), although we could also fill in the event abstract if we assumed the non-standard view of I and VP. Chierchia (1985) suggests that the DP that for takes as argument is the possessor of the property denoted by the infinitival. There are two ways that this could work. One might take the for to introduce the conversion operation, applying the partial DRS introduced by the DP to the predicative DRS introduced by the infinitival. But then, on our general assumptions about abstract entity anaphora, partial DRSs would be structures that, like predictive DRSs and DRSs, we can quantify over or anaphorically refer to. But that does not seem to be the case, so given our assumptions, we must reject this analysis of for. The second interpretation is to assume that the for PP introduces a function that takes an individual and a property as arguments and returns a proposition; in DRT terms, for(x, K), where x is an individual discourse referent and K a predicative DRS, is a function that relative to an embedding function f denotes a projective proposition in which f(x) is the agent realizing the event-type denoted by the predicative DRS K. This approach will only yield a de re interpretation of the NP in the PP. Let's now work out a simple example like,

)'~

5.2 Chierchia's Analysis of Infinitivals

Having described my analysis and some arguments for it, let us examine a prominent alternative, Chierchia's (1984) (1985) theory. One might analyze for infinitivals in terms of a nominalized verb phrase denotation and some sort of interpretation of the prepositional phrase. 43 A principal argument for this view is semantic in nature. Chierchia claims that the following argument is valid. (44)

Paul tried whatever Mary tried. Mary tried to climb the Eiger. So Paul tried to climb the Eiger.

Chierchia claims that if one takes a standard syntactic analysis of this construction on which the complement of try is at least a full IP and the PRO in subject or Agent position is understood as necessarily coreferential with the subject of try, then one cannot explain the validity of the argument. On the other hand, if one analyzes the object of try as a nominalized verb phrase and for as a preposition, then the validity of (44) has a straightforward explanation. This is Chierchia's principal argument for his view. But one can also account for this argument on a view in which infinitivals denote projective propositions. But first let us see how the view fares on other grounds. On Chierchia's view, infinitivals would be taken to be VP nominalizations, just as that clauses are sentential nominalizations. They would function as terms in the characterization relation "", but they might also occur as arguments to certain verbs-typically the modals and auxiliaries, have and do. They would also be arguments of certain nouns or adjectives. The construction algorithm would treat the nominalization of a VP node analogously to a that clause. Such nominals would introduce predicative DRSs. Assuming that nominalizations of VPs and VPs are to be treated in parallel, the predicative DRSs formed from VP nominalizations would always have a A-abstracted event discourse referent and a A-abstracted discourse referent over the subject place argument of the verb in the VP. Such structures could serve to characterize concepts or properties of a particular kind--event or action types. On closer examination, several difficulties beset this view. First, there are some syntactic difficulties. Infmitivals often carry tense or aspectual information; infinitives like to have loved and to be crossing the street appear to convey both temporal and aspectual information. The CP analysis provides a natural place for inclusion of this information in its syntactic representation, but with the VP nominalization we cannot

(45)

185

For Fred to shoot Bill was wicked.

The translation of for is AX AQ AP[ {k}, {for(x, Q) This applies to the translation of Fred, to yield: AQAP

x, k Fred(x) for(x, Q) P(a)

= k & P[k]}] in the list notation.

=k

Note that Q is an abstract over a predicative DRS. Applying this now to the translation of the infinitival would yield, on this alternative proposal: AP

x, k Fred(x) for(x, AZ f-=-~u:L::.e_ _--I Bill(u) e-shoot(z, u) P(a)

)

=k

There is a problem with this interpretation of for too, however. The subject place argument in this analysis always has wide scope outside the property expression. It

SENTENTIAL NOMINALS is thus completely unclear how to get the de dicto reading on this alternative semantics. This seems to be a serious objection, since de dicto readings like those for (43.b-c) are the only acceptable readings. Chierchia does not address this difficulty. The only way I can see around it is to appeal to some curious procedure for inserting semantic material inside the subDRS using for. But then we have just reinstated a view equivalent to the one that infmitivals are CPs and denote saturated entities. Let us now return to Chierchia's main argument for his view, the argument pattern in (44), assuming now that infinitivals denote projective propositions. Chierchia is right about the objects over which the first premise of (44) quantifies; the reader evaluates the argument as an instance of quantifying over VP denotations, extracting the relevant VP denotations from the CP denotation. As some evidence for this view one might consider the synonymy of Whatever Mary tries, Sam tries with Whatever Mary tries to do, Sam tries to do. Thus, it seems we understand the first premise of (44) as containing a suppressed to do. Syntactically, the second argument place of this auxiliary use of do is a VP, which means that we get the following DRSs for the premises of (44). I'll assume that in trying one tries to realize a desire. The translation of this suppressed to do applies a VP denotation to the PRO subject of the to do infmitival. First Premise of (44): x,e,c John(xl) el-try(xJ, wi

Mary(x) ,..-_----, e-try(x,W f-----,z=-----1 Pro(z) x=z c(z)

Zl PrO(ZI) XI =Zl C(ZI)

I)

Second premise: Mary(X2) e2-try(x2, WI

Z2

I)

PrO(Z2) X2 = Z2 [X2 climb the Eiger]

The argument will be valid, if one postulates a principle of abstraction on which VP denotations can be recovered from propositions. As we shall see in chapter 6, we need such a principle, the principle of C(oncept) abstraction, to treat VP-ellipsis and concept anaphora in any case. This principle allows us to abstract the predicative DRS derived from the VP of the first premise, while the presence of auxiliary do

,

187

restricts the quantification in the first premise to VP-denotations. This analysis makes (44) a valid argument. The universal quantification above is over VP denotations, as Chierchia suggests, but this does not show that VP denotations must be the objects of try. The analysis uses a CP analysis for infinitivals and employs the uniform semantic translation procedure outlined here. It seems to me plausible, and it shows that Chierchia's argument for his approach to infinitivals is not compelling. Given the other difficulties with Chierchia's analysis of infinitivals, my CP based analysis seems preferable. So far we have seen examples of nominals that denote eventualities and nominals that denote abstract entities. The construction procedure for these nominals has been relatively straightforward and the syntactic structures for them relatively certain. We have exploited several principles over and over again to analyze these nominals: the DP analysis, (RLP), the notions of argument preserving and argument transforming nominals, the assumption of the existence of a null determiner, linking rules for various constructions, and the constraint that anaphoric pronouns must be anaphorically bound to lexically realized elements. In the next chapter, I turn to the problematic gerunds and return to some other headaches for the semantics of sentential nominals. IThe distinction between process and result nominals is due to Bach (1981). The observation about drift is reported in Lebeaux (1986). 2See for instance Higginbotham (1985a). 3 Many authors have argued for or assumed a theory of affix hopping for all gerunds (Jackendoff 1977, Baker 1985, Lebeaux 1986, and Abney 1987). Affixes liKe -ion or -ing are deverbalizing elements that take any verbal projection into a nommal one. A drawback is that a general theory of affix hopping for all gerunds dictates a division of labor between the syntax and lexicon that might seem unnatural. o!1e th~s of -ion and -ing as lexical affix~s, then a natlll1l! position would be that the syntax treats killmg, for mstance, as an atom. The unrestricted affi- hoppmg hypothesis puts certam transformations that are intuitively understood as lexical within the proVInce of syntax. I shall accordingly avoid such affix-hopping theories. 4See for instance Roeper (1985, 1989), Grimshaw (1990), Bierwisch (1989), 5Some authors like Grimshaw and Williams have argued that it is necessary to impose an ordering on the argument places. But this is not necessary on my approach, 6nIese labels may convey other information and be the basis of theories about what is an admissible Agent, for instance. See Dowty (1987), 71'01 Asher (1990b) I proposed a different ~d simple! hypothesis that exploited the simpler locality pnnclple. I fql!owed Roeper q988, 1989) m ,assummg that at some level of analysis the unfilled argumen,t poSItions, are filled With a,phonologlcally empty element, PRO. Semantically, PRO would behave like a definite noun phrase, m that it mtroduces a discourse referent that may be identified with some other accessiple discourse,referent already introduced in the ~~ourse or simply existentially bound when there IS, no approJlnate antecedent: Such aprocedure mdlcates that when all the semantic arguments of a predicate In a CFC a. are supplied by such empty elements, then a. may only introduce a saturated DR-theoretic structure or discourse referent into the context. I now believe, however, that the claim that PRO occurs in an empty argument position is false. The approach with PRO does not appear to be acceptable for languages like German, for example. In German syntax the PRO would have to occur in a position where it would receive case from the noun and so be governed as Bhatt (1989) has observed, But PRO must by definition be ungoverned. Hence the more complex principle (RLP), 8We need of course to allow for different discourse referents in Uf(a) from those declared in UK. Otherwise our defmition of characterization will be far too strict. 9In fact's is not a real determiner at all. Consider the phrase a friend ofJohn's, There would be no way to put the phrase together compositionally if 's were a determiner. Notice also that a friend of JoJ;n's IS not synonymous with Jolin's friend, I am indebted to Katsuhiko Yabushita for raising this QOmt. Another problem with taking's as a determiner is this. While this assumption might work (barring the difficulty just mentioned) for roSS-ing gerunds, of-ing gerunds, and derived nominals, one would lose,the uniform analysis of nominals that IS a feature of my account; one would need another semantics for nominals where this marking does not occur, as is the case with ACC-ing'

u:

~----------~=-~~--~~~~~~------~-----,~-----~~-------------------------

188

CHAPTER FOUR

gerunds, and subjectless gerunds. See my discussion of ACC-ing gerunds in chapter 5. TOOne might think that (1) below offers difficulties for this analysis, since there is no room for a null determiner. (1) The destruction of the city by the army. . But here the lexically realized nominal subject i.s assigned the appropriate case by ~e pre)J9sition, so this too fails to generate a counterargument agamst the hypothesIs tllat null determmers eXist and are essential case assigners. llPor instance Schubert and Pelletier (1988) make use of a null determiner 11 in connection with the semantics of mass nouns. 120ne can also easily get the appropriate translation for (22) if one co.untenances type shif~ meanings for quantifiers including null quantifiers. If we allow the null determmer to have a type shifted translation of APAAQ [{x}, {(P(x», Q(x)l], . . then we can get the wide scope reading qf the null detef1!1iner: is a yariable rangmg. over partial DRSs. Thus, the meaning of the qetermme~ has t)'pe S~lfted Its meru.ung from a function. of two predicative DRSs to a function taking a partIcular fUnction from predlcative DRSs to part!al DRSs as one argument and a predicative DRS as another. But I will not pursue this here. See lor mstance Asher (1990b). 13See for instance Prey's (1989) analysis of scope within German. He proposes just such a scoping procedure for IPs. His procedure and predictions carry over to the DP realm. 14It is also thus unclear to me how to take Grimshaw's (1990) claim that result nominals never have syntactically realized arguments. But perhaps I misunderstand her claim. l3Lebeaux (1986) suggests that this semantic distinction might have a syntactic correlate. He supposes that process derived nominals nominaliz~ a V'. If tha~ is r.igh~, then it woulq appear th~t w~ateyer. supplies the object argume!lt for a ~sitIve ,,:erb nommallza~on together WI~ the nomll~al1Zation Itself forms a constituent. On thiS syntactIc analysIs, then, we predict that destructIOn of the CIty forms a constituent. One test for constituenthood depends on wliether one could introduce an adjunct between the nominalization and the PP. But many poople find (a) the destruction by the army of the city (b) the destruction in 1458 of the city . . . ... grammatical, so by this test the constitl!enth~ of the nommalizatI9n together With Its object argument IS in some doubt. Some have called thiS the mtemal argument. (Grunshaw 1986, 1990). l6It is not always the case that a DP in possessive case fills the subject argument--e.g., The city's destruction by the army. . . . Exactly which part of the CPC fills which argument place of the head N m a nommal wIll depend on the particular prepositions used. 17Grimshaw speaks of this argument as the "internal argument." As does Lebeaux (see note 15), Grimshaw thinks that there is a syntactic difference between this argument position and the others. I do not see this distinction and it plays no part in my theory. l8As observed by Chomsky (1982), Lebeaux (1986), and Safir (1986). 119The semantics for the generic operator would follow that proposed in Asher and Morreau (1991). 201 am indebted to an anonymous reviewer for K1uwer for these examples. 21 A similar idea is proposed in Bierwisch (1989). 22In Asher (1990b) I offer a different account using two different phonologically unrealized determiners, abs and sthe. The account here seems slightly more elegant. 23 1 am indebted to A. Zucci for pointing this out to me. 24Lebeaux (1986) takes -ingto nomi!lalize a ~omplete ~entence. ~ut this. appears to ~o",,: for aqverbial modification of the embedded VP. Smce of-mg gerundives doesn t permit such modification, thiS analysis seems flawed. This analysis also m!Jkes the semantic inte~retation more difficult: Our rules would not yield an event as the designated discourse referent con!I:ibuted by the nommal given such a syntactic analy~is. In fact ~ don't know h9w to get ~ event den9tIng nOf!lmal from Lebeaux's construction Without resortIng to ad hockism. So I will take a different view below. 25The manner or property readings of of-ing gerunds alters the arguf!lent structure of the gerund. In (22.b) for instance, !tie denotation of the gerund is the manner in which John shoots. An~e Rossdeutscher of the University of Stuttgart pointed this reading out to me. In section 3.3. and in chapter 5, we will see other event type readings for such nominals. 26See Kamp and Reyle (199+). 27See Bartsch (1986) for some related observations for German and Dutch. See Milsark (1988) for a detailed diSCUSSion of a unified syntactic and lexical theory of -ing. 28 Events introduced by sentences in the progressive accept activity or process pre~icates--not ju~t stative predicates. So for instance, locatives are perfectly acceptable With progreSSives, but not With statives. 29See for instance Dowty (1979).

SENTENTIAL NOMINALS

189

300ddly enough, some event nominals share this dependence on defaults. Again the type of eventuality the nominal is taken to refer to is important. The launch of the space shuttle was aborted sounds 1l!l good to me as (26.b). !?~rt¥!!d· .. I lie th e !;Iill~~ accomplisllments ml!Y.[l';k.Lto.~t s. tative nominals onlY denote srares, 1I0wever.1here IS some w at a enve nominal can'represem-'-giVeli""tJiat it col'lUtiT!Sl'ltJaspecrtI!lfbr tense forms and given that any nonstative verbal complex can refer to a preparatory phase through the use of the progressive. Derived nominals exploit this leeway, as do ofmggerunds.

31This observation is due to Weir (1986), 32This is of a piece, I believe, with the more widespread ambiguity in natural language concerning events and event~l¥pes, on which verbs like happen and frequency adverbials may take either event~s or eventualitIes as arguments. One might also use this construction for the constructions denoting concepts--e.g. the concept of a

horse.

34See section 2.4 of this chapter for details. 350ne can of course say it is a fact that Mary is wise or it is a truth that Mary is wise, but these are not examples of a noun complement construction; these are cleft constructions. It is also of course perfectly acceptable to speak of a proposition that I have been entertaining, but in this NP that I have been entertaining is a relative claus~ an~ again not an example of the construction. Another apparent counterexample to my contention IS: (1) A claim that Mary is unhappy may spur the insurance company to action But (1) is a process or event nominal. So (1) is predicted to be OK. ~6Whe!l the DRS construction procedure is strictly followed in the processing of definites and mdefImtes, only those discourse referents introduced by indefinites will remam inside the subordinate D,RS; an .alphapetic variant of the conditions in the subI?RS is hence desired to avoid converting a de dicto attItude mto a de re one. See Asher (1987)for a discussion and Van der Sandt (1992) for a much more sophisticated analysis of presupposition. 37prom the perspective of a framework like Government and Binding. But there are other analyses, see for instance Chierchia (1985). 38Por details see Asher (1987). 39Thest: extensiqns of the context might be restricted in certain ways, so we would get a notion of eSlstemlc necessity such as advocated by Kratzer (1981). 4 See Chomsky (1971), als.o Abney (1987). 41There are two senses of be necessmy--one which takes an S' complement in the subjunctive the other .which takes an S' complement in the indicative mood. They appear to be slightly different in meanmg; the second is unalterably factive while the first is not. The first is used withm the more complicated in order to construction. 42Again a constraint like that proposed by W. Prey (1989) would do the job. But there may be others as well. 43Chierchia (1985) proposes a nominal analysis of infinitivals; the alternative analysis of for infinitivals I am ~uggesting would be Chierchian in spint. Chierchia notes that the nominal analysis of infinitives explams the mystery as to why most languages do not allow the formation of sentences with umnflected VPs. That is, if VPs and infinitIval phrases denote the same sort of entities, why do we have the following sorts of mismatches in so many languages? (a) *John to love Mary. (b) *John tries loves Mary. The syntactic analysis rules out both of these as malformed. But of course the CP analysis of infinitivals also predicts these examples to be ungrammatical.

PROBLEMS FOR THE SEMANTICS OF NOMINALS CHAPTER FIVE

PROBLEMS FOR THE SEMANTICS OF NOMINALS

This chapter continues the development of the DRS construction procedure for various types of nominals. I look at some problematic nominals--the ACC-ing ~nd POSS-ing nominals as well as the naked infinitive complements of perceptIon reports. I will argue that all are instances of an IP syntactic construction; this syntactic assumption, together with the assumptions already made in chapter 4 about the syntax-semantics interface and the DRS construction procedure, will account for much of the semantic behavior of these peculiar nominals. In the last two sections, I return to the difficulties for an account of nominals raised at the beginning of chapter 4.

1. IP GERUNDS AND SOME DATA ABOUT THEM The sentential nominals most challenging to analyze are ACC-ing and POSS-ing gerund phrases. Examples of ACC-ing ge~.E~,,~'()E§mW~g!1§ar~fred.§'flQQtiIJg)3ill, Mary being about to kiss John, C8.esar7iiiVing set up camp; ~Jl!~§_()fP9~S~illg constructions are F[.ecJ_'§.§l]QQtingJ3iJJr ,Mmy!s-being,about_tQ,kiss.John, Caesar's havingse't'upcamp:' Particularly intriguing are the (pOSS-ing) gerund phrases with null subjects like promptly firing Fred. I call all of these IP gerunds since I will claim that they are IP constructions. IP gerund phrases differ from of-ing gerund phrases in a number of ways. They never pluralize and do not take determiners. Further, some IP gerunds can have existential event readings without determiners or overt subjects. (La) (1.b) (1.c) (1.d)

*The building the Panama Canal took longer than expected. *Building of the Panama Canal took longer than expected. *John's hitting the ball were a welcome sight. John's kissings of Mary were a familiar part of homeroom.

In this, IP gerund phrases resemble that clauses and for infinitivals. Again like that clauses and infinitivals, IP gerunds may contain elements of tense and aspect: (2)

John's having kissed Mary.

IP gerund phra~~~ to_£ll~_!l:£~~,".~~~, NPs like idea or fa.ct in such constructions=as the idea of. These are very similar to the N' CP constructIon. Just as 190

191

with CP constructions involving that clauses or forinfinitivals, the head noun cannot be pluralized and only takes the determiner the. Of-ing gerund phrases may also enter ) into ofconstructions, but not so felicitously. (3.a) (3.b) (3.c) (3.d)

The idea of firing Fred The idea of Mary firing Fred nThe ideas of Mary's firing Fred ?The idea of Mary's firing of Fred

IP gerunds also resemble CP constructions in that they take felicitously some of the same predicates as that clauses (4.a-c) and infinitivals (4.h). Notably IP gerunds do not take felicitously predicates of pure propositions like true, attitude predicates or predicates of saying like say, assert, and so on except in certain adverbial constructions (4.i-j): (4.a) (4.b) (4.c) (4.d) (4.e) (4.f) (4.g) (4.h) (4.i) (4.j)

Mary's having hit Swanee is a fact (a possibility I hadn't thought of). Sam's being about to crown his brother is what his mother fears. Fred's kissing Susan surprised Bill, caused Mary to cry, and amazed Tina. *?Fred's kissing Mary is true. *?Fred kissing Mary is true. * Susan asserted Fred's hitting Bob. *Fred believed Sam's hitting Bob. Sam's crowning his brother was not a nice thing. Fred going out with Mary is something that Susan found hard to believe. It's hard to believe Aslan('s) running offlike that.

--

As the data in (3) already indicates, IP gerund phrases overlap in distribution with infinitivals. In fact, unmodified gerund phrases and infinitivals can often be used interchangeably; both IP gerund phrases and forinfinitivals can occur as arguments to permission verbs, though not with all projective attitude verbs or predicates: (5.a) (5.b) (5.c) (5.d)

Fred allowed Mary's sleeping in on Saturdays. Fred allowed Mary to sleep in on Saturdays. John's hitting Mary was a bad thing to do. *Mary wanted John's hitting Fred.

(5.a) and (5.b) do differ: (5.a) has a factive presupposition or at least implicature, \ which (5.b) lacks. The presupposition is that Mary did sleep in on Saturdays. (5.c) carries a similar presupposition. The data surveyed indicates that IP gerund phrases denote something in common ) with that clauses and infinitivals. The common ground of these constructions is the domain of facts and possibilities. So a plausible hypothesis is that IP gerunds denote h facts.1 IP gerunds do go well with ~!!!i'ye contexts--a pru:.@i~ f~c.l.C..9_Il~xt: John hitting Mary made her mad. We have/also seen that IP gerunds generate factive

s

{r"

f

CHAPTER FIVE

PROBLEMS FOR TIlE SEMANTICS OF NOMINALS

presuppositions. But notice that such presuppositions can be canceled in certain contexts:

subcategorized for possibilities or uncompleted events--at least events possible or incomplete with respect to the knowledge of the speaker--while those with past participles referring to completed events go well with predicates subcategorized for completed events or facts. Compare for instance:

192

(6)

Mary prevented John's kicking the cat.

(9.a) (9.b) (9.c) (9.d) (9.e) (9.f)

Given our analysis of the predicate fact, on which it generates a factive presupposition and a predicate typing the argument as a possibility, these examples should not oF .. /f,""'r' surprise. Thus, IP_g~ru!ld~m.~,YJ!lS!Hi~!!..()J~12Q§§i.l?Uiti~lwr.facts. There is some guestion as to wheth~!. IP ~~!!~_P.!t1:.~~!_s!~!l9~§.x<mLuaJities. Most IP gerund phrases combine with eventuality predicates very infelicitously. (7.a) (7.b) (7.c) (7.d) (7.e) (7.f) (7.g) (7.h) (7.i)

Ij I, II

i

??Fred's hitting Bill started after their argument. ?? Fred's shooting Bill was bloody. ?Fred's shooting Bill took place behind the bar. ?Fred's shooting Bill happened yesterday. *?She cried after his singing the Marseillaise. (Vendler) *Fred hitting Bill happened yesterday (started after their argument). *Fred shooting Bill was bloody. *Fred shooting Bill took place behind the bar. *She cried after him singing the Marseillaise.

?Mary's hitting John is a fact. Mary's hitting John occurred last Tuesday. Mary's having hit John is a fact. ?Mary's having hit John is a possibility I haven't thought of. *Mary's having hit John occurred last Tuesday. Mary's hitting John is a possibility I have thought of.

The predicate fact is also sensitive to aspect; it goes better with achievement or accomplishment verbs than stative or activity verbs. For instance, John's loving Mary ) is a fact is questionable, while John's winning the race is a fact is more acceptable.

2. TIlE SYNTACTIC AND SEMANTIC ANALYSIS OF IP GERUNDS The syntactic analysis of IP gerunds is of a piece with the syntactic analyses of other norninals in chapter 4. The differences between the various gerunds begin with the scope of -ing in the syntactic analysis. In of-ing gerunds, the -ing has a V in its scope. My syntactic hypothesis concerning ACC-ing and POSS-ing gerunds is that they are nominalizations of a projection of V which contains at least some elements of the I structure (the aspectual and perhaps the tense, though not the modal features of English); that means that if we adhere to X' theory then an IP is a constituent of such gerund phrases. This syntactic assumption has important semantic consequences. The syntactic analyses of these constructions is much less secure than those examined in chapter 4. Both ACC- ing and POSS-ing gerund constructions contain at least a VP within the norninalization to account for the possibility of VP adverbial modification in these constructions. But arguments that such constructions contain I are controversial. Many analyses of these constructions have been proposed. 4 None is completely satisfactory. I have mostly followed the syntactic analyses suggested J by Reuland (1983) and Abney (1987). In some places I have diverged from their, accounts in order to solve problems that confront them.

These examples indicate that there is a big difference between IP gerunds and of-ing gerunds. Speakers find the same sentences with of-ing gerund phrases substituted in ( for the IP gerund phrases m..!!£!!.jJetter than (7.a-i). It is interesting to note that predicates like take place and happen are much more felicitous at least with these POSS-ingconstructions than other event-like predicates, but these two predicates are prime examples of predicates that take event-type arguments. All the other predicates in (7) are plainly event predicates, which leads one to suspect that IP gerund phrases don't introduce events. In particular, ACC-ing gerund phrases sound very bad with event predicates. In languages like French which have a form corresponding to the ACC-ing gerund (though not one corresponding to the POSS-ing gerund), gerund phrases cannot combine grammatically with such event predicates. 2 On the other hand, some data suggests that POSS-ing gerund phrases, especially tho~_~Hh9l!tl~1Q9_a)!Y1:~l!Ji~l:;fL~JL,*c.ts, go well with predicates that we would think ( , of as event predicates. Contrast, for instance, the examples in (7) with those of (8).3 (8.a) (8.b)

193

Building the Panama Canal took longer than expected. Gathering pecans in Central Texas starts in September.

2.1 ACC-ing Constructions as IPs

To complicate the pi~er, it appears that the tense and aspect of the verbal participle makes quite a difference in terms of the denotation of the IP gerund phrase as a whole. Propositional predicates sound worse with present and future tensed participles than with perfect or past participles. POSS-ing gerund phrases with present or future participles are perhaps slightly more felicitous with predicates

I tum now to the details of the ACC-ing gerund phrase. The subjects of ACC-ing constructions have accusative case, not possessive case. This signals an important difference for the syntactic structure of these constructions in contrast to the other gerund constructions and derived norninals. Another important difference between derived norninals and of-ing gerunds is that ACC-ing and POSS-ing gerunds do not

\

i

r

FIVE

admit adjectival modification of the nominal. So the syntactic structure for such nominals cannot contain an NP node, since the presence of such a node would entail the possibility of adjectival modification, as with of-ing gerund phrases and derived nominals. 5 But X' theory only requires for the DP analysis that D' have as daughters D and some maximal projection. That maximal projection could be lP itself. The -ing affix has an aspectual force, as we have already seen. So it naturally goes in I, with the result of making I and its projections (-v, +n). This commits us to a form of affixhopping; the -ing must hop from I to the verb. But this is no different from the usual affix-hopping required to explain the movement of tense and agreement features from I to the verb in English. I suppose that only lPs with the feature <-v, +n> may stay in a complement position of a DP. This leads to the following structure. DP, 'D'

D~~IP(+N,-V)

DP/~ I' (+N, - V)

I

I~VP

John +A-ing ~ kiss Mary In this structure, adjectival modification of the nominal is not possible. Adverbial modification is possible, since the structure contains a VP. One difficulty with the ACC-ing constructions is how to account for the case of the subject. Speakers prefer (lO.a) to (lO.b). (lO.a) Him hitting her so hard frightened Mary. (lO.b) ?He hitting her so hard frightened Mary. The subjects of the lP in an ACC-ing gerund construction get accusative case. My analysis offers one way to explain the accusative case that is assigned to the subject. 6 Since I is (-v, +n), there is no agreement marking in I. Consequently, I does not assign John nominative case. Since D and lP are sister nodes, however, it is possible in the above structure for the null determiner in D to assign case to John. I will assume that a lexically null determiner in D position optionally assigns exceptional case to the subject of the IP in the complement position. The null determiner assignsJohn accusative case in this configuration, according to a principle of exceptional case marking. 7 This case assigning configuration is not completely anomalous. For assigns case from the C position to the subject of an IP in the infinitival construction, and that configuration is analogous to this one. The structure I have proposed is not without problems, but I believe it can be defended. The first potential problem is that this analysis predicts that sentential adverbs are admissible in ACC-ing gerund constructions. They are inadmissable in

PROBLEMS FOR THE SEMANTICS OF NOMINALS

195

argument position--e.g., (ll.a). But they can occur in second position--e.g.,(11.b-c). 8 (l1.a) *Probably John going to the store was the result of their discussion. (11.b) John probably being a spy was hard news for the director of the Agency to take. (ll.c) The teacher's comment about Fred possibly having to repeat second grade came as no surprise to his parents. There is a possible explanation of this behavior. If we allow sentential adverbs in sentence initial position, then presumably they must attach to IP. This, however, would break the appropriate case assigning relation between the null determiner in the main D slot and John, at least if we assume that accusative case is assigned to John by the D. This case assigning relation appears similar to that in infinitival CP or exceptional case marking constructions, since sentential adverbs in front position are not allowed there either: (12.a) *For probably Fred to be a spy was unthinkable. (12.b) *John thought probably Fred to be a spy. (12.c) *John believed probably Fred to be a spy. In these constructions, the placement of the adverb breaks the case assignment relation. This seems to be good evidence that the explanation of case assignment in ACC-ing constructions also explains the distributional data about sentential adverbs. The requirement of case assignment would rule out the occurrence of sentential adverbs in front of the subject DP both for infinitivals and for ACC-ing constructions. With a syntactic analysis in place, the semantic interpretation of the ACC-ing construction is relatively straightforward. My hypothesis about case assignment entails that there must be a null determiner in the head position--sthe. But the nominal contains an entire lP. This yields under translation an entire subDRS, and so there are no argument places for the translation of the determiner to fill within the translation of the complement of the DP, which has given us the subDRS. If we suppose in natural language that vacuous quantification is prohibited, an assumption that has robust support, then we must assume that the nominal has an argument structure like that of a that clause and analogous to that given by the abstract argument transformation of derived nominals. The following transformation of the translation of the IP, where K is the DRS that usually results from IP, is forced by the presence of the sister D, if we are to avoid vacuous quantification. The silent determiner in the head D of the construction fills in the possibility argument place.

Both the syntax and the semantics of IP gerunds contribute to determining the appropriate type of discourse referent. An IP gerund construction introduces a

PROBLEMS FOR THE SEMANTICS OF NOMINALS possibility or a fact into the discourse. But according to my analysis of the predicate fact, this simply means that ACC-ing constructions introduce a possibility discourse referent and a factive presupposition. Some predicates of ACC-ing constructions may block this factive presupposition, in which case the ACC-ing construction will denote a possibility. If nothing blocks the factive presupposition, the ACC-ing construction will denote a fact. Possibilities are in effect possible facts, with the same identity conditions as facts. Facts, however, must always be actual. In the case of John kissing Mary, we introduce and characterize a possibility discourse referent, po, in the following partial DRS structure:

construction introduces in effect a fact discourse referent. Given the processing rule for presuppositions discussed in chapter 4 (section 4.3), alphabetic variants of the conditions and discourse referents declared in the characterizing DRS are entered into the main DRS. With the processing of the factive presupposition, the sentences (l3.a-b) are truth conditionally equivalent. Here is the DRS for (l3.a): f, x', e', y' f'"

AQ po '" I x, e, y John(x) Mary(y) e- kiss(x,y) Q(po)

(4.e)

x,e,y John(x) Bill(y) e- sprint past(x,y)

po

The null determiner introduces a discourse referent which the syntactic and semantic structure and content of the nominalized IP determine to be of possibility or fact type. This makes ACC-ing gerunds semantically very different from other nominals. The mandatory typing of the discourse referent as possibilities or facts accounts for the unacceptability of sentences like (4.e), repeated here:

197

welcome-sight(f) John(x') Bill(y') e'- sprint past(x',y')

2.2 POSS-ing Constructions as IPs The syntactic structure and semantic interpretation of POSS-ing gerunds is very close to that for ACC-ing constructions. Here is my analysis for John's kissing Mary.

*?Fred kissing Mary is true. DP

On the other hand, many attitude verbs and other complemented constructions accept facts as arguments. So my analysis allows that ACC-ing gerund constructions and CP constructions may occur in many of the same linguistic contexts. Also, ACC-ing gerunds yield completely standard subDRSs that include the content of the DP in accusative case. Abney (1987) reports that a sentence like some boy kissing Mary was too much for Fred to bear has both a wide and narrow scope reading for some boy; it may be some particular boy whose kissing of Mary breaks Fred, or it might be just any boy's kissing Mary that is too much for him. One can account for these scope ambiguities in the same way that one accounts for scope ambiguities involving that clauses. Finally, we must account for the synonymy of the pair (4.a-b) from chapter 4 repeated here: (l3.a) John sprinting past Bill was a welcome sight. (l3.b) John sprinted past Bill. It was a welcome sight. The difference between the two DRSs is only that the conditions introduced by the gerund phrase are not declared in the principal DRS (and so are not declared as "true"). The content of the gerund phrase is, however, presupposed in (l3.a). Here nothing blocks the factive presuppositions of the ACC-ing construction and so the

DP/~D' / Johni

D~IP(+N,-V) ~ DP/ ""-I' (+N, - V) li

I/~VP

+A-ing

~

kiss Mary I assume that John has moved before S-structure from its position within the IP to the specifying position of the whole DP, where it gets the usual possessive case that all DPs have in that position. Now I have assumed that D optionally assigns exceptional accusative case to the specifier position of the embedded IP. So in cases where D does not assign accusative case to the DP in situ, then John must move to the specifier position of the DP to receive case. Since the head of the DP dominates an I projection, the lexically null, abstract determiner must occur in the D position. The DP John in the specifier position of ,the main DP is the subject or Agent argument of the verb in the IP of POSS-ing gerunds, with case being assigned by the lexically null determiner. POSS-ing gerunds, like ACC-ing constructions, are

CHAPTER FIVE

PROBLEMS FOR TIlE SEMANTICS OF NOMINALS

predicted not to take lexically overt determiners, because the determiner position is already filled with the lexically null detenniner, which is needed to assign the appropriate case to the nominal subject. ACC-ing and POSS-ing gerunds are also both predicted to accept VP adverbial modification but not adjectival modification. In spite of these similarities, many syntacticians, however, have argued that there is a considerable difference between POSS-ing and ACC-ing gerund constructions. Horn (1975) produced many putative tests to show the difference between these constructions. Given that I am claiming that the syntactic structures between these two constructions are very close, I must examine these arguments carefully. Luckily for me, however, Portner (1990) has already pointed out that many of these tests do not work. For the few that do, a unifonn IP analysis of such constructions makes the appropriate predictions. (A discussion of the spurious differences between ACC-ing and POSS-ingconstructions occurs in the footnote to this sentence. 9) One distinction that Horn observes does indicate a syntactic difference between POSS-ing and ACCing constructions. He notes that pied piping for WH possessives is allowed in POSS-ingconstructions, but not for WH accusatives in ACC-ingconstructions:

a maximal projection, then it must dominate an IP. If the analysis is wrong, we must either reject the syntactic treatment of tense and aspect or X' theory, both of which are well established. I turn now to the semantic analysis. The syntactic structure of POSS-ing gerunds resembles that of ACC-ing gerunds. Let us again consider the POSS-ing construction John's kissing Mary. By my syntactic analysis, this construction includes an embedded IP, and so in particular the event argument place of kissing will be filled by the translation of the I, as is familiar from chapter 2. Again in order to avoid vacuous quantification, we are forced to the following translation of the IP. I assume that the movement of the DP John yields a lambda bound discourse referent variable and a linking rule connecting the argument place to the discourse referent introduced by John.

(14.a) The man whose flirting with your wife you took such exception to. (14.b) *The man who(m) flirting with your wife you took such exception to. But the syntactic analysis I am using accounts for this one observed difference between ACC-ing and POSS-ing constructions; it permits pied piping with POSSing gerunds, while the analysis for the ACC-ing construction does not. 10 My syntactic analysis does run into a familiar difficulty, however. The syntactic analysis of POSS-ing gerunds predicts that they should accept sentential (IP) modifiers. But several authors have claimed that POSS-ing gerunds do not combine with sentential adverbs or sentential adverbial PPs, when those adverbials occur in the second position (15.a-b).1 1 This contrasts with the behavior of ACC-ing gerunds. But it seems that such constructions are OK for some speakers if we change the tense or move the sentential adverbial as in (15.c-d): (I5.a) ? John's probably being a spy made the committee reject his application for a security clearance. (I5.b) ?? John's, to our delight, leaving so early distressed Susan. (15.c) John's probably having been a spy made the committee reject his application for a security clearance. (I5.d) John's leaving, to our delight, so early distressed Susan.

'Apo 'Ax po ""

199

e,y Mary(y) e- kiss(x, y)

My assumptions about case, familiar from chapter 4, imply a null determiner in head D position. The predicative DRS now combines with the partial DRS derived from sthe to get the following partial DRS:

'Ax 'AQ

po e,y po ""

Mary(y) e- kiss(x , y)

Q(po) This combines with the translation of John in the usual way, giving us:

'AQ

po, u John(u) po"" e,y Mary(y) e- kiss(u, y) Q(po)

(15.a-b), I conclude, fail to show that POSS-ing gerunds do not have an analysis on which the DP dominates an IP.12 The DP over IP analysis is, in any case, implied by some well-entrenched assumptions: since POSS-ing gerund phrases take temporal and aspectual modifications (an auxiliary verb is sometimes included within a gerund), the construction must contain some component of I. If the D' is to dominate a maximal projection,. then it must dominate an IP. If the analysis is wrong, we must

As with ACC-ing constructions, the presence of the DP over IP introduces a type restriction on the discourse referent introduced by the nominal. Given that a possibility discourse referent is introduced which may turn into a fact discourse referent if nothing blocks the factive presuppositions of the construction, we cannot combine such a construction with a true propositional predicate. We thus predict the

CHAPTER FIVE

200

r I

If the factive presuppositions of an IP gerund are not blocked, it will end up denoting a fact. But sometimes these presuppositions are blocked. This occurs for example in (6), repeated below, where the factive presupposition is blocked by the main verb.

(6)

Mary prevented John's kicking the cat.

In contrast to the DRS for (l3.a), there is no copying of the conditions of the subDRS into the principal DRS. The semantics of prevent prevents this. Since the factive presuppositions are blocked in this case, the construction procedure will yield the following DRS for (6): po, u, x, e Mary(u) e'- prevent(u, po) John(x) e,y po'" cat(y) e- kick(x,y) Let us take stock of my analysis of IP gerunds. First it explains why IP gerunds in general do not go well with event predicates. IP gerunds, which incorporate an I, cannot introduce event discourse referents that could fill the event argument places in those event predicates. Incorporating inflectional elements within the ACC-ing and POSS-ing gerund nominal, however, yields appropriate translations for the past and present forms of the gerund, which are present in many languages. While the inflection node in a present gerund introduces a discourse referent that overlaps the temporal perspective point set by the reference point of the matrix verb, the I in a past gerund introduces an event discourse referent that is prior to the reference point set by the matrix clause verb, as is evident from this sentence: (16)

His having lost his driver's license once made John an especially careful driver when the cops were around.

If we treat having lost as a past tense or perfective gerund, we would have to interpret its syntactic structure as containing an I node. My syntactic analysis seems to be required for those gerunds in which inflection is lexically realized, if we wish to keep within the bounds of X' syntax. My general principles for semantic interpretation then predict that IP gerunds with past tense or perfective gerunds, which must have an IP analysis, are always infelicitous with event predicates. Such IP gerunds must denote saturated abstract entities like possibilities or facts. Second, my analysis explains semantically why gerund phrases don't combine with standard overt determiners. Such determiners contribute a discourse referent to a

PROBLEMS FOR THE SEMANTICS OF NOMINALS

201

predicative DRS and may introduce a complex logical structure. But if one of these lexically realized determiners were to combine with the translation of an 1', e, the discourse referent introduced by the determiner would have to go in for the subject argument of e to prevent vacuous quantification. But then we would not be able to find a suitable interpretation for the DP in specifier position of these abstract nominals. Only the abstract determiner introduces the condition to avoid this difficulty. Third, my analysis gives a semantic account of why gerund nominals do not pluralize. 13 Pluralization of NPs is an operation that converts A-abstracts (the translations of N') of one type into A-abstracts of another type. For instance, pluralization converts of-ing gerunds from a A-abstract over individual events to a Aabstract over groups of events. But in the case of I gerunds, the relation", takes a DRS structure and a discourse referent as semantic arguments. The denotation of a DRS s~cture is just itself, never a group of objects. Further, the DRS uniquely charactenzes the other argument of "'. Pluralization of an IP gerund would make no sense semantically. Fourth, in the semantic interpretation, fact and possibility discourse referents typically map under an embedding function to abstract objects that obey the law of intensional identity. This accords with the data on facts of chapter 1. Since we have distinguished between facts and propositions, my analysis also explains why IP gerund constructions do not go well with predicates like true that take only proposition like entities as arguments. Fifth, my analysis predicts, given the flexibility of the DRS construction procedure, scope ambiguities for the quantifier in subject position.1 4 One can interpret the DP in subject position as being contained within the semantic content of either form of the IP gerund: (17.a) John's puerile behavior precluded anyone's having a good time at the party. (17.b) John's puerile behavior precluded anyone having a good time at the party. In (17 .a-b) anyone is a negative polarity item, and so it must be included within the complement of the verb, preclude, which creates a negative polarity context. The DRS construction procedure permits the noun phrase to be interpreted as having wide scope over the null determiner as well, if we appeal to the usual scoping mechanisms used within DRS construction. By combining the partial DRS produced from the moved DP with the predicative DRS constructed from the I' , we can get the desired narrow scope reading. The construction procedure, with its flexible routines for combining partial and predicative DRSs, allows both interpretations of John's loving Mary. 15 Difficulties for the DP over IP analysis arise with the POSS-ing gerunds examples (8.a-b) (8.a)

Building the Panama Canal took longer than expected.

PROBLEMS FOR THE SEMANTICS OF NOMINALS (8.b)

Gathering pecans in Central Texas starts in September.

The gerund in (8.a-b) must denote an event and not a specific fact, because of the selectional restrictions of the main verb. The general interpretive rules do not permit the nominal to contribute an event discourse referent as an argument to the main verb. To explain the apparent event readings of POSS-ing gerunds, one might claim that at least some POSS-ing constructions have a different syntactic analysis, which I'll call the DP over VP analysis. On the DP over VP analysis, the nominalizing affix has as a VP the maximal verbal projection in its scope rather than an IP. I do not know how to give such an analysis within the confines of X' theory without at the same time introducing an NP node, which would then wrongly predict that adjectival modification for POSS-ing gerunds is possible.1 6 The best I can do is the unorthodox tree: DP, 'D'

/"'- VP

D -ing

The DP over VP analysis commits us to a stronger form of the affix hopping hypothesis than the IP analyses commit us to. Further, the DP over VP analysis does not seem to be possible for either ACC-ing gerunds or POSS-ing gerunds with lexically realized inflectional elements; the inflectional elements belong to I and so such constructions naturally subscribe to the DP over IP analysis. Finally, the DP over VP analysis predicts that POSS-ing gerunds do not take sentential adverbs, but they do in at least some positions. So the DP over VP analysis has flaws. A crucial difference between the DP over VP analysis and the DP over IP analysis for POSS-ing gerunds appears in the semantic interpretation. For the semantic interpretation of a VP in my theory is a two place property. One of the argument places of the VP property is of event type. For instance, the translation of the VP in (8.a) is:

MAe

y

r---~--------~

x -build(e, y) Panama Canal(y)

One should compare this predicative DRS with one that is the translation of an IP like that on page 199. A predicative DRS like that above may combine according to the principles of DRS construction with the translation of the determiner sthe. Such a translation will contribute an event argument to the VP translation. The result of this combination will be a familiar partial DRS:

AX AQ

203

e, Y e-build(x, y) Panama Canal(y) Q(e)

The locality principle (RLP) fills in the missing subject argument with a discourse referent declared within the DRS component of the partial DRS constructed for the DP.

AQ

I

e,x, y e-build(x, y) Panama Canal(y) Q(e)

The DP over VP analysis also predicts fact readings of POSS-ing gerunds, if the abstract argument transformation of the gerund is used. (RLP) then fills in both the event and subject argument place of the nominal. But it does not tell us why both readings are not always possible--and hence it fails to predict the judgments in (7). The DP over VP analysis is also not ideal, because it fails to explain why no standard determiners combine with any of the gerund constructions. Why cannot standard determiners bind event arguments in gerunds when they can do so in derived nominal and of-ing constructions? But subjectless gerunds with clear event readings refuse to take ordinary determiners: (18)

*Some (a) building the Panama Canal took longer than expected.

The DP over IP analysis supplies a neat explanation for this phenomenon. Further, the examples motivating the DP over VP analysis are quite fragile. An obvious eventuality predicate in (19.a) does not combine with the POSS-ing construction; much better is the event denoting of-ing gerund. (19.a) *?Gathering pecans in Central Texas lasted two months. (19.b) The gathering of pecans in Central Texas lasted two months. (19.a) indicates that the POSS-ing gerund does not denote an event. So perhaps some curious interaction between the generic interpretation of the present tense and the fact denoted by gathering pecans in Central Texas accounts for the iterative event reading of (8.b). There is perhaps something peculiar about the predicates take and start. Infmitivals also take these predicates, although their syntactic analysis as CPs is quite secure and with the usual DRS construction procedure they do not introduce eventuality discourse referents. So do some noun phrases with abstract nouns. (20.a) To build the Panama Canal took longer than expected (20.b) For America to build the Panama Canal took longer than expected. _

PROBLEMS FOR TIlE SEMANTICS OF NOMINALS (20.c) This possibility starts in September. (20.d) This possibility has taken longer to materialize than we had hoped. A possible hypothesis is that the event readings of sentences such as (20.a-b) or (8.ab) rely on a particular semantic function of these predicates. The predicate take longer than expected might in some cases also take abstract objects like projective propositions or possibilities and return events; such predicates are about the realization of their abstract object arguments. If that is right, we do not need a special syntactic analysis, then, to account for the eventuality-denoting behavior of POSS-ing gerunds. The DP over VP analysis is not compelling, at the very least. The DP over IP analysis seems best both for ACC-ing and POSS-ing gerunds.

3. NAKED INFINITIVES The last sentential nominal I will discuss is the naked infinitive construction. In chapter 1, I assigned a special sort of denotation to NI complements. This tight correlation between syntactic type and type of abstract object is suspicious; it does not exist anywhere else in natural language metaphysics. It turns out that this fit may indeed be an illusion. Like the gerunds, NI complements have a mysterious and controversial syntactic structure. Many claim NI complements to be sentential nominalizations of some sort. On this view, the syntax of NI perception contexts yields the following labeled bracketing: [NP [see [NP VP]IP]Yp]S. Others have denied that NI complements are real syntactic constituents. They have taken the structure of a naked infinitive perception report to be [NP [see NP VP]yp]S. As I argued in chapter 1, however, at the semantic level, NI perception verbs have an object argument that can be referred to and quantified over.

of seeing, and the event-type given by the embedded verb, and assume that the construction presupposes that the event-type argument is realized. This suggests the following gloss on NI perception. First, NI perception involves a particular psychological state, the state of perceiving an event of a certain type. The predicative subDRS that is an argument to the perception predicate see context serves to characterize the psychological state in a way similar to the way subDRSs structurally characterize belief states. If the semantics of perception reports exploits the structure and content of the DRS in the way that the semantics for propositional attitudes in chapter 3 exploits the content and structure of the propositional object of those attitudes, the mental state component of the seeing will be highly intensional. But if the noun phrases in the embedded IP are taken to have wide scope over the seeing context, the construction procedure dictates that only the condition given by the verb falls inside the DRS. This condition is the intensional component of NI perception contexts argued for in Asher and Bonevac (1985b). An NI perception context also generates a particular sort of factive presupposition or condition. The factive presupposition copies the material inside the subDRS into the main DRS, but always within the scope of the quantifiers from the NI clause. Thus if a negative quantifier occurs within the NI clause and has wide scope over the NI context as our construction requires, the factive presupposition will be automatically blocked. This captures the factivity inferences described in Asher and Bonevac (I985b). As an example of this approach to NI perception contexts, let us consider the processing of the first clause of (2I.a). The IP argument to see contributes a predicative DRS. Assuming that the DPs involved in the IP obligatorily take wide scope over see and so quantify into the seeing context,18 we end up with the DRS on the left for the first clause of (21.a) without the processing of the factive presupposition and the DRS on the right with the factive presupposition displayed. 19 x y, e

(2l.a) John sees Mary run, and Sam sees it too. (2I.b) John saw whatever Mary saw. There are a number of constraints upon any satisfactory analysis of NI perception contexts. Perception verbs are semi-transparent attitudes in that they license a considerable number of substitution inferences, but they are not wholly transparent. 17 Accordingly, noun phrases in an NI complement are to be interpreted as if they had wide scope over the seeing context, as in Asher and Bonevac (1985a). Since NI complements are taken to have null inflection, they yield, according to the DRS construction procedure I have developed, a predicative DRS with an abstracted eventuality argument place or event type. In order to verify the inferences required of NI perception reports in Asher and Bonevac (I985b), one must identify the arguments of a perception verb as involving the property ascribed to that event determined by the verb in the NI complement report. One might be tempted then to take the semantic arguments of the NI perception predicate to be the agent, the event

205

John(x) Mary(y) e-see(x, Ae'

x, y, e e'

~)

John(x) Mary(y) e-see(x, Ae' ~)

~

e'-run(y)

~

My approach to NI perception contexts does away with situations, but it preserves the inference patterns that motivated the introduction of situations. Further, it predicts some of the observations that have motivated the view of Higginbotham (1985) and Parsons (1990) that NI perception complements denote events--in particular the synonymy between (22.a) John saw Mary arrive. (22.b) John saw an arrival of Mary. (22.c) John saw an arriving of Mary.

CHAPTERFNE

PROBLEMS FOR THE SEMANTICS OF NOMINALS

While the nominals in (22.b-c) denote eventualities among the saturated entities, both of-ing gerunds and derived nominals may also denote event types in the appropriate contexts using (RLP) and the abstract argument translation. Moreover, there is a serious flaw with the event analysis of NI complements when we look at the anaphoric examples. Consider:

DRSs relative to Ef, where Ef is the relation determined by sameness of intensional content. To state the principle in more ordinary, philosophical language: for any possible facts fl and f2' 0 (Obtain(f l ) <-> Obtain(f2» ~ fl = f2' where Obtain(f l ) is true at a world and time iff f is actual at w and t. The construction procedure also yields a very liberal principle of comprehension. This supports our constraints on the domain of facts elaborated in chapter 1. Propositions, on the other hand, are characterized by alphabetic variant DRSs, DRSs varying possibly only on the discourse referents declared in them. For propositions PI and P2, PI = P2 just in case they are characterized by the same equivalence class of DRSs relative to Ep, where Ep is the equivalence relation determined by alphabetic variance. Further, the DRS construction procedure and the definition of a DRS automatically yield together the idempotence axiom and a liberal principle of comprehension. Thus we have remained faithful to the view of propositions sketched in chapter 1. The DRS construction procedure, on the other hand, requires that eventualities be rather coarse grained and extensional entities. Again this accords with the picture of chapter 1. But other individuation principles for events, like Kim's (1966), are also possible.

206

(23)

John did not see Sam take the money, and Mary didn't see it either.

The difficulty for the event theorist in getting the truth conditions of (23) right is that the event discourse referent putatively introduced by the complement of see in the first clause lies within the scope of the negation sign. Thus, it is not accessible to the discourse referent introduced by it in the second clause, unless the negation has scope over the second clause too. But this scope for negation would give incorrect truth conditions. The acceptability of the anaphoric link has to do with the way the discourse structure affects anaphora. The parallel structure between the two clauses allows us to get an appropriate anaphoric link, though not to an event. Details will come in chapters 6-8 .

207

.1

4. CORRESPONDENCES AND CONNECTIONS BETWEEN ABSTRACT OBJECTS My analysis of nominals began with three problems that any such analysis should solve. I return to them now. The first was to give a systematic account of the semantics of sentential nominals. I have done that, and I have exhibited the relations between the semantics for sentences and their nominalizations. The second problem concerned the spectra of nouniness and world immanence. I have shown how to account for that correlation too, though some open questions remain--e.g., about the relation of facts to events and about the plastic character of the typology. I address these problems now. Section 5 will concern itself with the last problem, the problem of event negation.

4.2 The Spectra of Nouniness and World Immanence do not Correlate Completely Philosophers have traditionally associated many of these sentential nominals with different denotations. That clauses were claimed to denote propositions or facts, gerund phrases facts or possibilities, and derived nominals events or processes. 20 A closer look at the syntactic analyses and a general account of the syntax-semantics interface has revealed that there is no simple correlation of semantic and syntactic types. One and the same type nominal may denote several different kinds of abstract object, and some nominals may denote either abstract objects or eventualities. Further, one and the same type of abstract object may be expressed by several different syntactic types. In general, the sentential nominals do not pattern neatly along the lines of the complex typology reviewed in chapter 1, although there is a rough correspondence between the spectrum of world immanence and the spectrum of nouniness. This confirms Vendler's distinction discussed in chapter 1.

4.1 The Structure of Abstract Object Domains in Natural Language Metaphysics In chapter 1, I placed constraints on the structure of the domains of various types. The types introduced at the level of natural language metaphysics--eventualities, facts and fact-like possibilities, propositions and projective propositions, all have a distinct status when analyzed at the level of DRS construction. But what is the reflection of the domain structure, in particular its closure principles, at the level of the DRT analysis? For facts and propositions, the structure is encoded within the characterization relation. If we follow the suggestions of chapter 1, facts and possibilities are defined in terms of intensional contents; if fl and f2 are facts or possibilities, then f 1 = f 2 iff they are characterized by the same equivalence class of

4.3 Proposition Readings for Fact Nominals: Shifts up the Spectrum of World Immanence.

While natural language metaphysics distinguishes various types of abstract objects and eventualities, it also makes plain that there are connections between them. We have seen an obvious connection between event nominals and their fact or proposition readings. There is also a similar connection between facts and propositions. IP gerunds generate fact discourse referents and subDRSs that characterize these discourse referents. In general the characterization of fact discourse

PROBLEMS FOR THE SEMANTICS OF NOMINALS referents using intensional equivalence as suggested is appropriate. But there are also contexts in which the denotation of a gerund nominal is intuitively much more like a proposition. (24.a) Superman's kissing Lois surprised Jimmy. (24.b) It surprised Jimmy that Superman kissed Lois. (24.c) The fact that Superman kissed Lois surprised Jimmy. (24.a-c) are synonymous. But it seems clear that Superman's kissing Lois may be surprising to Jimmy whereas Clark Kent's kissing Lois may not. Or again: the fact that Superman kissed Lois may be surprising whereas the fact that Clark Kent kissed Lois may not. Nevertheless, the fact that Clark Kent kissed Lois is the same fact as the fact that Superman kissed Lois. In these examples, both Superman's kissing Lois and the complex noun phrase in (24.c) introduce fact discourse referents characterized by subDRS. But the characterization relation must be, in order to explain Jimmy's judgments about Clark Kent and Lois, appropriate to propositions. Further, this phenomenon is not limited to constructions in which gerunds fill argument places of attitude verbs; it can also occur within nominal constructions, as in: (24.d) The thought of John kissing Mary was too much for Fred to bear. If (24.a) and (24.b) are truly synonymous, then it appears that (24.a) must exploit the structure of the characterizing subDRS in the same way that it exploits the subDRS in (24.b)--most likely along the lines specified in chapter 3 for the semantics of belief. Just as there is a shift with event nominals from events to facts or propositions, so too there seems to be a shift with fact nominals. In the case of the shift from eventualities to abstract objects, we needed to transform the argument structure of the nominal. The shift from facts to propositions, however, is different; fact or possibility nominals still introduce fact or possibility discourse referents, but they are used in a different way. In particular, we need to exploit a different characterization relation than the one that is usual for the type of entity represented by the discourse referent. I have assumed that ordinarily when a certain predicate types a discourse referent as a fact, it also types the characterization relation--specifying the generic characterization relation'" as a fact-appropriate one by means of the condition charfO. But a context may permit both the use of Charf and Charp; in this case the proposition characterization relation is overriding. To see how this is possible, suppose we convert a partial DRS AP K2 with a discourse referent f already typed as a fact discourse referent with a predicative DRS U K 3, in which k is an argument of an attitude verb for which any characterization relation on k is construed in a propositional manner. This constraint is realized by having Charp(k) as a condition in K 3. But K2 contains a constraint on the characterization relation of the form Charr(f), since f is a fact discourse referent. Recall that Ai
209

. condition will require that a DRS Ko may characterize k' iff k' represents a DRS that is an alphabetic variant of Ko. Let us suppose that Kl thus has two constraints on "", Charp(f) and Charr(f), and that indeed there is some DRS Ko such that f '" Ko. These three conditions are of course compatible in the sense that there are DRS values for f under which both Charp(f) and Charf(f) are satisfied; the upshot is that f", Ko iff f represents a structure that is an alphabetic variant of Ko. By applying the partial DRS to the predicative DRS, we combine constraints on correct interpretation. Thus, an attitudinal concept that may take either facts or propositions as arguments may take a fact discourse referent as an argument and yet further require that any DRS characterizing it must do so according to the charp relation. This predicts that sentences like those in (24) may be equivalent in meaning, even though facts are introduced in one context and propositions, apparently, in another. This guarantees that the DRSs for (24.a) and (24.b) are truth conditionally equivalent. The solution to the problem that sentences like (24) pose for the interpretation of fact nominals predicts that, although one can shift the interpretation of a fact nominal to a propositional reading at least as far as the characterization relation is concerned, one cannot shift a proposition nominal to a factive reading of the characterization relation. The simultaneous satisfaction of a fact and proposition characterization relation will guarantee that the more restrictive propositional relation is satisfied. Suppose, in contrast to the situation with (24.a), that we have a partial DRS of the form AP K with the discourse referent already typed as propositional and that we attempt to combine this with a predicative DRS AX Kl> where Kl contains the condition Charf(x). This will nevertheless not give us a fact reading for the propositional nominal, because Charr(x) is already satisfied whenever Charp(x) is. The new condition does not impose any constraints on p which it does not already satisfy. This parallels the other unidirectional shift from event readings to fact readings; the interpretation procedure developed in this chapter does not allow a fact nominal to have an eventuality reading. Nor does the possibility of a fact denoting nominal obeying propositional identity conditions imply that fact nominals may go with predicates restricted to propositional arguments. While the conditions on the characterization relation are compatible, the conditions fact(k) and proposition(k) are not. They represent distinct types of natural language metaphysics. One cannot identify two discourse referents when they are of incompatible types. As we have seen, the typology of natural language metaphysics is imposed by the predicates derived from various common nouns and verbs. Some predicates applying to abstract objects generate typing restrictions on the discourse referents introduced by the NP of which they are part. Incompatibilities of certain abstract nominals with complemented verbs may stem from a conflict of factivity between the predicates introduced by the common noun phrases and the verbs. Thus, it is awkward to say that one knows a conjecture, supposition, or possibility,21 impossible to say that one knows a falsehood, but fine to say that one knows a theorem, a proposition, the fact that
210

PROBLEMS FOR THE SEMANTICS OF NOMINALS

examples occur below in (25.a-d). Note that predicate incompatibilities also affect anaphoric reference to abstract objects--as in (25.e). (25.a) (25.b) (25.c) (25.d) (25.e)

??The fact that Mary is wise is a claim that I would make. ??The event of John's kissing Mary amazed Tina. *Sam desires the possibility that Mary be pregnant, ??John knows the falsehood that the circle can be squared. ??John believed the claim that Mary would leave him. He feared it.

In (25.a) the DPs type the discourse referents they introduce as fact-like and propositional, while the is identifies the two discourse referents. But this identity is infelicitous, since these types have incompatible properties. Similarly for (25.b) except that different types of entities are involved--facts and eventualities. (25.c) is infelicitous because of the semantic differences between projective propositions and facts or possibilities. (25.d) is an example of a clash of factive presuppositions. Finally, the DRS construction procedure and our finding that possibilities and propositions are distinct types predicts that the anaphoric report in (25.e) requires one entity to be of two incompatible types and hence that the report itself is infelicitous. Of course not all nominals introduce typed discourse referents--in particular, that clauses and infinitivals, and not all types are incompatible--for instance, facts and possibilities. For instance, while it is a triviality to say the fact that so and so is a possibility, it is perfectly acceptable to say the possibility that Fred and Leslie will come to dinner is now a fact.

4.4 Predicate Incompatibilities and Polymorphic Characterizing Structures.

According to the DRS construction procedure developed in the earlier parts of this chapter, CPs and even gerunds (as in 3.a-b) may characterize abstract entities in the N CP or in the N of DP constructions. I have also taken the characterizing structures introduced by sentential nominals to-have the status of entities. I have taken DRSs and DRSs under projective operators as special constants, designating themselves. But these entities are not of any particular type of abstract entity, in the sense of the typology of chapter 1. Perhaps not surprisingly then, the predicate and typing restrictions of the previous section do not apply to characterizing constructions. This observation would account for the relative acceptability of (26.a) versus (25.e). Further, one can certainly relabel what someone believes a possibility or describe a belief as a conjecture as in (26.b-d): (26.a) ?John believed that Mary would leave him. He feared it. (26.b) John sometimes entertains the thought that the universe was created in a big explosion, but it's now an established fact he ought to be aware of. (26.c) John knows that Mary is married, but Fred believes that that is only a conjecture on his part.

211

(26.d) Fred fears the possibility that Mary may leave John. But as far as John is concerned, that is not a thought worth bothering about. (26.e) That Franz will leave is a proposition that K has often entertained. The possibility has worried Bob. Let us suppose that a definite like the possibility and the anaphoric pronouns in (26.bc) introduce a discourse referent that may be identified anaphorically, using the predicate "", with the structure introduced by the sentential nominal. I will say a good deal more about this in the next chapter on anaphora. What this data suggests is that the DRS introduced by a that clause may characterize two discourse referents whose predicates indicate they are of quite different types. This is a puzzle about constructions denoting abstract objects that I introduced in chapter 1. In (26.b), the incompatible predicates are entertain and thought on the one hand, and fact on the other; in (26.c) knows and conjecture, in (26.d) possibility and thought. The puzzle about polymorphism is that that one can make anaphoric links between incompatible types of abstract objects. We now have the resources to solve this puzzle. As the examples in (26) suggest, the situations in which a subDRS characterizing one type of object may come to characterize a different type of object through an anaphoric connection appear linked to something like a "switch in perspective." The examples in (26) contrast two points of view, and it is this contrast which facilitates the use of the same subDRS in characterizing two different sorts of abstract entity. As long as one can accommodate the demands of the incompatible predicates by--e.g., exploiting differing points of view, the sentences are felicitous. Characterizing structures are polymorphic, because they have no determinate type. SubDRSs may characterize facts, propositions, possibilities, etc.; but they are neither facts, propositions, nor possibilities. A similar conclusion concerns predicative DRSs as characterizations of various sorts of concepts. In accounting for this polymorphism and the type restrictions on discourse referents of various types, it is essential to distinguish clearly between characterizing structures and discourse referents. The polymorphic character of characterizing structures also accounts for anaphoric examples like the following from chapter 1, in which different abstract objects of incompatible types seem to be able to sum together: (27)

[The fact that Sam ran off with his secretary is outrageous. Mary's expectation that he would be unfaithful is also a pretty grim commentary on his character]j. All of itj makes plain the typical, sad state of modem marriages.

SubDRSs derived from that clauses which characterize incompatible sorts of entities like facts and propositions may nevertheless unify together to form wholes that may serve to characterize discourse referents introduced by anaphoric pronouns. As long as we clearly distinguish between the restrictions that the head noun predicates place on discourse referents and the structures used to characterize the entities for which

CHAPTER FIVE

PROBLEMS FOR THE SEMANTICS OF NOMINALS

these discourse referents stand proxy, there is no problem. Roughly, the pronoun in (27) picks up and is characterized by the sum of the various characterizations of abstract entities. The characterizations that are summed are all subDRSs; the summation operation over these uniform structures is just the DRS update or DRtheoretic union operation defined in chapter 2. So while the types of entities the subDRSs in (27) characterize may be incompatible, the characterizing structures themselves may sum to produce another characterizing structure--one that in example (27) characterizes the discourse referent introduced by the pronoun. While subDRSs do not denote any particular sort of abstract entity in the domain of natural language metaphysics, we must distinguish between the various sorts of DRS structures. The structures introduced by for infinitival phrases differ structurally and semantically from those introduced by that clauses or gerund phrases. As the following examples from chapter 1 make evident, it is impossible to quantify over propositions and projective propositions.

facts. Recently, Jonathan Bennett (1988) has argued that events might be defined in terms of a spatiotemporal zone and the facts that obtain in that zone. His thesis is that events are special sorts of facts. In this section, I investigate this thesis and refute it. The type of events and the type of facts cannot be identified, because events and facts don't share all their properties. Facts and fact-like entities don't take

212

(28.a) (28.b) (28.c) (28.d) (28.e) (28.f)

*There is something that John believes and Mary allows. There is something that John wants and Mary fears. John asks for something that Mary wants. Everything that John believes is true. *John desires everything that Mary believes. *Everything Mary asks for is true.

The quantification is ruled out in (28.a,e,f), because there is no common structure to quantify over. DRSs and DRSs prefixed by various operators are not at all the same type of semantic object and cannot be identified. On the other hand the quantification succeeds in (28.b-d) because all of the attitude verbs in these sentences have as objects something of a common type at a suitable level of abstraction. The common type is a projective proposition.

4.5 Metaphysical Relations between Eventualities and Abstract Objects in Natural Language Metaphysics The possible interpretation shifts along the spectrum of world immanence and the

213

i~~~;~~~~~ot1~~~1~c[t~~~~t~~t~u~tOb~~~~i~~n~:~~:~o~:~:~fi~~~~i~~~

case that facts are a special type of eventuality, since it seems reasonable to hold that if is a SUbtype of 1:' then every property attributable to a member of 1:' should be attributable to a member of 1:. This leaves only the possibility that eventualities are a special type of fact. Bennett defends this hypothesis. The main difficulty with this hypothesis is to explain why events may have spatiotemporal properties, while facts may not. Bennett claims that event nominals denote very specific facts, certainly not the ones they might be thought to express. Let us suppose that facts are closed under a join operation and that facts are realized within a certain spatiotemporallocation. An event for Bennett, then, is the join of all those facts that are realized in a given location. It is a "fully specific fact," of which ~ the joined fac~ are "parts." To say that Caesar's crossing of the Rubicon happened III 53 Be., according to Bennett, is to say that the fully specific fact of which that fact that .Caesar crossed the R~bicon is a component obtained in 53 BC. But if fully speCIfic facts can have spatlOtemporal properties, why cannot less than fully specific facts have spatiotemporal properties--in particular facts that mention temporal properties like the one in (29)? Nevertheless, (29) is completely out. 1:

.(29) *The fact that we went drinking on Monday happened on Monday. There are difficulties with other properties that events have and that facts do not. Events can be bloody, savage, etc. But it is a category mistake to speak of a fact as savage or bloody. Bennett's response to this problem, insofar as I understand it, is far from satisfactory. He says that facts are analytically savage or not savage. For example, the fact that Fred fought savagely is savage because that property is constitutive of the fact in a particular way. So the statement (30.a) The fact that Fred fought savagely is savage

I polymorphism of characterizing structures indicate a liberality in the semantic function

'2t1!q"~,tri!£UtQ,mipals. In natural language, it often seemsnoffirmatterwh[ch"sort of abstract object one is referring to. This stems perhaps fu>m the lack of clear identity cri te~~?!,_~J.l.~~_,!y..R~A"QLabs,trac,L 0 bjects. Additionall y, facts andeventsare especially closely linked in natural language metaphysics. Factive constructions presuppose the existence of eventualities. Eventuality denoting derived nominals , always have fact readings. Also, as many have readily observed (for instance Bennett 1988 and Vendler 1957), almost all of the possible predicates for IP gerundive phrases also hold of nominals that obviously denote events. One might wonder then I whether natural language metaphysics really supports a difference between events and

l

is analytically true. This seems quite the wrong prediction to make in this case. It also suggests that (29.b) should be analytically true--when it is in fact nonsense. Further, this view seems to imply that if eventualities are special kind of facts, then (30.b) Fred's fight was savage expresses a fact that is also savage. This seems absurd and is enough to cast doubt on the thesis that eventualities are a special kind of fact. None of the arguments I have given so far speak against an eventual

--------------------------------------

CHAPTER FIVE

PROBLEMS FOR THE SEMANTICS OF NOMINALS

reconstruction of events in tenus of facts and spatiotemporal zones or against a reconstruction of facts in tenus of events. Such reconstructions belong to the realm of real or revisionist metaphysics. I have only argued against the thesis that the types of eventualities and facts in natural language metaphysics can be subsumed into one. Nevertheless, we must still explain the closeness of eventualities and facts in natural language metaphysics. Bennett makes a convincing case that the individuation principles of events are vague at best within the realm of natural language metaphysics. At times the individuation of events with respect to spatiotemporal position does justice to our natural language intuitions. Sometimes we must appeal to the event-type to individuate the event properly. But with every event that we can describe, we can associate an event type. From the standpoint of natural language metaphysics, the event type determines uniquely a fact (the fact is just the saturation of the event type). So there is a natural correspondence between eventualities and facts. Within this framework, we can make the correspondence precise at the level of intensions. Facts are determined by contents, or sets of possible worlds. So let us say that an event type Aee is realized relative to an embedding function f and world w just in case 3g::>e U{e'}f [<{e'}, {Aee(e')}>, g]w' Then we may say that the set of worlds in which an event type Me is realized determines a possibility. While natural language metaphysics does not decide the relation between events, facts, and propositions, it indicates some strong correlations. Every event discourse referent introduced into a discourse has perforce a companion fact, the fact determined by the event type of which the event is an instance. Also every fact characterized by a subDRS K perforce has a companion proposition that exploits the propositional characterization relation with K. Finally, with event type realizations, we can associate a proposition with each event. These associations are unique, though for a given proposition or fact there is no unique event that constitutes its realization. Such strong connections between entities, however, suggest that natural language metaphysics slides easily from "semi-concrete" eventualities to abstract entities.

event of no event's ever happening in the universe. Since the domain of events is not closed under complementation, it is dubious, assuming a compositional semantics, that negated event descriptions denote events. In particular, it gets the meaning of the nominals wrong if we postulate events like the non-arrival of the train or the failure of Bill to kiss Mary. These nominals imply that certain events didn't happen. Given our typology, it seems plausible that negated event descriptions might denote either states or facts. There are in fact three ways wemightt~stJQse~w.ht:;thyr a negated. e'Yent.g!l~~ment (a sentenc-e-inftoaucing·-a.ne~ent discourse referent) mtroduces a state. These tests do not all agree in this case, so we must interpret their resuits JudiCiously. I tum to the tests now.

214

5. THE PROBLEM OF EVENT NEGATION SOLVED The last outstanding task I set for myself was to give a solution to the problem of event negation. The problem is to discover how negation affects the denotation of an event nominal so as to account both for Cresswell's observations about the train's not arriving and the train's non arrival, neither of which denotes an eventuality, as well as for Krifka's observations about wide scope temporal adverbials with negated event sentences, where there are reasons for thinking that negated eventuality sentences seem to introduce eventualities. Given my treatment of sentential nominals and the types of objects countenanced in natural language metaphysics, the train's non arrival could denote either a state, an event, or a fact. But the domain of events is not closed under negation; Le., it is not the case that if cp denotes an event, then -,cp also denotes an event. To suppose otherwise is to countenance as possible absurdities like the

215

I

5.1 Three Tests for Negation and Event Descriptions The first test examines how adverbial modifiers combine with negated event descriptions. It assumes that adverbial modifiers yiel~edicates of eventualities. 22 According to the fIrst test, negated event or state descriptions ofanyki~d are capable of introducing states, when the adverbial modifIer is taken to have wide scope. (31.a) (31.b) (31.c) (31.d)

No one died in the hospital for over two hours. (achievement verb) No one knew the answer for several days. (state verb) No one crossed the picket line for several hours. (accomplishment verb) No one laughed for over two hours. (activity verb)

If we look only at this test, we would quickly conclude that negation always\

transfonus an event inside its scope into a state outside its scope. Compare now the outcomes of the two other tests for the same range of event descriptions. Here are the outcomes of the anaphora test, again using achievement, state, accomplishment, and state introducing verbs. (32.a) *No one died in the hospital. This lasted for several days. (32.b) No one knew the answer. This lasted for several days. (32.c) ??No one crossed the picket line. This lasted for several hours until the police arrived. (32.d) ?No one laughed. This lasted for only a few seconds, however. From these examples, it appears as though the standard DRT account for such sentences rightly predicts at least those sentences containing achievement verbs to be incoherent. Also very awkward are anaphoric references to states introduced by sentences containing an accomplishment verb (32.c) or an activity verb (32.d) under the scope of a negation. The acceptability is higher for the state anaphora in (32.b) with a negated state verb. Consider the results of the third, "Vendlerian" test, on which we see whether negated nominals go well with predicates that apply to states.

I

216

CHAPTER FIVE

(33.a) (33.b) (33.c) (33.d) (33.e)

*No one's dying in the hospital lasted for several days. *?No one's knowing the answer lasted for several days. ??John's not knowing the answer lasted for over several days. *?No one's crossing the picket line lasted for several hours. ??The manager's not crossing the picket line lasted only until the police arrived. (33.f) *No one's sleeping lasted for hours. (33.g) ??Sheila's not sleeping lasted for hours.

( All involve IP gerunds, and all seem bad. Consider also, however, derived and ofing gerund phrases, in which the negation must be non-verbal. There are several ways of forming nominal negations--non, the prefixes un - and in-, and the suffix -lessness. (34.a) (34.b) (34.c) (34.d) (34.e) (34.f) (34.g)

*The non-arrival of the train lasted over two hours. ??The failure of John's attempt to fmd an apartment lasted for months. John's inability to understand arithmetic lasted until he was in ftfth grade. *No one's knowledge of the answer lasted for hours. *No one's crossing of the picket line lasted for several hours. Sheila's sleeplessness lasted for hours. The professor's non-smoking lasted only until his wife left.

The data clearly shows that the scope of negation is relevant. When negation combines with the subject quantifier of a sentential nominal (34.d-e), the nominals cannot denote states. When negation is present somewhere within the nominalized verb, the nominals sometimes denote states. But there are other factors affecting the denotation of a negated nominal besides the scope of negation. The type of eventuality discourse referent introduced within the scope of the negation sign, for instance, also affects the denotation. Our typology of natural language metaphysics distinguishes eventualities into activities, states, accomplishments and achievements. These types behave differently with respect to negation. In particular, achievement nominals that incorporate negation fail to denote eventualities, as (34.a) indicates. 23 When combined with negation, nominals formed from achievement verbs are synonymous with fact or possibility denoting that clauses; they simply deny that an event or state of a certain type occurred. Thus, the non-arrival of the train put everyone in a bad mood is simply synonymous with the fact that the train did not arrive put everyone in a bad mood. The negations of accomplishment nominals also fail to yield eventualities. Only states are closed under a principle of complementation, as I argued in chapter 1. It is noteworthy, however, that one cannot simply exploit complementation principles at the levels of denotations to get a sensible theory. To capture the d~ta, one must suppose that negation is a partial function from eventuality denotmg nominals into fact denoting nominals. But if facts are closed under complementation-

I

PROBLEMS FOR THE SEMANTICS OF NOMINALS

217

-as seems entirely reasonable, then one quickly gets difficulties by considering, for instance, double negations. If

5.2 Negation Without Wide Scope Adverbials I make the following assumption concerning the place of negation in syntactic structure. Negation may either combine with a noun to give us essentially a new sort of predicate, or it must go in I, or it must go in the quantificational force of a determiner. When a sentence adverbial with wide scope is not present, negation in I or in the quantificational force of a determiner prefers wide scope over the event discourse referents introduced in I. It prefers wide scope over the discourse referents introduced by the translation of I, especially when the negation occurs combined with a subject determiner. Thus, the sentences in (32.a-d) repeated here (32.a) *No one died in the hospital. This lasted for several days. (32.b) No one knew the answer. This lasted for several days. (32.c) ??No one crossed the picket line. This lasted for several hours until the police arrived. (32.d) ?No one laughed. This lasted for only a few seconds, however. have the following translation into first order logic if we follow the results of the DRS construction procedure (32')

VX(
-->

-ae 'JI(e».

In order for there to be an eventuality for the second sentences in (32) to refer anaphorically to, we would need to suppose that eventualities are closed both under summation and complementation. Then from (32') we might assume that there is the event that is the sum of all the not 'JI-ing events for each x. But eventualities, though closed under summation, are not in general closed under complementation; only states are. So sentences introducing event discourse referents under negation will not in general yield suitable antecedents for event anaphora. States, on the other hand, are closed under complementation; more precisely according to (S2) of chapter 1, if -.3s s-
CHAPTER FIVE

PROBLEMS FOR THE SEMANTICS OF NOMINALS

There also seems to be a difference in the negation properties of the various types of eventualities. Achievements are definitely not closed under negation; accomplishments under negation do not seem to yield states either. It appears even dlfficult to get activities to yield states in the absence of an adverbial modifier, though these are decidedly more felicitous than the others. The reason for this felicity may be that non-telic events may act at least similarly to states with respect to complementation.

referents for anaphoric reference. But it does seem as though we can refer to these times with a pronoun or at any rate with a definite description. And it seems one can introduce a temporal discourse referent and then attach the temporal discourse referent introduced by the verbal complex to this temporal discourse referent.

218

5.3 Negation and Wide Scope Adverbials

While negation in I prefers wide scope over the elements introducing discourse referents, it appears plausible to suppose that in the presence of durative adverbials we introduce a state discourse referent outside the scope of the negation. The examples in (31) support this view.24 One might think then that the solution is a tale of accommodation. Whenever a sentential adverb takes wide scope, speakers accommodate this by constructing a particular eventuality to be the bearer of the property introduced by the adverbial. However, if adverbials license the introduction of a state discourse referent, why doesn't anaphora? But speakers cannot accommodate to handle anaphora, given the ungrammaticality of (32.a, c-d).25 Accommodation cannot explain the asymmetry between the behavior of adverbials and anaphora. Our difficulty depends on the assumption that adverbials generate event predicates. But it isn't clear that temporal adverbial modifiers of the sort present in (31) must generate event predicates. An alternative analysis compatible with a DRT framework is that such adverbials generate predicates of times. On this analysis, these temporal discourse referents are introduced by an inflectional component and they are rel~ted to the event discourse referent introduced by I by a predicate like holds. 26 For any event e and time t, holds(e,t) is true iff e occurs during t (t is an interval). Unlike the event discourse referent, however, the temporal discourse referent may have any scope--this, we saw in chapter 2, is not possible for the event discourse referent. This sketch of an analysis would lead to the following DRS for (31.c):27

u, t picket-line(u) for several hours(t) I x I e I person(x) I "* hold(e,t) -, e- cross(x, u)

A chief obstacle of this view might be the predicted availability of these temporal

219

U «.... VLU .....

(36.a) No one crossed the picket line. It was 10 a.m. At 10:02 the governor's troops arrived. (36.b) No one crossed the picket line. The time was 10 a.m. At 1002 the governor's troops arrived. (36.c) It was 1 a.m. No one knew the answer to the problem. So it appears that these temporal discourse referents have the expected anaphoric potential. Krifka and proponents of the state analysis are right in postulating a discourse entity outside the scope of the negation. But that entity is not an eventuality.

5.4 Negation and Event Nominals

We now have left only the data of the third test to account for. Given what I have said about the structure of sentential nominals, the construction procedure immediately predicts that no state or eventuality should be postulated to exist in examples (33). These are all IP gerund phrases with the verbal negation not. Verbal negation goes in I, and this requires an inflection node. But the construction procedure for IP gerunds indicates that all of them denote facts, not events. So it is no surprise that negated IP gerunds also all denote facts and not events. For this reason, sentences predicating spatiotemporal properties of such nominals like those in (33) are bad. What about the data concerning derived nominals, of-ing gerunds and nominal negation? Whenever the negation is contained in the subject DP quantificational structure, the sentences are bad. My translation of no one,

AQ

I u

I

I person(u) I

"*

-,Q

will not allow the wide scope readings of the durative properties in (34) when the partial DRS derived from the possessive modifier DP is applied after the partial DRS derived from the null determiner. To get the wide scope readings, we would need to apply the translation for sthe after we applied the translation of the possessive modifier DP to the translation of the NP. But there are general limits on the order of conversion when negation is concerned, as we saw in chapter 4; negation in the specifier position of the DP always takes wide scope with respect to the quantifier

CHAPTER FIVE

PROBLEMS FOR mE SEMANTICS OF NOMINALS

introduced by the head of the DP. The head detenniner of a DP cannot have wide scope over the quantifier in specifier position when the specifier is a negated quantifier. This then predicts that (34.d-e) fail to have comprehensible wide scope readings for the adverbial modifier. Of those nominals in (34) that have a truly nominal negation, negations of nominals with the particle non seem to be generally bad, as are constructions of the form the failure of <po I repeat (34.a):

into the discourse. (34.c, e-g) incorporate negation into the verb at the lexical level. These lexical operations modify the verbal property and do not have scope over any event discourse referents; thus they induce state types and the detenniners introduces states as the denotation of these nominals, as the aspectual understanding of negation in (34. c, e-g) would suggest. Consequently, with nominals employing such negation particles, sthe can occur in the head D position and we can get an eventuality reading in the normal way. An intriguing case is the one concerning the nominal the professor's non-smoking. Non combines differently with smoking than it does with an achievement nominal like arrival--taking wide scope over eventualities introduced to fill the event argument place in the achievement nominal but not with the activity nominal. This may be simply because non-smoking has just become a lexical element in the language on its own. This form of negation is not completely productive; non-walking and non-sleeping, for instance, are not really viable. Thus, I conclude that negated event descriptions may denote facts or states--which type of entity they denote will depend on the scope of the negation and on the construction rules for nominals I have developed.

(34.a) *The non-arrival of the train lasted over two hours. The principles of my analysis of nominals account for these examples too. Non is a form of not that goes with a (+n, -v) element. It is a nominal modifier that is formed lexically. Its translation is the same as not and it may take an unsaturated predicative DRS as an argument as well as an ordinary DRS. AP

F::==1

L::!J

When we convert the structure above with the translation of arrival of the train, we get a A-abstracted event discourse referent outside the scope of the negation symbol. But this conflicts with the semantic principles about complementation. Events are not closed under complementation; in fact the complements of telic eventualities are not eventualities of any kind. So conversion fails to give us a semantically acceptable structure. Luckily, there is an alternative reading that RLP gives us--namely, one on which the negation takes a saturated DRS as an argument. We are then forced to use the abstract argument transform of the nominal's translation in order to be able to convert with the translation of the determiner the. The event argument place of the nominal has already been filled, and the DP in the PP fills the subject place argument of the nominal. Thus, the representation we end up with for (34.a) is: x,f

AP f'" P(t)

,I

e e-arrive(x)

I

train (x) Charf (f)

The nominal in example (34.b) also does not denote an eventuality. The explanation of this semantic behavior differs from that given for (34.a), but it is also familiar from my analysis of nominals. Failure denotes a possibility with factive presuppositions; a failure is a possibility that does not get realized. The nominal attempt to find an apartment has an abstract reading which characterizes the possibility that is not realized; thus, (34.b) does not introduce an eventuality discourse

221

6. CONCLUSIONS CONCERNING DRS CONSTRUCTION FOR NOMINALS: LESSONS FOR NATURAL LANGUAGE METAPHYSICS I have introduced a great many new types of entities at the level of DRSs. I have treated facts, eventualities, propositions, and projective propositions as distinct types at this level. There are a number of distinctions one can draw at the level of the DRS-distinctions between types of discourse referents and distinctions between types of characterizing structures. While distinctions of type between discourse referents are relevant for natural language metaphysics, they need not carryover to the domain of real metaphysics. The natural language metaphysical entities need only be mapped onto DR-theoretic structures to satisfy the characterization constraints. The distinctions between the projective DRSs, DRSs, predicative DRSs and spatio temporal regions are the ones that are fundamental for real metaphysics. Nothing, for instance, precludes facts and propositions from being reduced to some other type of object at the level of the model theory. In the last chapter and its appendix, we will see that the model theory reduces the natural language metaphysical types to DRtheoretic entities. But before we do that, we must investigate how we refer anaphorically to abstract entities. This is the subject of the next four chapters.

lSeveral philosophers have advanced this view. Some philosophers, for instance Wells (1942), Williamson (1976) take IP gerunds to denote only facts. 2This observation is due to Philippe Alcouffe. 3This observation is due to Weir (1986). ) 4See Zucci (1989) or Abney (1987) for a relatively comprehensive survey. SAbney's analysis is one which contains an NP node and so must be rejected for English. In

222

PROBLEMS FOR mE SEMANTICS OF NOMINALS

CHAPTER FIVE

other languages such as Italian and Dutch, however, as Zucci (1989) observes, there are nominalizations containing VPs that do admit adjectival as well as adverbial modification. German infinitival constructions like seinfortwiihrend(es) dem Vater flilchtig Zuh6ren also seem to show evidence of both adjectival and adverbial modification. This observation is due to Antje Rossdeutscher. For German en nominal infinitives and perhaps also the Dutch and Italian constructions, the syntactic analysis below might be right. Subjects would need to be moved so that they could be assigned the appropriate case, which is genitive, by the D in the German construction. Here is a tree for Johanns Maria kilssen: DP

DP~D' I /~NP Johanni

D

I

-en

even if the data in (4) are persuasive, they don't seem to prove Horn's point. (4.c) That Nixon was a crook we all firmly believed. (4.d) *Nixon's having ordered the covernp Haldeman denied. Horn also claims that extraction is possible from ACC-ing but not from POSS-ing constructions. (5.a) ??Which city do you remember his describing? (5.b) Which city do you remember him describing? I agree with the data as presented in (5) but it does not show a distinction between ACC-ing and POSS-in$.constructions. (5.c) for instance seems to me perfectly fine. (5.c) ~ich documents do you remember Reagan's lying aDout? BeSides Horn, Chierchia and Abney have both professed to find syntactic differences between POSS-ing and ACC-ingconstructions. But Portner argues convincingly that none of their arguments reveals a genuine difference. Chierchia, for instance, claims that ACC-ing constructions are subject to a "double -ing" filter, while POSS-ing constructions are not. An exampfe will make clear what I

mean.

~ N' N/~ IP

~

DP"

I

ei

..... r

I~VP ~ III

Mariakiiss

6 A flaw with Abney's analysis (see note 5) is that it would seem to predict nominative case for

the subject. 7D fun"tions somewhat like a preposition on this proposal. I am indebted to H. Haider for this suggestlon. 8This observation is due to Abney (1987). 90ne difference that Horn claims to find is that conjoined ACC-ing constructions always require singular verb agreement, whereas conjoined POSS-ing constructions require a plural verb agreement. As Portner notes, however, the followmg examples sound reasonable, and so Horn's claim is doubtful: a) John eating apples and Mary sailing around the world bother me. Ib) John's coming and M 's consequently leaving bothers me. second difference Hornag'aimed to find was that while subjectless ACC-ing gerundives allow only a "controlled interpretation," subjectJess POSS-ing gerundives allow only a non-controlled interpretation. In DR-theoretic terms, a controlled interpretation is one in which the discourse referent introduced to fill the subject argument place of the gerund construction a must be identified with a discourse referent introduced by an argument of a predicate ~ of a--~ "controlling" which discourse referent that is. Portner argues persuasively, however, that this difference does not stand up to scrutiny. Defend, for instance, is a DP that takes only POSS-ingconstructions. Nevertheless, we see that in the subjectJess construction, we ~uire below a controlled interpretation. (2.a) John defended attacking Egypt. (2.b) Israel defended attacking Egypt. Another of Horn's apparent distmctions is that ACC-ing gerunds cannot cleft or undergo subject AUX inversion. (These are Horn's judgments). 3.a) ??It was John kissing Mary tfiat upset Susan. 3.b) It was John's kissing Mary that upset Susan. 3.c) ??Did John kissing Mary annoy Susan? 3.d) Did John's kissin Mary annoy Susan? I fin these judgments unsta'ble or inconclusive. While for instance I agree with the judgment that (3.b) is better than (3.a), I find (3.e) also acceptable. (3.e) It is John singing the Marseillaise that will be too much to bear. It is difficult for me to distmguish (3.c-d). I have similar difficulties with another of Horn's tests. He claims that topicalization is acceptable for POSS-ingtonstructions but not for ACC-in$constructions. From this he wants to conclude that POSS-ingconstructions are noun-like but ACC-mgconstructions are not. Here are his data: (4.a) *John kissing Mary we remembered. (4.b) John's kissing Mary we remembered. I don't think (4.a) is so bad. Furthermore, it seems we can get topicalization with IPs within CPs, so

(6.a) *John was keeping singing the national anthem. Portner, however, provides a convincing counterexample to this claim: (6.b) John was imagining (Mary) catching trout. Chierchia (1984) also claims that only POSS-mg can passivize. But this also seems to be incorrect as Portner shows: (7) John kissing Mary was imagined by everyone. (portner) Finally, Abney (1981) claims iliat reciprocals in subject position is permissible only in POSS-ing constructions. But this also seems incorrect. 8.a) *They thought that each other giving up the shi{> was unforgivable. 8.b). They thought that each other's giving up the ship was unforgivable. 8.c) ??They thought that John givin up the ship was unforgivable. 8.d). They took exception to each o~er flirting with their wives. (portner judgment) lOSuppose we allow, following Abney (1987), WH+ features to percolate uR a tree. Further we allow an entire constituent to Pled pipe or move into the specifier position of CP, if it is marked with the feature WH+. There a{>pear to be general limits to the ~rcolation ofWH+ features. IPs constitute a barrier to J?efcolation. Thus, one cannot mark as WH+ DPs that contain a WH+ element embedded within a that clause and so one cannot pied piIJC them. (14.c) *The man that who flirts with your wife you took such exception to. But if IPs constitute a barrier to the percolation of WH+ features, as has been suggested in the syntactic literature, then we predict tliat (14.a) is grammatical but (14.b) is not, because the WH+ element occurs underneath an Here are the respective syntactic structures. (14.a) DP_______ , D /------ N'

~

NP.

:--5t--. D{ ----------

P

~

j

223

I

the

man

~~

DP(WH+)

IP

~----=-----=----

IP

you took such exception to ti

6

wJose

III flirting with your wife

(14.b) DP

I

D'

O-------N' I the ~ -----------cP man

DP~_________ IP

~

~

whom

flirting with your wife

~~

you took such exception tot i

224

CHAPTER FIVE

llSee Abney (1987) for details. 1211 is not really clear to me why the position in (IS.c-d) of the sentential adverbial makes such a difference, but still that is a mystery rather than an argument against the view. Here is one J.>Ossible explanation for the discrepancy, though 1 must admit it is liighly speculative. If a POSSmg gerund did contain a complete IP then the adverbials in (lS .. a-b) would occur as adjuncts to !P. This could preclude the movement of the DP from within the IP outside, if one makes the hypothesis that such adjuncts would create barriers to movement. Here 1 have in mind a story like that told in Chomsky's Barners. But the notion of barrier here needs much more exploration. i30f course syntacticians rule out pluralization here by speaking of a verbal form. But the appeal to verbal form here does not in itself explain much. 14Abney (1987) claims that the subject of POSS-ing gerund constructions must always be read as having wide scope over negation. But as the exarnpfes in the text indicate, 1 don't think this holds. 15 Further evidence for the narrow scope reading for the DP in specifier position comes from anaphoric examples. If the noun phrase introduced a discourse referent into the main DRS, then we should be ab1e to get the anapfioric reading for the following sentences. But such readings are not to be had. a) *1 won't permit a dog i licking Shirley's hand. She is terrified of iti. b) *1 won't permit a dOg'Si licking Shirley's hand. She is terrified of iti. c ) *A dog's not being housetrained drives my mother crazy. IIi is so messy. Permit is a verb that is non-factive and takes IP-gerunds as complements. The indefinite a dog prefers a narrow scope reading in the examples above, so the intended anaphoric links seem bad to me. DRT predicts the intended anaphonc link to be possible if a plural anaphoric pronoun is

~

used.

16This is Abney's actual syntactic structure for POSS-ing gerundive phrases. But something like the DP over NP analysis has been around for a while. For instance, see Schachter (1976), Chomsky (1981), and Jackendoff (1977). 17For details see Asher and Bonevac (198Sa). 18Again this might be accomplished in a number of ways in this framework. 19With a negative quantifier inside the IP, we cannot pull the factive presupposition outside the DRS K created by the IP, because the presupJlOsed material Will use the discourse referent introduced by the negative quantifier which is declarea within a subDRS of K-- thus we cannot infer from John saw no boys dance that there was a dancing event, which is what is wanted and argued for in Asher and Bonevac (198Sa). 20See Ducasse (1940), Wells (1949), van Frassen (1969). Philosophers of course did not agree on the nature of facts, propositions, etc.! 21 Though not that a certain conjecture, supposition, or possibility is true or a fact. 22 Adverbial modifier clauses are phrases like until the doctors ran out ofplasma. So the sentence No one died in the hospital until the doctors ran out of blood plasma. is perfectly acceptable. 23This observation is due originally to Cresswell. For a discussion see Bauerle (1987). 24The wide scope reading of the adverbial in these examples is preferred. There are other ~entences, however, where a narrow scope reading is much more plausible. Consider for Instance, No one laughs for five days. 25 1 am indebted to a reviewer of Kluwer's for making me see that my earlier account of accommodation ~Asher 1990b) was flawed. 6See for instance Lascarides and Asher (1991). Fredericke Moltrnann suggested to me such a ~ssibility . 7What needs to be done is to analyze in detail the contribution of various features in the inflection nod~. Unfortunately the syntactic analysis of 1 is still rather unclear and any semantic analysis must aWaIt some sort of syntactic consensus.

ANAPHORA AND ABSTRACT ENTITmS

The investigations of previous chapters suggest that subDRSs and predicative DRSs, as well as discourse referents, may serve as terms of anaphoric relations. The use of DRSs as anaphoric antecedents has already pointed to the curious ability of pronouns to refer anaphorically to a sum of what seem to be disparate, abstract objects. In this chapter, I discuss various types of abstract entity anaphora within the DRT framework--in particular, anaphoric reference to events, facts, and propositions, which are representative of eventuality and abstract object anaphora generally. I will indicate how various anaphoric phenomena involving eventualities and abstract entities have a uniform analysis within the DRT framework. This will lay the groundwork for the next three chapters, in which I examine the intricate effects of discourse structure on these anaphoric relations. Even without bringing in discourse structure, however, there is much to say about abstract entity anaphora. The principal finding of this chapter is that many abstract nominals behave very Isimilarly to proper names in anaphora. A proper name may serve as a potential antecedent to a pronoun no matter how deeply embedded is the context in which it occurs. Discourse referents introduced by proper names are always accessible. Similarly, the DR-theoretic structures that characterize abstract entities introduced by IP and CP constructs are always accessible to discourse referents introduced \ subsequently by pronouns in the discourse. The explanation of this anaphoric behavior depends on the semantic analysis of the nominals, on which the characterizing DR-theoretic structures in effect are names of themselves. I

!'

1. TOWARD A UNIFIED ANALYSIS OF ABSTRACT ENTITY ANAPHORA

Abstract ~E!!~y ~naEh,2~seHh!~~A!f(~r~.!lU~.Y..£!!.P.l~2:\!D·§.:J!!{~.__!!!f!!.L~g
226

CHAPTER SIX

r" :'1i;-:

ANAPHORA AND ABSTRACT ENTITIES

227

!

The range of phenomena that fall under the heading of abstract entity anaphora is quite large. Anaphoric antecedents referring to saturated, abstract entities arise from six kinds of linguistic constructions: (i) that clauses, (ii) infinitival phrases, (iii) gerund phrases, (iv) naked infinitive complements, (v) noun phrases that appear to denote proposition-like entities, (v) clauses with parasitic gaps, and even (vi) implicit "chunks" of the text. In (La) for instance, a that clause is the antecedent for the pronoun. In (I.b) it is an infinitival phrase, in (I.c) it is a gerund phrase, in (I.d) a noun phrase, in (I.f) a clause with a parasitic gap. (I.e) is a form of anaphora in which reference is made to a concept. It exploits a verb phrase antecedent. The coindexing below indicates the intended antecedents in these examples. (La) (I.b) (I.c) (l.d) (I.e) (l.f) (l.g)

John believed [that Mary was sick]i. The teacher believed iti too. Fred wanted [to go to the moviesL. But his mother wouldn't allow it i. [John's hitting Fred]i got everyone in trouble, for iti led to a brawl. Iti also indicated that they must have been pretty mad at each other. [The claim that Susan got a C on the test]i was surprising. John did not believe it i. Fred [hit a home runL and then Sally did it i. Fred believed that [Mary was not nice enough to try to please]i. But Bill didn't believe that i (thisj, it i). The "liberation" of the village had been a disaster. [First on a sweep through the town some of the Marines had gone crazy and killed some innocent villagers. To cover up the "mistake," the rest of the squad had torched the village. To cap it off, the lieutenant called in an air strike.]i At first the battalion commander hadn't believed it i.

(l.g) is in many ways the most mysterious sort of abstract anaphora, because it is unclear how to pick out a "chunk" of text; it is not clearly grammatically determined. I will study such examples in detail in chapters 7 and 8. Here I will concentrate on the more standard examples as well as discuss anaphora in general. Notice that I have used several anaphors above--this, that, and it. Stressed it, this and that are often interchangeable, but there are also some interesting differences. 2 Stressed it may refer deictically but its referent must be the topic of conversation. That, on the other hand, may refer only to a more peripheral object. This and that follow the same patterns when referring to abstract entities that have been expressed in a text. Consider for instance the use of the pronoun that in (I.g) intead of it. That picks up easily the proposition expressed by the previous clause in (l.g)--the proposition about the lieutenant's calling in an air strike, while this tends for me to pick up the entire topic (the "liberation" of the village). It ialso tends to pick up the whole topic. The preference for a proximate deictic referent on the part of this translates into a preference for a topic anaphoric antecedent. That prefers an antecedent that is peripheral or not part of the topic.3 There is a clear distinction between the topic oriented use of this and the non-topic oriented uses of

that and it. In deictic contexts the topic orientation of this may be exploited to form self-referential propositions. Anaphoric reference to abstract objects and eventualities involves anaphoric reference to a great variety of entities. I call those constructions in which anaphoric reference is made to an event event anaphora, anaphora in which reference is made to a proposition proposition anaphora, etc. There are important similarities between event, proposition, and property anaphora that a general theory of anaphora should \ capture. Although I believe that there is a general analysis of anaphora, it is not clear that 4 all forms of anaphora intuitively "referring" to abstract entities have a common analysis with individual and plural anaphora. Some of these forms are known in the literature as "surface anaphora," because they appear to exploit surface features of the syntax; they include constructions like VP ellipsis, gapping, and sluicing. Hankamer and Sag, for instance, have argued that surface anaphora and "deep" or pronominal anaphora do not have a common analysis. (2) gives examples of surface anaphora, as well as some other forms of anaphora which have a "surfacelike" feel. 4 In (2.d), we have yet another sort of concept anaphora; there the antecedent appears to be the common noun phrase. 5 We might call this N' anaphora. A closely related if not identical anaphoric phenomenon in (2.e) uses one or other numerals as anaphors. (2.a) (2.b) (2.c) (2.d) (2.e)

Fred hit a home run, and then Sally did too. (VP ellipsis) Mary beat Fred at chess on Thursday and Sam on Friday. (Gapping) Fred's playing the Mozart K.333 sonata. B: Yeah, but not very well. (Sluicing) Many villagers came to the wedding; they like that sort of thing. Fred ate one sandwich, but Sam ate two.

Surface forms of abstract entity anaphora and those employing overt pronouns share some features that make abstract entity anaphora different from anaphoric reference to individuals. Examples like (l.b), for instance, indicate the considerable complexity in determining the appropriate antecedents in proposition anaphora and abstract entity anaphora generally. In (l.b), the part is an infinitival phrase; the proposition picked up by the pronoun (namely, that Fred goes to the movies), however, results from combining the content of the infinitival phrase with the subject, Fred, of the entire sentence. Such "reconstructions" of propositions remind one of the constructions in (2). Another trademark of a surface form like VP ellipsis is that it often gives rise to ambiguities between strict and sloppy readings, as in (3)

Fred wanted to go to a restaurant that Suzie had recommended to him. Bill wanted to also.

The second sentence in (3) can be interpreted in one of two ways. It refers to either

ANAPHORA AND ABSTRACT ENTITIES a restaurant recommended to Bill (sloppy) or a restaurant recommended to Fred (strict). Proposition and property anaphora with overt pronouns also exhibit sloppy-strict ambiguities, The ambiguities of sloppy and strict readings appear to be a general trademark of abstract entity anaphora. But the different anaphors appear to license sloppy readings to different degrees. this and that and descriptions like the same thing support sloppy identity anaphora easily, while it has more difficulty in doing so. Contrast (4.a) or (4.b) with (4.f): (4. a) (4.b) (4.c) (4.d) (4.f)

Mary has been going around saying that Al proposed to her, but Jo has been saying this (that) too. Mary has been going around saying that Al proposed to her, but Jo has been claiming the same thing. John finished grading his paper before that happened to the teacher. John told Mary that she should go out with him, and Fred did this too. Mary has been going around saying that Al proposed to her, but Jo has been saying it too.

Most speakers easily get the sloppy reading for (4.a), in which what Jo has been saying is that Al proposed to Jo, with both this and that as anaphors. Many speakers do not get the sloppy reading of (4.f); the highly preferred reading is the (nonsloppy) reading on which Jo has been saying that Al proposed to Mary. 6 Analyses of VP ellipsis like those of Sag (1976) and Williams (1977) exploit the specific grammatical structure of the antecedent or source VP to account for strictsloppy readings. Sag and Williams require that an alphabetic variant of the logical form of the antecedent be inserted in place of the ellipsis (Sag) or the null VP node in its interpretation at logical form (Williams). In this way they would account for the ambiguities illustrated in (3), as well as the impossibility of VP-ellipsis in cases such as (S.b). The distinction between (S.a) and (S.b) appears to hinge on the fact that the antecedent of (S.b) is not of the right grammatical sort to combine with the auxiliary did. (S.a) (S.b)

Someone had to take out the garbage. So Bill did. *The garbage had to be taken out. So Bill did.

The similarities between proposition anaphora, property anaphora, and VPellipsis suggest that the link in proposition anaphora between antecedent structure and the discourse referent introduced by a pronoun should involve at least the attention to structure that typifies the analyses of VP ellipsis by Sag and Williams. This clearly reflects a dissimilarity between abstract and "concrete" entity anaphora. One might go further, however, and suggest that the pronouns in (1)-(2) are "pronouns of laziness," which just stand in for a phrase or a bit of syntactic structure. This thesis would make abstract entity anaphora quite different from the semantic analysis of individual anaphora, as, for example, DRT develops it. But

229

this thesis is not plausible for abstract anaphora in general. If it in the last sentence of (log), for example, were a pronoun of laziness, it should be possible to replace it with its intended linguistic antecedent or its syntactic structure. But this yields outright ungrammaticality, if we assume any reasonable syntactic structure for attitude constructions. So it cannot be a pronoun of laziness insofar as it is a place holder for some piece of syntactic structure. A further argument for insisting on a semantic analysis of abstract entity anaphora is that abstract entity anaphora with explicit antecedents also shares significant parallels with individual NP anaphora. These similarities suggest a uniform treatment of both abstract and concrete entity anaphora. The first and obvious point is that proposition and concept anaphora involving overt pronouns may, like individual anaphora, exploit noun phrases as antecedents. Compare (lod), for instance, with (6)

[The man in the black raincoat]j looked suspicious. Frank did not trust himj.

The anaphors and their intended antecedents appear to connect with the antecedent definite noun phrases in an entirely similar way. It seems prima facie implausible that these examples of anaphora should be analyzed in radically different ways. To say otherwise is to give up a uniform analysis of noun phrases with little to show for it. Thus, we seem committed at least in certain cases to a parallel analysis between abstract entity anaphora and singular individual anaphora. The similarity between surface and other forms of abstract entity anaphora makes desirable a unified analysis of all anaphoric forms. Another argument for a common analysis of all forms of anaphora using overt pronouns is that they all may be used either deictically or anaphorically. Pronouns can even refer to propositions, events, and concepts without a linguistic antecedent of a particular form or indeed without any linguistic antecedent at all. The pronouns this and that are typically used deictically when they are taken to refer to individuals'? So one can certainly use that deictically to pick up an object in the discourse situation which might be classified as an eventuality. Imagine in the discourse context of (7) that the speaker has just seen Carl Lewis break the world record for the 100 meter dash. He or she might very well say, (7)

That was amazingly fast.

Given the context, that refers to the event of Lewis's race. But one can also use this or that to refer to propositions or event-types by hooking them up with salient events in the context. In the same context as (7) one might also utter (8): (8)

Susan won't believe this.

(8) is a more complex case of deictic anaphora than ordinarily discussed. One

ANAPHORA AND ABSTRACT ENTITIES might say that this has some relation to the event of Lewis's breaking the world record. 8 But the semantics of believe forces this to refer to the proposition that describes the event--i.e., the proposition that Lewis broke the world's record. The shift in reference from the concrete to the abstract end of the spectrum of world immanence is familiar from previous chapters. It seems to me that it, at least with the appropriate intonational stress, can also be used in such contexts to refer deictically to abstract entities. Consider the following variants of (7-8), which sound passable to me; (9.a) (9.b) (9.c)

I didn't believe he could do it. Susan won't believe it. It was amazingly fast.

In addition to events and event-types, one may also use it to refer to a proposition without exploiting a piece of logical form given by previous discourse. Suppose, for instance, that the following sentence is uttered in a context of looking at a particular sign. (10)

I don't believe it.

Since believe is an attitude verb, it must refer to a proposition--a proposition correlated with the sign the utterer sees. But the sign itself might not directly express any proposition at all. It might just be a sign that indicates that the road ahead is closed for repairs. This contextual use of pronouns to refer to objects deictically is a common feature of all forms of anaphora that exploit anaphoric pronouns. Supposing then that we opt for a unified analysis of anaphoric phenomena, what should this common analysis be? The general analysis of abstract entity anaphora does not fall within the scope of any known syntactic binding theory.9 Such analyses rely on a syntactic mechanism to coindex the pronoun and its NP antecedent. With such a coindexing mechanism for noun phrases, it is then usually routine to derive a translation for sentences with intrasentential anaphora in which the antecedent NP

231

can, of course, make use of syntactic information. The difference is that a semantic theory seeks to explain anaphora by means of semantic concepts like reference, variable interpretations, and truth conditions; a syntactic theory would not. The DRT account of anaphora is designed to handle anaphoric reference across sentences and so offers a more flexible framework than syntactic binding theories. This flexibility is essential in giving a general account of abstract entity anaphora. The examples in (1) and (2) show that proposition anaphora works intersententially. But there are also examples of intersentential anaphora with events and with concepts. Consider (I 1. a) and (l1.b); (I1.a) John kicked i Sam on Monday, and itihurt. (I1.b) John kicked i Sam on Monday. Iti hurt. Surely, the anaphora in (II.a) and (11. b) should have the same analysis. The DRT account highlights the close connection between deictic and anaphoric uses of the pronouns. Deictic reference, as opposed to anaphoric reference (insofar as this is a real distinction), uses as referents those non-linguistically described objects that are part of the discourse context, while anaphoric reference is dependent upon a linguistically expressed antecedent. As a cognitive theory, however, DRT postulates a common form of representation for information derived from different sources. DRT is thus able to exploit the similarities between deictic and anaphoric reference. DRT's semantic analysis commits us to entities like propositions and concepts at the DRS level of semantic analysis, which is the level of natural language metaphysics. It might be nice to avoid the complications introduced by such commitments. But almost any plausible analysis of noun phrases yields this commitment when it is applied to noun phrases that intuitively denote abstract objects. Natural language metaphysics is in any case committed to the existence of these entities. If these arguments carry weight concerning the analysis of pronominal forms of abstract entity anaphora, what about the analysis of similar forms of anaphora like VP ellipsis? Recently Fiengo and May (1990) have showed how VP ellipsis may be treated by copying pieces of syntactic structure after quantifier movement at logical form, and they have made interesting discoveries. But their approach misses parallels between abstract entity anaphora with overt pronouns and VP ellipsis, which will surface in this chapter and the next two.l o Moreover, one can make sense of VP-ellipsis as a form of semantic anaphora within DRT. Klein (1986), for instance, proposes that a null VP node introduces a concept discourse referent with which an alphabetic variant of the predicative DRS derived from an appropriate verb phrase may be identified. I shall adopt a uniform, DR-theoretic, semantic treatment for VP ellipsis and abstract entity anaphora.

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ANAPHORA AND ABSTRACT ENTITIES

2. EVENT ANAPHORA The simplest case of event anaphora is one in which an event nominal--e.g., a ( derived nominal or an of-ing gerund--introduces an event discourse referent to which a pronoun anaphorically refers. As analyzed in chapter 4, derived nominals and of-ing gerunds denote a unique event relative to the values for the argument and the discourse context. The theory predicts such gerund and derived nominal phrases will behave like definite noun phrases with respect to accessibility and anaphora, if the arguments are definite. They should behave like indefinite noun phrases if one of the arguments is indefinite or non-specific. These predictions tum out to be well supported. (12.a) Everyone mourned [the city's destruction]i. Iti was bloody. (12.b) No one believed that Mary heard [that dog's loud barking]i. Iti lasted for hours. (12.c) *If [a dog's loud barking]i had woken Mary up, then I would have been mad. Iti lasted for hours. In (12.a) the derived nominal destruction behaves like a definite and licenses the event anaphora. There are no scope ambiguities in the first sentence of (12.a)--no reading on which everyone mourned some destruction of the city but no destruction of the city such that everyone mourned it. Similarly, in (12.b), the nominal has a definite argument. According to the analysis of chapter 4, the discourse referent it introduces is accessible to the discourse referent z introduced by the pronoun, and so DRT predicts the intended anaphoric link in (12.b) to be fine, even though that dog's loud barking occurs within the scope of a negation and an attitude predicate. In (12.c), however, the nominal has an argument that prefers a non-specific reading. The event discourse referent is then simply introduced within the scope of the conditional operator and not linked to any top level discourse referent, which would happen if the nominal were a definite. The discourse referent is thus inaccessible to the discourse referent introduced by the pronoun, and so the accessibility constraint forbids the intended anaphoric connection indicated by the indices in (12.c) and predicts its ungrammaticality. The partially completed DRS for (12.c) shows this in graphic terms. To avoid clutter in the DRSs, I omit the temporal discourse referents, temporal conditions, and complications with temporal adverbials introduced in chapter 5.

233

z Ie, e', x,

U

dog(x) e- bark(x) e'-keep-awake(e, u) Mary(u) last night(e')

I

s, i ~

s- mad(i)

z=? terrible(z) A second type of event anaphora involves anaphoric reference to an eventuality discourse referent introduced by the inflection node. In chapter 2 we saw how the inflectional components of action verbs introduced discourse referents in a way similar to indefinite noun phrases. There is no counterpart to the rule of quantifier raising for inflectional nodes, however. So in a sentence containing true quantificational noun phrases, which generate complex conditions and subDRSs, the event discourse referent introduced by the inflection node must always be introduced within the subDRS in which the verb's condition is introduced. It is not introduced into the universe of the principal DRS in such cases. The theory predicts that an event discourse referent introduced by the inflectional component of a sentence does not take "wide scope" and so will be inaccessible to the discourse referents introduced by pronouns in (13.a), just as the individual discourse referent intr~duced by any boy is inaccessible in (13.b).l1 In (13.d) it is possible to refer to a raising of the flag by a patriot. The explanations of the acceptability of (13.c, e) are the same as those for (13.d, t), which are given in chapter 2. (13.a) *No jet passedi over the reviewing stand. Iti lasted a few seconds. (13.b) *No girl kissed any bOYi. Hei was then very cross. (13.c) If a patriot were to raisei the flag of the Republic, it would cause a sensation. Iti would alarm the ruling junta. (13.c) If a professor were to own a Mustangi> he would not be able to maintain it. Iti would cost him too much to fix. (13.e) If Timmy hits i John, iti will cause a fight. (13.t) If Pedro owns a donkeYi> he beats it i. The evidence in (13) suggests that the accessibility constraint works as expected for event anaphora in examples using negation or negative quantifiers (13.a-b) and conditionals (13.e-t). There are also examples of modal subordination with event anaphora that parallel those that involve individual anaphora (13.c-d). On the other hand, the DRS construction procedure and accessibility constraint predict that (14.a) should be bad, assuming that we treat event anaphora just like individual anaphora and that the construction procedure is correct, since these assumptions entail that (14.a) has the same logical form as the narrow scope reading

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for a donkey in (14.b) (14.a) In every village, someone raised the flag of the democratic movement. It alarmed the ruling junta. (14.b) Every farmer owns a donkey. It is unhappy. In the DRS for (14.a) below, the event discourse referent standing for a raising of the flag is not accessible to the discourse referent introduced by the pronoun. (K14.a) Z,

w,e

Il . x !

l

I

I vlllage(x) I

V x

z= ? ruling-junta(w) e'-alarm(z, w)

I

X,O,O,V

I

in(x, e) flag of the democratic movement( u) e-raise(u, v)

Since there is no accessible discourse referent with the appropriate features with which z may be identified, the DRS for (14.a) cannot be completed, and so (14.a) is predicted to be bad. But (14.a) is good. Is the accessibility constraint wrong for event anaphora? Before revising accessibility, we should examine our two main assumptions. First, we might reconsider our approach to inflection and consider whether inflection acts like a definite so that the discourse referent it introduces is always accessible. On the other hand, event discourse referents introduced by the inflection node I seem to behave quite analogously to individual discourse referents introduced by indefinite noun phrases rather than definites. They do not behave like the event nominals in (12.a-b). The second assumption is that event anaphora is completely on a par with the familiar theory of individual anaphora. But event anaphora shares a common trait with plural anaphora and mass noun anaphora; this trait will offer us an account of (14.a). Like individuals, events may sum together. I discussed the general principles for event summation in chapter 1. Events that are temporally, spatially, causally, or thematically connected 12 may sum together to form larger events. Consider the following discourse. (15)

The Ashers were predictably short of groceries the day of the party. Nicholas Asher went out to get some, got lost and arrived back only after the party had ended. Because of this, the committee made sure that the Ashers never gave a party for the Society again.

The pronoun in boldface has a number of possible antecedents. Each clause in (15),

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for instance, introduces an eventuality. The first state, being short of groceries, thematically motivates or "occasions," to use Hobbs's term, the following event of Nicholas's going out to get groceries, which then occasions the event of his getting lost, which causes the late arrival after the party's ending. The events in this sequence are clearly causally and thematically related. According to the principles of event summation described in chapter 1, these events may combine or merge to form a sum event. Natural language metaphysics treats sums of events, however, as individual, singular events--not aggregates or groups thereof. Thus as in (15), a singular pronoun like this, that or it may anaphorically pick up a sum of event. The partially completed DRS is below; EB denotes the summation operation for eventualities.

x, s, y, e, W, el e2, e3, e*,

e', z

the Ashers = X s- X short of W groceries(W) Nicholas(y) e- y went out to get W el- Y got lost er y arrived back the party = x erend(x) after(e3, e2) e* = s EB e EB el EB e2 because-of(z, e') z=? [e'-the committee ... ] e* represents the sum of the four events and states, and it is accessible to and a potential antecedent for z, the discourse referent introduced by this. A puzzle w~ich this account cannot answer is why other discourse referents are not pOSSIble antecedents for z. Clearly, world knowledge has much to do with ruling out e3 (why should the committee be upset that the party ended), e' (events are typically not their own causes in natural language metaphysics). But there are no obvious bits of world knowledge that rule out s, e, and el. Yet it seems almost impossible to get e or el. To narrow down the range of potential anaphoric antecedents and eliminate e and el as potential antecedents for z, we must appeal to discourse structure. An account of such examples using discourse structure appears in chapter 8.

3. EVENT-TYPE ANAPHORA AND USING EVENT-TYPES TO CONSTRUCT EVENT SUMS Example (15) shows that a discourse referent z introduced by a pronoun can be linked to a discourse referent representing a sum of events, each of which is

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ANAPHORA AND ABSTRACT ENTITIES

represented by a discourse referent accessible to z. But if we tum our attention back to finding an appropriate antecedent for (14.a), we see that the sorts of sums formed to account for (15) will not help in finding an appropriate antecedent for the pronoun there; for in (14.a) there are no accessible event discourse referents whatsoever. Luckily, we may form sums in another way--by using the event-type expressed by a complex condition. In chapter 2, I noted that one could form groups by means of the operation of abstraction, and it appears that one can similarly form a sum event by an analogous principle of event abstraction. Abstraction is not an independent principle of anaphoric reference, but rather a consequence of the accessibility of event-types, or, in the more general case, properties. Event-type anaphora serves as an introduction to abstract entity anaphoric reference. The simplest kind of event-type anaphora occurs with pronouns bound to nominals that denote event-types.1 3 As we saw in chapter 4, saturated event-types may be introduced by bare gerunds and derived nominals, as well as NI perception clauses. The examples in (16) show that we can refer anaphorically to event-types. (16.a) [Unsafe flying]i is foolish. Iti causes accidents. (16.b) John sees [Mary run]i, and Sam sees iti too. The gerund in (16.a) introduces an event-type, denoted by the predicative DRS, an alphabetic variant of which is identified anaphorically with the discourse referent introduced by the pronoun. The use of an alphabetic variant is needed in order to avoid any possible clashes of binding of discourse referent values by embedding functions. z, Y,e' foolish(Ae

x,y

)

237

K behaves as though it were a discourse referent also declared in UK'. When there are no such discourse referents, K behaves like a proper name or simple constant. Thus, a predicative DRS K will be accessible to a discourse referent u so long as all the discourse referents not declared in UK but occurring in K are accessible to u. The anaphoric data bears out this prediction: (17.a) Everyone believes that Fred should not allow [unsafe flying in his airplanel. Iti led to an accident before and iti will lead to an accident again. (17.b) John didn't see [Mary leave]i and Sam didn't see iti either. (17.c) *Mary saw [no one leave the building]i and Sam saw iti (that i) too. (17.d) *Mary saw [Fred hit no bOY]i. Jean saw iti (that i) too. (17.e) ??Mary saw [Fred give no present to a child in the orphanage]i. Sam saw iti too. The event-type occurs within the scope of a negation operator, a quantifier and an attitude operator in (17.a) and inside a negation operator in (17.b). Yet the anaphoric connections intended in (17.a-b) are perfectly felicitous. Accor~ng to our analysis the event-types with their definite arguments should be accesslb~e to any subsequently introduced discourse referents, and so the examples are predicted to be OK. On the other hand, (17.c-e) are decidedly out for most people. Consider, for instance, (17.c). In this example, we see how the accessibility of subDRSs is limited by the accessibility of the discourse referents that occur but are not declared in them. Following the outlines of the treatment of NI perception contexts, we get the following DRS and factive presuppositions with the appropriate scope.

e -fly(x, y) unsafe(e) e'-cause(z, Y) accidents(Y) x',y' Ae" e" -fly(x', y') z= unsafe(e" )

Mary(x) building(u) e, e'

...., e-see(x, Ae

I

I)

1e -leave(y, u)1 The DRS and explanation for the anaphoric links in (16.b) are analogous. As we saw in chapter 4, the use of predicative DRSs to characterize abstract entities makes them have a term interpretation. Such DR-theoretic structures name themselves. Given that characterizing predicative DRSs function like names, the semantics predicts that the constructions giving rise to such structures should behave just the way definite noun phrases do. The prediction is that if the discourse referents occurring in conditions of a predicative DRS or subDRS K that are not declared in UK are declared at UK', then

Sam(v) et-see(v, z) z=?

e'-leave(y, u)

Suppose the DRS above is true at a world of evaluation w. Since y is not acc~ssible to z, the discourse referent introduced by the pronoun, the subDRS denotmg the state of affairs of seeing y leave u is also inaccessible to z. If we attempt to put the identification in the main DRS as the DRS construction procedure requires, then y

CHAPTER SIX

238

will occur in a condition in the main DRS and outside the universe in which it is declared. This is incoherent. In order to identify the concept with the anaphor in a coherent way, we would have to put the contents of the entire second sentence under the scope of the negation sign. The DRS construction procedure does not allow this, and in any case this would yield the wrong truth conditions. 14 The hypothesis that the structures characterizing event-types or event-type denoting nominals behave in the way discussed yields analyses of discourses that prove difficult to handle on a pure event analysis. Let us suppose that either events or event-types may be the subject and object place arguments of happen and do respectively, though facts might also fill those argument places. (18)

John now belie~at Mary will leave him. Fred has been expecting frj to happen all along.

In (18) it could refer to an event or event-type, depending on which analysis of the verb happen one chooses. On the event analysis, the intended antecedent is the event of Mary's leaving. But this event is in principle inaccessible, since the discourse referent standing proxy for it is introduced within a belief context. But if it picks up the event-type of Mary's leaving John, then the predicative DRS given by A-abstracting over the event discourse referent in the subDRS constructed from the complement of believe is accessible; (18) is then predicted to be felicitous. Here the identification between the discourse referent introduced by it and the event-type characterizing structure will be direct, not functional. This appears to be the simplest explanation of this sort of puzzling case. One might try to save a purely event based analysis of the anaphora in (18) by postulating some kind of communicative or causal link between Fred and John and claim that it is this link that makes the event John has a belief about the same event that Fred has been expecting to occur.15 Whatever the merits of this ploy in the case of (18), the strategy to save the event analysis won't work for (19): (19)

Everyone who owns an airplane is in danger of having it stolen. That happened to Harry last week.

There is no event discourse referent in the DRS for (19) accessible to the one introduced by that. The event analysis would thus have to assign incorrect truth conditions or violate the conditions on accessibility of discourse referents in order to account for the intended anaphoric link in (19). On the event type analysis, however, the pronoun that picks up the event-type of having one's airplane stolen, which is accessible to the discourse referent introduced by that. The hypothesis about the definiteness of event-type denoting expressions also allows us finally to account for the anaphoric connection in (14.a) in a general way. Consider again (14.a), or the troubling examples from chapter 1 repeated here with their intended anaphoric antecedents:

ANAPHORA AND ABSTRACT ENTITIES

239

(14.a) In every village, someone raised i the flag of the democratic movement. It i alarmed the ruling junta. (20.a) Three men raised i the flag of the republic. It i took the ruling junta by surprise. (20.b) Every pledge is viciously hazed i • It i hurts them deeply. Implicit in the fIrst sentence of (14.a), for instance, is an event-type being described. It is the event-type of someone raising the flag of the democratic movement. The DRS construction procedure actually displays this event-type; it is an alphabetic variant of the DRS-union of the subDRSs of the complex condition in (KI4.a)-again omitting the temporal information: x', u', v'

Ae f-:-=-'---'c-;:--------------i village(x') in(x',e) flag of the democratic movement(u') e -raise(u', v') Such event-types when explicitly constructed are always accessible, so long as all discourse referents not declared in UK but occurring in K are accessible. But here the difficulty is that the event-type DRS has not been constructed. What licenses this construction? A particular sort of discourse structure licenses the construction of the event-types. A given discourse confIguration forces us to add or to alter what the simple DRS construction procedure offers. Here it is the appearance of a condition introduced by the pronoun and a complex duplex condition in the already constructed DRS that makes us rewrite the latter constituent so as to contain the appropriate event-type. We shall see many more instances of such effects of discourse structure in chapters 7 and 8. The anaphoric connection between the event-type (or property in the case of plural anaphora) and the pronoun, however, is indirect. The link between the discourse referent introduced by the pronoun and the structure characterizing the event-type is not one of identity, but one of functionality. That is, the discourse referent introduced by the pronoun is to be identifIed with an object that is a function of the event-type. The particular function we need takes an event-type as an argument and returns the event that is the sum of all those events satisfying the event-type. My notation for this function is the sum operator L; the sum event relative to some event description AeK is L {e': AeK(e')}, which denotes the event relative to a world w and time t and an embedding function g that is the sum of all those events gee') such that [g, K[e'/e]]w, t. Here is the rule for event summation: Suppose a complex condition of the form O(KJ> K 2) occurs in Ko and that a is a DRS operator that is not monotone decreasing. Then if e E UK" one may form the sum L {e': Ae {(K 1 U K2)[e/e]}(e')}in ConKo and use it as an antecedent for anaphora resolution. 16 It is important to note that this way of forming the mereological sum of events

ANAPHORA AND ABSTRACT ENTITIES does not presuppose in any way that the individual event discourse referents standing proxy for each flag-raising are accessible to the pronoun. What is accessible to the pronoun is the event-type, which is an abstract entity and functions like a definite with respect to accessibility. Further, this way of fonning the mereological sum of events adheres to the constraints on summation for events explored in chapter 1, because we are summing across events satisfying event-types and not across arbitrary collections of events. This hypothesis yields one reading of (20.a)--namely what surprised the ruling junta was the sum of three individual flag raisings. It also accounts for the sorts of plural anaphora observed in chapter 3 and evident in (I4.a) and (20.b))7 The completed DRS for (14.a) is below. n,z, w,e' x viIIage(x)

<J>

e' <now ruling-junta(w) e'-alarm(z, w)

z '" L {el: I.e

x,e,u,v in(x, e) e<now flag of the democratic movement(u) e-raise(u, v)

x' u', v' (el) } yiIIa,ge)x') m(x,e e <now flag of the democratic movement(u') e -raise(u', v')

Since the event-type used to define the sum may have discourse referents that are not declared in its universe, the set of events satisfying the event-type must be defined relative only to embeddings which properly embed not only the copied subDRS but all the superordinate DRSs in which discourse referents occurring in K are declared. This imposes constraints on where we can sum up events. Given a complex condition in Ko introduced by a quantifier of the fonn Q(KI, K 2), we may perhaps only exploit the event-type for event summation on KI U K2 within Ko, if discourse referents declared in Ko are used in KI or K 2. We can, however, exploit the event summation procedure iteratively. Thus, if we have a condition in Ko of the fonn KI QI K2 and K3 Q2 K4 E ConK 2 , where QI and Q2 are operators and e is an event discourse referent that is introduced in UK 3 , then one may first fonn within ConK 2 the condition z = L {e: I.e' [(K3 U K4)[e'le)] (e)} and declare z within UK,. One may then fonn the sum of all the z's by exploiting the event-type provided by K 2 • By allowing the iterative application of the summation principle, one can predict that the following are felicitous examples of event anaphora: (2l.a) Every boy kissed i at least three girls. This i upset the chaperones so

241

much that they called the principal. (2l.b) Every boy who kissed i at least three girls was happy. But this i so upset the chaperones that they called the principal. In both of these cases, it seems possible to identify the anaphoric antecedent of this as the event or state consisting of all the individual kissing events. Not all logical structures felicitously allow event summation. Contrast (20.a-b), for instance, with (22.a-c): (22. a) At least four women believed that three men had raised the flag of the Republic. This took the ruling Junta by surprise. (22.b) It is false that three men raised the flag of the Republic. But according to the ruling Junta, this will signal a general revolution. (22.c) No one raised the flag of the Republic. This took the Junta by surprise. In (22.a) the antecedent of this cannot be the sum of the three flag raisings. We have a semantic explanation for this effect. Natural language quantification, as many have remarked, is almost always restricted to some nonempty domain. The use in natural language of a non-monotone-decreasing quantifier 18 Q then presupposes that whenever the condition Q(KJ, K 2) is satisfied and KI U K2 defines an event-type I.e KI U K 2 , then there are at least some instances of the event-type I.e KI U K 2 • The quantifiers in (20) and (21) are all monotone increasing, and so the discourse's truth conditions presuppose that there are some events of the appropriate type. (22.a) on the other hand has no such presupposition. This line of reasoning predicts that event summation will not yield acceptable results in (22.b-c) either. The anaphors in (22.b-c) may refer to event-types simpliciter to facts or propositions. But one cannot interpret the pronouns as referring to the sum of three flag raising events.

4. PROPOSITION ANAPHORA In this section, I concentrate on the anaphoric properties of pure proposition denoting nominals. Many of the morals about proposition anaphora can also be drawn for projective proposition anaphora. In chapter 8, I wiIIlook more closely at projective proposition anaphora. Let's look at an analysis of a proposition denoting nominal. Consider the following discourse: (23)

John believes that [Mary is a genius]j. Fred is certain of iti •

The pronoun it introduces a discourse referent p I of propositional type. p I gets the propositional type from the subcategorization frame of the verb, be certain (of), of which it is an argument; it stands in for the characterization of the mental state of

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Fred's that the reporter is attempting to describe. Since p I is introduced by an anaphoric pronoun, it must be linked to an accessible antecedent of the appropriate, propositional type. An alphabetic variant of the subDRS constructed from the that clause in the first sentence serves as an antecedent of propositional type, while the predicate'" represents the anaphoric relation introduced by the pronoun. Again I have identified PI with an alphabetic variant of the original subDRS to avoid any problems with the DR-theoretic analogue of variable clash. My analysis of abstract entity anaphora yields the following DRS for (23).

denoting propositions also seem to act in a familiar way. In (24.c), for instance, the indefinite NP introduces a proposition discourse referent that is (preferably) introduced within the scope of a negation operator and thus remains inaccessible to the discourse referent introduced by the pronoun outside of the negation's scope. The theory predicts this to be bad. Because of the processing rules for definites, the definite NP in (24.d) introduces in effect a proposition discourse referent that is entered into the universe of the principal DRS; this is represented in the DRS below for (24.d). The theory predicts that this discourse referent is accessible to the discourse referent introduced by the pronoun outside of the scope of the conditional operator.

x, s, y, Ph s'

p, u,

S,

243

P2

claim(p) s-make(u, p) John(u)

Fred(y) s'-be certain(y, PI) PI '"

IU2. S2

I

Mary(u2) S2 - genius(u2)

I

I

From the discussions in chapters 3, 4, and 5, the interpretation of all these conditions is familiar: a condition of the form p '" K, where p is a proposition discourse referent and K a subDRS, is satisfied relative to an embedding function f, world wand time t just in case f(P) is an alphabetic variant of K; a condition of the form a(x, p) is satisfied relative to f, w, t just in case f(P) is a DRS K such that a(x, K) is satisfied relative to f, w, t. The formal definitions are given in the appendix to chapter 10. Some DPs give rise to proposition discourse referents according to the rules for DRS construction in chapter 4. The same rules for accessibility that apply to DPs introducing individual discourse referents also apply to DPs introducing proposition discourse referents. Consider, for instance: (24.a) *John owns every Mustang i in Driftwood. It i runs very well. (24.b) *John believes everythingj Sam says. Fred believes itj too. (24.c) *Bob has not had an interesting thoughti in five years. I wish I had had iti' (24.d) If Mary believes [the claim that John is making]j, she will believe anything. Iti's preposterous. The same DRT principles that rule out the suggested anaphoric link in (24.a) above, also rule it out in (24.b), on the assumption that proposition discourse referents introduced within a complex condition by the DP everything in (24.b) act no differently from individual discourse referents. Other singular and plural DPs

v, s Mary(v) s-believe(v, p)

I

PI

I

D~

s' s'-believe(z, PI) z=v

preposterous(p 2) p= P2 The DRSs derived from that clauses uniquely characterize abstract entities like propositions. As we saw in chapter 4, the subDRSs that clauses introduce imply a prima facie existential commitment by denoting an abstract object of polymorphic type. Not surprisingly, then, subDRSs can also act as antecedents for discourse referents introduced by pronouns. (23) is an example in which a subDRS is linked with the discourse referent introduced by the pronoun. We must examine how subDRSs behave as anaphoric antecedents. On my treatment of proposition anaphora, only full proposition denoting noun phrases give rise to proposition discourse referents; that clauses simply give rise to subDRSs. Such characterizing subDRSs, just like the predicative DRSs of the previous section, function like rigid terms denoting DR-theoretic structures in virtue of the satisfaction conditions for predicates of DRSs. Thus, we predict that a subDRS K is accessible to a discourse referent u, so long as all discourse referents not declared in UK but occurring in K are accessible to u. Indeed, that clauses introduce subDRSs that are available as antecedents in situations where DR theory would predict indefinites to be inaccessible. Consider for instance the following: (25.a) John does not believe that [Mary is treating him fairlY]j. But Fred is certain of it i.

AND ABSTRACT ENTITIES (25.b) Sam doubts that John believes that [Mary is treating him unfairlY]j. Fred doubts that John believes thatj too. (25.c) If Al believes that [Pedro beats donkeys]i, he will yell at him. But Al doesn't believe thatj, so Pedro will escape with hearing intact.

245

predicts that the indefinite (with its strongly preferred narrow scope reading) cannot ~ a potential antecedent of the pronoun.

5. FACT ANAPHORA Consider for instance the partially completed DRS for (25.c) below and note the position of the subDRS constructed from the processing of that Pedro beats donkeys relative to that of the discourse referent introduced by it. The bracketed conditions below as usual indicate incompletely processed conditions. (K25.c)

u x,s AI(x) s-believe(x, I-----'y'-----------j Pedro(y) [beats donkeys(y)]

z,w [z will yell at w] z=x w=y

(27)

John did not hit Bill, and Bill did not hit John. Those are the facts.

presupp~~it@}lCg~~§i:I!~f"1iX~Xa~!~Y_~.'l!g!!!!!1.111§_·:=aiid"contexfii:-""Proposltlon x, s, p s-believe(r:x,,--,Pw)~_ _ _--, y P"" Pedro(y) [beats donkeys(y)]

I

I

I

l I

[So Pedro will escape with his hearing intact] The claim that abstract entity denoting nominals function as definites makes the right predictions. The intended anaphoric link between the subDRS and p is fine, and no scope ambiguity characteristic of the behavior of indefinites occurs here.19 Thus, the subDRS would behave just like a discourse referent introduced by a definite NP with respect to interpretation in the delineated DRS. The anaphoric link between p and the relevant subDRS in (K25.c) is acceptable given the principle of accessibility, only if we assume that such abstract entity characterizing structures behave like the discourse referents introduced by definites. In contrast to the behavior of subDRS introducing constructions, contrast the following example with indefinite noun phrases: (26)

'o-r

Fact anaphora also differs from prop9.,~!!!9}!,~Eaphora because of the fll~,!~ye

AI(u)

....,

So far we have examined proposition, event, and event-type anaphora. But there are Other types abSiractenililes~-aruroffiefTypesooraosfracrell"ti.tyanaphora --in particular fact anaphora. In the previous chapter, I observed a correspondence between facts and events. The "facts" or possibilities to which one may refer in a discourse are typically those associated with each main clause in a discourse. Often with each main clause is associated an accessible event discourse referent in the DRS. So there is a close correlation between anaphoric reference to facts and ) anaphoric reference to events. But since facts are abstract objects, one can refer to facts, for example in (27) below, in context where the events are not accessible.

*If Al believes that Pedro beats a donkeYi, he will yell at him. But Al doesn't believe that he beats itb so Pedro will escape with hearing intact.

The intended anaphoric link in (26) is hopelessly bad, unless a donkey is read as having wide scope, which is not the preferred reading. The accessibility constraint

introducing or characterizing constructions do not generate such presuppositions. When a pronoun occurs in a context which forces the discourse referent z it introduces to be of fact type, z must be identified with a structure or discourse referent in such a way that the factive presuppositions are fulfilled in the context in which z is declared. Otherwise, we have failed to identify the discourse referent with a fact. Consider the examples below: (28.a) Mary proved [that the defendant was lying about the President's ignorance of the cover-up]j. TEisj shows that the cover-up is much larger than previously thought. (28.b) No one heeded the government's curfew orders]j. TEis j shows that the Junta can no longer control the people. (28.c) [John's viciously kicking Mary]j was the outcome of their argument. Thisj indicates that they are not getting along at all well. (28.d) ?Fred believes that [John's viciously kicking MarY]j was the outcome of their argument. Thisj indicates they are not getting along at all well. (28.e) #Fred prevented [John's viciously kicking MarY]j. 'Lhisj will lead to a lawsuit. (28.t) #Fred believes [that John viciously kicked MarY]j. TEisj indicates that they are not getting along at all well. In (28.a-c), the relevant, the context verifies factive presuppositions of the anaphoric link; these discourses are predicted to be OK. But the factive presuppositions of the intended anaphoric reading are not fulfilled in (28.d-e), because the matrix verbs,

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believe and prevent, block any possible presupposition inheritance from the subDRSs. In (28.t) the that clause must denote a proposition and so carries no factive presuppositions with it in any case. Thus, I predict (28.d-t) to be out on their intended readings. 20

v, s person(v) VI. x, e I) s- have (v, 0 1 e- take-out(vI. x) VI =v garbage(x)

6. CONCEPT ANAPHORA IN DRT The analysis of proposition anaphora transfers readily to the domain of concept anaphora. There are close enough parallels between the "deep" concept anaphora (anaphora with explicit anaphors) and what Sag (1876) has called "surface" forms of anaphora like VP ellipsis, gapping, sluicing, stripping, and V' and N' deletion to warrant subsuming all of them under a uniform analysis. With the machinery for the analysis of saturated, abstract entity anaphora now in place, it is time to look again at the comparisons between deep proposition anaphora, deep concept anaphora, and surface anaphora.

6.1 Concept Anaphora with Explicit Anaphors Concept anaphora which uses an explicit anaphor has much in common with proposition anaphora. Instead of using a subDRS or a proposition-type discourse referent as an antecedent, the antecedent of an anaphoric pronoun denoting a concept is typically a predicative DRS. Moreover, that predicative DRS is often a property of events or what I call an event-type. Consider again the sentence (29) with its intended antecedent marked by coindexing: (29)

Someone [had to take out the garbage]j, and Bill did itj.

The modal auxiliary functions as the main predicate of the first clause, whose arguments are the translation of the infinitival phrase and the individual-type discourse referent y introduced by someone. In keeping with my analysis of infinitivals from chapter 4, the infinitival introduces a projective subDRS with a particular projective operator--the verb have determines it to be the necessity operator N. An instance of PRO fills in the subject of the verb in the infinitival. In (29) the subject of the main verb controls the PRO subject of the infinitival; the semantic effect of PRO, then, is to identify v with VI in the DRS below. Thus the first sentence of (29) yields the DRS:

247

In the second clause of (29), did is an action verb and also a predicate that takes an individual discourse referent and a concept discourse referent as arguments. The second discourse referent is introduced by an anaphoric pronoun, and so it must be identified with some appropriate antecedent. The action verb analysis of do subcategorizes one of its arguments as an event-type, a property of events. Do has two arguments, an event-type and an agent subject. The semantics of do converts the event-type, with its subject argument and with the event discourse referent. Given the nature of DRS conversion, and the interpretation of "', if CI '" AXAe KI , do(u, CI) E ConK, then e'- do(u, CI) and CI '" AX Ae KI may be replaced in ConK by all those conditions in ConK, (u/x )(e'/e) (i.e., all those conditions in ConK, with u replacing x and e' replacing e in the argument positions), while all the discourse referents in UK, - {x, e} are added to UK. In (29) the appropriate antecedent is the event-type identified by the predicative DRS derived from the verb phrase of the infinitival phrase. But how can we get this antecedent? Do VPs even give us semantic constituents? VPs generate predicative DRSs that appear to have the same existential force as do subDRSs. The following valid argument is identical to the one given earlier involving quantification over the CP position; in (30) the quantification is over properties denoted by VPs. (30)

Fred does everything Bill does. Bill went over to his friend's house to play make-believe games. So, Fred went over to his friend's house to play make-believe games.

This argument is perfectly acceptable. It shows that we may quantify over verb phrase argument positions and that verb phrases may at least in certain contexts act like constants--contributing an instance of a quantifier expression. I have followed other philosophers in interpreting such arguments as leading us to countenance that clauses, for instance, as contributing distinct semantic structures and even distinct semantic denotations to interpretation. So it seems that we should also acknowledge the same possibility for verb phrases. The predicative DRSs derived from verb phrases represent event-types and as such are abstract objects. So according to our theory, they are accessible so long as any discourse referents not declared in their universes but occurring in them are accessible, which (31) indicates is the case. (31)

Fred believed that Mary didn't have to [study for the Latin test]j. But she

___

~------,.,-;;rif~=~~=~-~~---~-~;-';'-:~;:;-;::~~~~------~----~"

CHAPTER SIX

__

---~~'~----

ANAPHORA AND ABSTRACT ENTITIES

One difference, however, from other types of abstract entity anaphora is that with concept anaph~ra the event-type derived from a VP is not explicitly marked by the DRS constructIOn procedure. We could represent it explicitly within the DRS language, but this would not in general help us all that much. Verb phrases themselves do not always contribute the appropriate anaphoric antecedent for concept anaphora. Consider for example, (32.a) The garbage [had to be taken out]j. So Bill did it j. (32. b) [~o~n's teasing of Mary]j was wrong, but he was not the only one who did Itj.

VP translation for (29) x e -take-out(v, x) the garbage(x)

DEFINITION: A part of a DRS K is a DRS K' such that UK' ~ UK and ConK' ~

ConK. DEFINITION: C-Abstraction

Suppose that a DRS K is derived from a text T and that K' is a part of K" and K" is subordinate to or = K. (i) If do(x, c) is a condition in a DRS K and is derived from non-auxiliary do, then c may be identified with AU K*, where K* is an alphabetic variant of K' and U E UK*, if there is a condition in K* that has a e grid of which U fills the Agent argument place. (ii) If c(x, e) is a condition in a DRS K and is derived from auxiliary do, then c may be identified with AU K*, where K* is an alphabetic variant of K', if: (a) the conditions predicated of x in K are compatible with the features assigned to U by the e grids of which U fills an argument place in K*, (b) u fills an argument place of a condition derived from a verb in K*, and (c) AU K* may be derived from a verb phrase or a Boolean combination of verb phrases in T. (iii) If true-of(c, Xb ... , xm) or do(xb C, X2, ... , xn) is a condition in a DRS K, then c may be identified with the m-ary relation AUb ... , AumK* where K* is an alphabetic variant of K' and Ui occurs in an argument place of some condition in ConK*, if for each Uj the conditions predicated of Xj in K are compatible with the features assigned to U j by the e grids of which Ui fills an argument place in K*.

VP translation for (32.a) Ae AU

VI f----'-------I

e -take-out(v 11

U )

The ev~nt-type derived from the VP in the infinitival phrase in (32.a) is not of the appropnate sort to serve as the antecedent of the pronoun in the second sentence of (32.a). What is wanted is rather an event-type with the same content as that of the event-typederived from the verb phrase in (29). We need a me~hanism to abstract the appropriate event-type from a given co~text: ~ore precIsely, we need to abstract on a given argument in the event-type. Th:s ~nncIple of C(o~cept) ~bstraction is needed for concept anaphora and for VP ellIpsIs. In the restncted dIscourse structures that we will examine, only DRSs result from the processing of the DRS construction procedure. Where anaphoric reference.to concepts, and hence predicative DRSs, is involved, we must appeal to an op~ratIOn of a?straction, "C-abstraction," that will supply predicative DRSs as potential anaphonc antecedents. C-abstraction makes use of the argument structure of verbs, a concept familiar from chapter 4. A verb comes with an argument ~tructure that can be. ~haracterized by e roles, which is known as its e grid. For ~nst.ance the no?-a~~Ihary verb do has the e grid ; the agent e role I~ fIlled by an mdivIdual discourse referent while the theme is filled by a concept discourse referent. The e grid carries over to the condition derived from the verb or noun, and the e roles constitute features of the discourse referents that fill the argument ?laces of the verb's translation. These features must be respected when a concept dIscourse referent is identified with a predicative DRS and then applied to

249

an individual discourse referent, in the sense that the features associated with the abstracted discourse referent in the predicative DRS and the features associated with the discourse referent to which the predicative DRS is applied must be jointly satisfiable. I will assume that the application of a concept discourse referent c to an individual x is represented by a condition of the form do(x, c) or a condition of the form true-of(c, Xb ... , xm). Accordingly, we have the following definition of Cabstraction21 . But first an auxiliary definition.

My and most other analyses of of-ing gerund nominals predict that there is no VP in the intended antecedent in (32.b). In (32.a) the translation of the VP of the pass~vi~ed infiniti~al differs from the translation of the VP of the infinitival in (29), and It IS not the nght event-type to be picked up by the pronoun. I give the VP translations for both (32.a) and (29).

Ae AV

.- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

C-abstraction makes use of several sorts of conditions that might contain concept discourse referents; this gives us the different clauses. An example like (29) makes use of clause (i), while VP ellipsis will make use of clause (ii). Notice that clause (ii) imposes a number of additional constraints on VP ellipsis. Cabstraction in conjunction with VP ellipsis may produce only a predicative DRS that is derived from a verb phrase or a Boolean conjunction of verb phrases and in which the lambda abstracted discourse referent is an argument to a verb. I shall comment on these restrictions when we get to VP ellipsis. Clause (iii) is designed to handle examples like: (33)

Every Swiss farmer who owns a donkey beats it. But that's not true of an Austrian farmer and any donkey he owns.

- . - - - - - - - - - - - - - - _ .__._----

"""..,-----::-:~~~~-~~:=::-~~--~---~.".~-~""-~-..

250

CHAPTER SIX

ANAPHORA AND ABSTRACT ENTITIES

Of course, C-abstraction as defined here makes sense only given the following assumption. 22

alphabetic variance and is thus familiar from the discussion of proposition anaphora. This strict interpretation of '" is needed to handle strict/sloppy identities and also to preserve the highly intentional character of concepts as objects of attit~de~.24 The identification relation between concept discourse referents and predicative DRS structures is of a familiar kind: CI '" ~, where ~ is a predicative DRS, will be satisfied in a model M under an embedding function f (at a world w and time t) just in case f(cI) in M is isomorphic up to discourse referents declared in CI with~. The content of a concept is defined analogously to that for a proposition: the content of an n-place concept characterized by a predicative DRS AX), ... , AXnK within a DRS K' is the function from worlds to sets of n-tuples such that for each n-tuple in the value of this function when applied to some world w, there is a proper embedding g of K at w such that g(Xj) = tj for 1~ i ~ n. 25 C-abstraction also allows us to handle Chierchia's argument against an interpretation of infinitivals like mine in chapter 4. Chierchia argues that this pattern of argument shows that infinitival phrases must denote properties.

The syntax of a sentence giving rise to a given DRS K in a given constituent can be recovered, so that we can compute what the contribution of any syntactic constituent is to K.

ASSUMPTION:

C-abstraction allows us to complete the anaphoric link in the DRS for (29). v, x, s, u, c), e' person(v) v), x, e ) e- take-out(v), x) VI =v garbage(x)

s- have (v, 0

Bill(u) e'- do(u, CI) CI '"

I.e

AVJ

I

I

x'

Ie - take-out(v

J,

x')

garbage(x') We use clause (i) of the definition of C-abstraction to abstract over the Agent role, which corresponds to the subject argument place in the surface syntactic structure. We must also use C-abstraction over the Agent role on the subDRS to get an antecedent of the appropriate kind for the concept discourse referent introduced by the pronoun in (32.a). In (32.a), however, we must abstract on a different syntactic argument place from that in (29), because the Agent role is lexically suppressed. though it is present in the semantic translation of the verb. Notice also that the VP is embedded within a projective operator. 23 Nevertheless, C-abstraction allows this sort of abstraction., so we can derive the DRS for (32.a): x, s, u, c), e'

251

John wants everything that Fred wants. Fred wants to be chair. Therefore, John wants to be chair too. But contexts like that created by want are not the only place where VP quantification is licensed; it also occurs with verbs that obviously take clausal complements as syntactic arguments--consider the following pattern: John believes everything that Sam believes. Sam believes that he himself is best suited for the job. So John believes that he himself is best suited for the job. As intimated.in chapter 4, we can account for this argument by quantifying over the properties derived from VPs. These properties can be formed by C-abstraction. What licenses the C-abstraction in this case? I hypothesize it is the particle therefore, which requires as part of its semantics that it be the conclusion of an argument--and .if possible a valid argument. Only by using C-abstraction can we construct a valId argument. This is an instance where the discourse structure required by particles like therefore has a semantic effect upon the content of the discourse. We shall see much more of this in the next chapters.

garbage(x) s- have ( 0

,.------, I v 10 e I) e- take-out(v), x) I

6.2 VP Ellipsis in DR Theory

r

Bill(u) e'- do(u, CI) CI '" Av' Ae' I

I

J

Ie' - take-out(v', x)

The interpretation of '" relative to concept discourse referent denotations is

We have so far discussed property and proposition anaphoric relations involving overt anaphoric pronouns. But there are many anaphoric phenomena involving reference to abstract entities employing no overt pronouns. The most studied of these is VP ellipsis or VP deletion, but there are other related phenomena: sluicing, gapping, V' and N' anaphora.2 6 Very similar to overt pronominal anaphora but also lacking an overt pronoun is null complement anaphora. In this section I want to illustrate how my approach to abstract anaphora might extend to a treatment of VP

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CHAPTER SIX

ANAPHORA AND ABSTRACT ENTITIES

ellipsis. VP ellipsis differs, as noted by Sag (1976) and Sag and Hankamer (1984), in at least one dramatic way from concept anaphora with explicit anaphors. Compare (34.a-b) to (29) and (32.a):

It seems to me that the elided VP could pick out the property of getting sick and going to the hospital. Yet no actually occurring VP in the text yields such a property. This means that we must keep track of what were the VPs in anteced~nt discourse in order to handle VP ellipsis. But I do not see any other way of handlIng the phenomena. Finally, the auxiliary form of do, as it comes from the inflection node I, introduces an event discourse referent that fills in one of the argument places to the event-type. This form of do does not introduce a condition. So VP-ellipsis has a slightly different form from overt concept anaphora and a syntax that indicates that discourse referents may stand for denotations of predicates. This gives the DRS fragment for VP ellipsis a second-order rather than a first-order syntax. As to interpretation, successful VP-ellipsis, like deep concept anaphora, demands that the characterization of the concept discourse referent c introduced by a phonologically null VP node with an appropriate predicative DRS K, be of a strict and familiar kind: alphabetic variance with respect to all discourse referents declared in K. 28 Predicative DRSs introduced in a discourse are always accessible to a discourse referent introduced by a pronoun no matter how deeply embedded. This also goes for the predicative DRSs produced by C-abstraction for overt concept anaphora and VP ellipsis. Consider the following examples.

252

(34.a) Someone had to take out the garbage, and Bill did. (34.b) *The garbage had to be taken out. So Bill did. In other words, VP-ellipsis restricts the use of the C-abstraction principle. There have been several proposals for treating VP ellipsis. Earliest were proposals that VP ellipsis resulted from a transformation deleting a full verb phrase at deep structure. A more recent proposal by Williams (1977) claims that VP ellipsis involves an interpretation of a null VP in the syntactic structure. Both proposals extend to similar non-pronominal anaphoric phenomena like gapping, sluicing and N' and V' anaphora. Another point about which such analyses may differ concerns where and when the deletion transformation or interpretation of empty nodes should take place. Sag (1976), who follows the deletion approach, and Williams have argued convincingly that a proper interpretation of VP ellipsis should take place after quantifier scoping (in GB after quantifier raising). Thus VP deletion or null node interpretation should take place at a level of logical form. Sag and Williams's arguments fit nicely into a DR-theoretic approach to VPellipsis too. For a DRS serves as the logical form of a discourse in DRT. Following Sag, it would be natural in DR theory to insert an alphabetic variant of the predicative DRS constructed from the verb phrase in place of the ellipsis. In view of the arguments in Rooth (1987), I will adopt an interpretive approach. My treatment will differ from other interpretive approaches, however, in that I will, like Klein (1986), make an explicit connection between VP ellipsis and other forms of abstract entity anaphora. Indeed I believe that these share basically the same mechanisms.27 My treatment goes as follows. VP ellipsis is a form of concept anaphora. A null VP introduces during DRS construction a concept discourse referent for which a suitable antecedent must be found. Following Klein, I shall thus analyze VPellipsis as an anaphoric relation between a predicative DRS and a discourse referent. C-abstraction again isolates an appropriate event-type. In the definition of Cabstraction, C-abstraction may only yield a predicative DRS derived from either a verb phrase denotation or a Boolean combination of verb phrases as an antecedent for the discourse referent introduced by the null VP. No other event-types are allowed to be identified with concept discourse referents introduced by null VP anaphors. The restriction of C-abstraction to VP translations and their Boolean combinations is designed to take account of some of the more complex examples of VP ellipsis, in which a VP ellipsis refers to a complex property built up out of several VP denotations. Consider, (35)

John got sick. He went to the hospital. Fred did too.

(36.a) If John says that Mary [hit himli, everyone will believe him. But she didn't ¢j. (36.b) If John says that Mary [hit him]j, everyone will believe him. But she didn't do thatj. The intended antecedent in both cases is the property derived from the lower VP hit him. The material there is deeply embedded and a discourse referent declared in the DRS in which the contribution of that VP resides would be inaccessible to the discourse referent introduced either by the null VP or the pronoun in the second clauses of (36.a-b). But since these examples are fine, it seems that accessibility does not constrain C-abstraction or those instances of concept anaphora in which the antecedents are taken to be predicative DRSs, except in the familiar way: any discourse referents occurring in the predicative DRS but not declared in its DRS component must themselves be accessible. This completes the sketch of various forms of abstract entity anaphora. We have seen that DR-theoretic structures are always accessible modulo the proviso about discourse referents occurring within them, and so accessibility does not much constrain the set of possible anaphoric antecedents. The task now is to see how discourse structure affects the anaphoric relations. We shall see that discourse structure imposes very tight constraints on possible antecedents. lSee Dahlgren and Lord (1990) for a discussion of such findings in the newspaper commentary genre. 2Webber (1988) claims that this and that are used much more frequen.tIy than it to n;:fer to a di~course segment. This preference clearly, however, does not preclude It from refernng to a dIscourse

CHAPTER SIX

ANAPHORA AND ABSTRACf ENTITIES

segment-- witnes~ (l.g) above . .I might add that none of Webber's examples for me becomes bad if we replace that WIth unstressed It. ' 3Th Loe fidndin g that this picks up a topic antecedent, while that picks up a non topic antecedent is due to r and1)ahlgren (1989). ~Th~ term suri.ace fIDaphora is due, I think, to Sag (1976). ThIS observatIon IS due to Wynn Chao. 6For more discussion of this problem see chapter 9. 7T~icallY, it is not used to re.fer to indiyid!lals de~c*ally. This has prompted Bonnie Webber (1 8) to suggest that !lses of this and that ~dIcate deICtIc. ref<:rlinc~, which she claims is a different proces~ from. an~pho~IC reference. Accordmg to her, usmg It mdIcates anaphoric reference As I ~av~ ~ed to mdIcate 10 the text, I do not find tbis distinction convincing. . TRhTIS IS per~apfs the same event as Johnson's race, but perhaps not. Nothing forces us to say in the D analysIs 0 anaphora, one way or another. 9There is a freat deal of 'York on anaphora in the slntactic literature. Some seminal works include Langacker 1969), .who mtroduced the notion 0 "precede and command" Ross (1967 and Jacken~off 1972) frrst explored anaphora in relation to the scope of negation and quantifier ~cope rlispe.ctIvely. Choms~y (1973) a~d ~asnik (1976) developed the approach of syntactic constraints on dIsJomt reference, while Remharts dIssertatIon (1967) first introduced the notion of c-command The rules of c-'ioml!land have carried on into the binding theory of Chomsky (1982) Reinhart (1983) offers a qUIte dIffereI!t pro~s~ distinguishing "bounil anapfiora" in which the notion of c-command operates ffom the notion of "dIscourse anaphora" which is governed bY'pragmatic rules For work on W~~~(1989fRT, see Kamp (1981, 1983), Partee (1984), Asher (198/), Roberts (1987), Asher and

1?N~veI1heless, it s~ould be ~oted that -fiel)go and ~ay make a case that syntactic information about b!ndmg IS relevant 10 resolvmg VP elhpsIS-- especIally for sloppy readings of VP ellipses For a d ISCUSSIon see Asher (1991). . Assuming that an>: is a neg~tive pol~ty item and acts like an existential inside the negation. Re~al! that thematic connections may mvolve common agents or actors or simply arise from certain ~ssocIatI9ns betw~en types of events in world knowledge. An example of the fatter concerns events llike gettmg the bIll.at a restau~ant and then paying it. This is simply a connection of events one eams as part of getting around m the world of restaurants. l~Event-type a!1aphora also qccurs with VP ellipsis and other forms of concept anaphora which I'll li cUSS bnefly 10 the last sectIon of thIS chapter. ' Thhe example~ (a-b) belO\y present a challenge to th account of event-type anaphora Most people . get t e anapfionc reference 10 (a) and(b). (ab) Fred watched [every child in t~e 9rphanage receive a present];, and Sam watched it; too. ( ) Jqh!1.saw [no on~ leave the buildm.g];. Sll!" sl!w the same thing;. Th~ pqssIj)Ihty of the mtended an.aphonc rea!img 10 (a) seems to be licensed by some sort of sUDRrSdi!latI°h~ phenomenon. ~y puttmg both seemgs under the scope of quantifier every child we get 10 w Ich the anaphora IS resolved: ' a

g

di

x,u,v Fred(x) orphanage(u) Sam(v)

I

y child(y) in(y,u)

I

Q

I

I

e, el e-see(y, Ae

w present(w) e -receive(y, w)

)

el-see(v, z) z'" Ae'

w' present(w') e' -receive(y, w')

(b) seems very similar to (17.c) yet the anaphoric link appears to be perfectly OK. Why is this? We WIllll have to explore the way dIscourse structure affects concept anaphora to understand these matters f u y.

255

150n such a strategy, one would assimilate such anaphoric connections to a DRT analysis of Geach's Hob-Nob example. For details see Asher (1987). 16 All the monotonic decreasing quantifiers of natural language except for no allow for event summation. Thus, few boys kissed a girl, but this upset the chaperones anywax. is acceptable for many people. My answer is that in these cases the monotone decreasing quantifiers, ttogether with the contrastive, generate an implicature that there are some relevant instances. Thus, few boys kissed a girl, together with the contrastive particle but, generate an implicature that there were some kissings. This implicature appears to license the anaphoric element here and becomes part of the content of the discourse once tfie anaphor is introduced. To handle such cases, I would have to refine the principle of summation by investigating more closely the interaction between discourse structIrre, yresupposition, implicature, and anapfiora. I will not do so here. 7(21.b) is interesting, because it indicates that a distributive reading for the sum event identified with it is possible; this seems to indicate that one may decompose the sum back into its constituent parts using the event type. The example is due to Andy Schwartz. 18For a definition see Van Bentham (1984), where the concept is defined for determiners. 19 If a full processing of definites were pursued here along the lines suggested in chapter 3, the subDRS would get identified with a discourse referent or delineated DRS occurring in the delineated DRS of the interpreter. This discourse referent or DRS would lie outside the scope of all the opyrators in the DRS above and so show that indeed the subDRS was accessible (via that link). Here I abstract from the difficulties of DDRS construction. 20An interesting example similar to those in (28) whose analysis requires the full context-sensitive interpretation of attitudes and notions of discourse structIrre is: Fred believes that [John's viciously kicking Mary]; was the outcome of their argument. He also believes this; will lead to Mary's asking for a divorce. 21The definition of C-abstraction makes use of the notion of subordination. I will assume that not only maya DRS be subordinate to another but also a predicative DRS may be subordinate to another ~redicatIve DRS or DRS, if the two are in the requisite configuration. 2Specific forms of concept anaphora may have more specific constraints. For instance, VP ellipsis and gapping are very particular 10 the sort of structures that constitute sources. To have any hope of makfug sense of these constraints, we need syntactic information. 23Since we assume that this argument place is filled by a discourse referent in the completed DRS, a potential problem arises in other examples of passive construction: this discourse referent is never accessible to a pronoun in a subsequent clause. One might suppose that PRO fills the lexically suppressed argument place and PRO, when not controlled, IS "arbItrary PRO" and this arbitrary PRO intrOduces a duplex condition. This leads us into difficult territory especially for the DRT theorist, because the meaning of arbitrary PRO should at least in this case be something like an indefinite. The positing of a duplex structure with an existential interpretation would raise questions about the DRT use of embedding functions to get the right interpretation of indefmites. 24For more on the highly intentional nature of concepts, one need only look at the vast literature on such puzzles about concepts as the paradox of analysis and the related Mates's puzzle. 25For details see the appendix to chapter 10. 26My approach to VP ellipsis follows the general outlines of Ewan Klein (1986) , but in the semantics and the constraints on anaphora the two theories differ quite a bit. The main idea, however, is not to present novel findings but to unify well-known facts with others that I have already mentioned in a much more general framework. This DR-theoretic interpretation of VP ellipsis and other surface anaphors is SImilar to the "logical form" proposals of Sag (1976), Williams &1977), and Sag and Hankamer (1984). 7For a detailed comparison of the Sag and DRT approaches, see Gardent (1991). 280ne might not have the null VP introduce a discourse referent. But nothing much hangs on this, and it seems easier to make all the treatments uniform. Unlike Klein (1986) r will not interpret the denotation of a concept-level discourse referent as a set of functions from individuals to embedding functions of DRSs. This avoids some logical complexities having to do with the semantic paradoxes, but it precludes a fully general analysis of concepts and propoSItions in a type-free setting. I make the values of concept-level discourse referents under embedding functions predicative DRSs.

A THEORY OF DISCOURSE STRUCTURE

257

CHAPTER SEVEN

A THEORY OF DISCOURSE STRUCTURE FOR AN ANALYSIS OF ABSTRACT ENTITY ANAPHORA

The last chapter introduced the DR-theoretic approach to abstract entity anaphora, on which various DR-theoretic structures derived from the DRS construction algorithm or C-abstraction may fumish antecedents to discourse referents introduced by pronouns. To handle the full range of abstract object anaphoric phenomena, however, one must be able to refer anaphorically not only to DR-theoretic structures introduced by the construction procedure but also to DRtheoretic structures constructed from bits of text that "naturally hang together." These segments generate DR-theoretic structures that also serve as anaphoric antecedents. The main task of this chapter is to develop a formal theory of discourse structure and discourse segmentation suitable for the analysis of abstract object anaphora. What follows borrows many ideas from the work of Hobbs, Polanyi, Mann and Thompson, and Grosz and Sidner. Webber's work on discourse deixis also has many common points with my efforts here. I have given a new formulation of a discourse theory in a dynamic way that extends the DR-theoretic dynamic notion of discourse meaning and accommodates an analysis of abstract entity anaphora. I have developed detailed construction procedures, even algorithms, for building discourse structures that exhibit the semantic effects of discourse structure as well as the effects of semantics on discourse structure. By tying an account of discourse structure to the semantics and logical characterization of abstract entities of the last chapters in a thoroughgoing way, it is possible to make precise and novel generalizations and predictions about abstract object anaphora. This is the principal contribution of this and the next two chapters. De'veloping such a theory forces us to take a much cloSer look at the notion of the dynamic meaning of a discourse. DRT conceives of the dynamic meaning of a discourse as evolving through the serial processing of its constituent sentences. The meaning of each sentence was construed as a function from truth conditions to truth ,conditions, and the truth conditional content of a discourse was gradually built up through a series of function applications. The notion of semantic updating in the original DRT fragment of Kamp (1981) and chapter 2 is extremely simple, except for the procedures for resolving pronouns and temporal elements, which the original theory did not spell out. To build a DRS for the discourse as a whole and thus to determine its truth conditions, one simply adds the DRS constructed for each constituent sentence to what one already had. This procedure is hopelessly inadequate, if one wants to build a theory of

256

discourse structure and discourse segmentation. The original DRT view is also of little use in the analysis of abstract entity anaphora. A more complex view of discourse updating must replace the simple notion currently realized by DRT. To account for discourse structure and abstract entity anaphora, I will postulate an additional level of discourse interpretation over and above the semantic construction rules of DRS construction. The basic entities at this new level are called segmented DRSs or SDRSs. The theory of discourse structure will develop principles for SDRS construction and interpretation. A number of issues already discussed come together in this chapter. First, the theory of SDRS construction will bring us back to a theme of chapter 1 by giving a theory of the structure of the space of propositions created by a text. Second, SDRS construction bears many similarities to delineated DRS construction. The problem of determining what are the constituents of a delineated DRS, discussed in chapter 3, is very similar, if not identical, to the problem of determining the constituents of an SDRS. Both SDRSs and delineated DRSs capture aspects of interpretation that go beyond the range of most truth conditional theories of meaning; yet in affecting anaphora and belief reports, these aspects of interpretation also affect truth conditions. The similarities between these two processes point to a larger, uniform theory of interpretation, of which SDRSs and delineated DRSs would be special cases. The integration of an account of discourse structure and an analysis of anaphora also brings linguistic and AI theories to bear on common problems. Linguistic theories of anaphora need to address questions concerning discourse structure. In chapter 2, I developed a DRT analysis of individual and plural anaphora. Many of the tools developed there help to understand eventuality and abstract object anaphora; but, without an account of discourse structure, they do yield by themselves a truly satisfactory account either of proposition anaphora or of event anaphora. On the other hand, discourse theorists in AI and linguistics need a semantics of abstract objects. They have often attempted to investigate discourse structure without articulating any clear connection between semantics--in particular the semantics of abstract objects--and discourse structure. 1 This has led to unclarity. Some people working in AI have even taken issue with the idea that a discou:-se structure and its constituents are a well defined object. 2 A tighter connectIon between discourse structure and semantics will enable us to see the precise semantic effects of principles of discourse structure. Though this seems to be an obvious goal for discourse theorists to pursue insofar as they have been interested in text understanding and understanding involves a relation to context, no discourse theorists, with the exception of Polanyi and Scha,3 have attempted to connect discourse structure with formal semantics. But the connection between formal semantics and discourse structure will not be made simply by assigning a semantics to constituents; there must be a careful study of the interaction between discourse structure and semantics. In fact I am convinced that only a dynamic semantics like DRT will be suitable to investigate this interaction. This is an attempt to do some detailed work in this direction. By paying careful attention,to the anaphoric

A THEORY OF DISCOURSE STRUCTURE possibilities in discourse contexts, we can exploit the anaphoric data to fonnulate and place ~ew constraints on discourse segmentation. Abstract enlli.Ll!lli!J.211w in pru:!Icular IS usef!!..lbecaUSUlf...o.uL.c.apac:.i.tY.tQ..[tf!~[..tQ.JmJire_dis.CQurse_s.egments. The relevance of anaphora to discourse theory might be analogous to the role of anaphora in syntax, where careful study of intrasentential anaphoric phenomena led to a much better understanding of syntactic structure in general. Semantic theories like DRT with discourse aspirations and theories of discourse structure need each other. This chapter begins the investigation of the effects of discourse structure on abstract entity anaphora. It lays the foundations of the account of discourse structure with the definitions of SDRS and the operations of separation and summation. It also elaborates the theory of SDRS construction and SDRS updating. The next chapter will give a general account of how the theory of discourse structure and a DRT account of anaphora interact.

l. THE PROBLEM OF DISCOURSE STRUCTURE AND ANAPHORA

II

One of the best ways to understand discourse structure is to look at its effects on abstract entity anaphora; indeed it is the analysis of anaphora for which my theory of discourse structure is designed. Abstract entity anaphora involves a wide range of linguistic constructions. Included within this domain are not only anaphoric phenomena involving overt anaphoric pronouns but also constructions like verb phrase ellipsis, sluicing, gapping, and common noun phrase ellipsis, in which something very much like anaphora appears to go on from the standpoint of semantic interpretation but where no overt pronoun or anaphoric DP exists in the sentence. As seen in the previous chapter, abstract entity anaphora and individual anaphora exploit many of the same explanatory concepts. In another respect, ho,;e.ver, abstract entity anaphora differs markedly from individual anaphora. Ind.Iy~.al2:-~~e~r~~~~to inill.YM.y~s 'YE~~_.pE?perties pertinent to ~he~\!":l.QJl1t!J.Qn"are-det~ued,m...most·.£.~~~~~tlliL~'Bbt the mdividuatIOn of abstract objects and even serm-concrete objects like events is problematic in a way that the individuation of individual objects is not. We have clues, for instance, about the individuation of individual objects from perception; we do not have such clues for abstract entities. Jhe individuation of abstract objects is l1l!~e.~:Y.ll_~~~~~~~.~_:2~ention within our conceptual schem;-WehilVet'Ofely on our thoughts and their veliiete;i-anguage;-tointlrViafiare''lfifin. This has important consequences for anaphora, especially proposition anaphora. The entities to which one is referring in proposition anaphora are individuated many times only by structural properties of the text itself, viz. its thematic and rhetorical organization. The StruJ;.ture-()f-a-diseourse..and-the_Segm~ntatien..e.fthe.diS.COll.T.'S.e... .ll1to...cOO..... stituent

I

Chfi·~~~.s,·.or-·bit&'..ma.Y:.rd!'lt~f!l1!!!x,"\Y.hai4.ab~!r~!!91,~~~,~~.L!!r~)j.~~!!!!:>l~J~!.11U?_horic

1

re erence.

-'An-~xample

makes clear the effects of discourse structure on anaphora.

259

Consider the following example:5 (1)

After thirty-eight months, America is back in space. The shuttle Discovery roared off the pad from Cape Kennedy at 10:38 this morning. The craft and crew perfonned flawlessly. Later in the day the TDRS shuttle communications satellite was successfully deployed. This has given a much needed boost to NASA morale.

Following research by Mann and Thompson (1985, 1986) and Hobbs (1985), one might suppose this discourse to have the following structure: the lead sentence gives topic of the discourse, with the next three sentences amplifying or elaborating on the topic. The anaphoric pronoun this might naturally refer to the "fact" described by the whole topic or to the elaboration given by the three previous sentences, which also might be taken to pick out a fact or an event. But the anaphoric pronoun might also pick up just the deployment of the TDRS satellite (another fact or event). In fact this last interpretation appears to be preferred when we use the pronoun that in place of it. Now consider what objects are available for anaphoric reference in another text about the same event. The sentences are almost the same, although their order is quite different. (2)

The shuttle Discovery roared off the pad from Cape Kennedy at 10:38 this morning. Later in the day the TDRS shuttle communications satellite was successfully deployed. The craft and crew perfonned flawlessly. After thirty eight months, America is back in space. This has given a much needed boost to NASA morale.

The reshuffling of these sentences produces a rather different discourse structure. The details of the theme of America's return to manned spaceflight precede the statement of the theme or general topic. The general topic closes off the details or the expansion, and the reader expects the start perhaps of a new topic in the article. The pronoun this in boldface can only pick up the topic statement and the content it summarizes--notthe launching of the TDRS satellite. Here is an example, this time from Russell Baker's column in The New York Times, which reveals something surprising about abstract entity anaphora: (3)

Human life expectancy gets longer and longer. At fIrst glance this seems like good news. But hold it. Human life is not the only thing getting longer. So are television miniseries. Well you may say, it only proves that Parkinson's law also fits human life: the entertainment expands to fit the time.

The boldfaced occurrence of it appears to pick up not only the claim that human life expectancy is getting longer and longer but that television miniseries are too.6 That content is not expressed by less than two sentences in the antecedent text. It is most

plausibly expressed by three sentences, the first, the fourth and the fifth.? The repetition of the content of the fIrst sentence in the third sets up a rhetorical structure contrasting the proposition about human life expectancy and the proposition about television miniseries. But this is not the content of all the text prior to the sentence in which the pronoun occurs; it does not include the content associated with the commentary, given by the text, at first this seems like good news. But hold it. Thus, the antecedents for abstract entity anaphora cannot be thought of as just those propositions expressed by a single clause or even a sequence of adjacent clauses. Rather, they may be the result of summing the contents of non-adjoining clauses. An even more dramatic text making this point is a modification of an example due to Bonnie Webber (1988): (4)

There are two houses you might be interested in: House A is in Palo Alto, House B in Portola Valley. Both were built in 1950, and both have 3 bedrooms. House A has 2 baths, and B, 4. House A also has a kidneyshaped pool. House A is on a quarter acre, with a lovely garden, while House B is on 4 acres of steep wooded slope, with a view of the mountains. The owner of House A is asking $425K, the owner of House B $600K. That's all I know about House A and that's all I know about House B.

Admittedly, one has some help from the predicates in figuring out what are the antecedents of the pronouns in the last sentence of (4). Nevertheless, the antecedents are not determined by syntactic or typographical features. The segments that are the antecedents of the pronouns must be defined in terms of the discourse content. In these examples, the structural properties of the text--specifically its thematic and rhetorical organization--determine the entities available for anaphoric reference, and what has come to be known in the AI literature on this subject, the global discourse structure. 8 TJ.1e global discourse structure carves lip the total inf.rumation given by a .discourse intQ., smaller J.lllits of information. These smaller units are de;telmined by a variety of factors: thematic content,logical and semantic structure, relation to the rhetorical structure of the discourse and finally but not least, the structure of the interpreter's knowledge of the subject matter. 9 I shall call the process o~~ing_1!£ ,t~e con.ten.LoLa.d.isGOm:se,..4iscD11I$","",§,.~~ion. '~entity anaphora may use the segments resulting from discourse segmentation as antecedents, as in examples (1) and (2) above. Those examples also indicate that in a complex discourse structure certain segments may be unavailable as antecedents for anaphoric pronouns. There have been many proposals for what ought to be the appropriate level of analysis of discourse structure and discourse segmentation. If we use the term discourse segment to refer to a "chunk of text" that readers feel forms some sort of unit, we still must analyze what sort of unit it is and in virtue of what principles do we take it to be a unit; answers to these questions constitute an analysis of discourse

~

segmentation and discourse structure. Some have suggested that the appropriate units of discourse structure are simply discourse segments (Grosz and Sidner 1985); others have argued for clauses (Polanyi 1985, 1988) in a syntactic representation. Still others have suggested events (Nakhimovsky 1988) or propositions (Van Dyck 1977, Van Dyck and Kintsch 1983). Authors have in general been unclear as to whether the theory of discourse structure and the process of discourse segmentation are best described at the level of the text, syntactic analysis or semantic structure, or some combination thereof. The analysis of anaphora yields a particular perspective on the question of what are the discourse structure constituents. It strongly suggests developing a notion of discourse structure at the level of semantic structures. Within the DRT framework, anaphora is to be accounted for semantically by postulating an appropriate relation between a discourse referent and another discourse referent or abstract entity characterizing structure. Many anaphoric uses involving discourse segments, as examples (1)-(4) show, make anaphoric reference to the semantic contents of discourse segments. lO If the segments of a discourse are thought of as anaphoric antecedents, they should introduce objects that are of the appropriate sort to be related to discourse referents. The anaphors in (1)-(4) must pick out propositions or proposition-characterizing structures, given the contexts in which those anaphors occur. Since segments typically include one or more sentences and sentences give rise to DRSs in the construction procedure, the natural semantic structure to be derived from a discourse segment should be a DRS or something of that sort. Nothing in what I have said so far forces an analysis of discourse structure in semantic terms. But a central tenet of my theory is that abstract object anaphora will also affect discourse structure and figure as an important component of the process of discourse segmentation. If that is right and one accepts the DRT approach to anaphora, then it behooves us to give an analysis of discourse structure and the process of discourse segmentation by appealing to contents and semantic structures. Another argument for a semantic theory of discourse structure is this. Other phenomena, which are usually cited as support for the idea of discourse structure in general and which a theory of discourse structure is supposed to explain, are largely semantic in nature. When evidence for discourse structure concerns the way the ' information of texts is stored in memory (Van Dyck and Kintsch 1983, Graesser and \}-Clark 1985) or speaker's intuitions about the "coherence" or "intelligibility" ?f ~e text, one is perforce thinking of discourse structure and discourse segmentatIOn III semantic terms. For it is semantic structures or contents that are understood and stored in long term memory. A fInal argument for thinking of discourse structure in semantic terms is that the relations that obtain between elements of a discourse structure are also usually described in semantic terms. Many researchers have appealed to "discourse relations" or "coherence relations" of various sorts in discussing discourse structure. Examples of such relations are Generalization, Instance, Comment, Elaboration, and others. I I The relations used in discussions of discourse structure form a rather

l

262

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heterogeneous collection; some relations, like Comment for example, appear to take propositions as terms;12 others, like Hobbs's (1985) Cause or Occasion relations, take events or perhaps facts as arguments. In the literature on discourse structure the semantics of these relations has not been investigated. But they do have a semantics, and the semantics for most of these relations implies that they are relations on semantic objects, not on texts themselves or syntactic structures, but rather on abstract objects like propositions. The task before us then is to construct a theory of discourse structure and discourse segmentation that will make sense of discourse constraints on abstract object anaphora. I will build on the semantic account of abstract objects begun in chapter 4 and integrate discourse structure constraints with the semantic and syntactic constraints on anaphora, discussed in chapters 2 and 6. In this chapter I add another level of structure--that of an SDRS.

2. DISCOURSE STRUCTURE AND DISCOURSE REPRESENTATION THEORY To make sense of the observations about anaphora and discourse structure in DRT, I must expand the DRT framework significantly. DRT currently employs only the simplest method imaginable of building up a representation of the content of a discourse prior to the routines of temporal and pronominal anaphora resolution. I described that method in chapter 2: the content of a discourse is represented by a large DRS, which is simply the DR-theoretic union or the DRS-update (defined in chapter two) of all the DRSs constructed from each constituent sentence. 13 This method takes no account of discourse structure. Up to now, DRT researchers have paid little attention to discourse structure. I propose to remedy this lacuna in DRT with the following suggestion. I will first postulate, along with many other discourse theorists, a set of discourse relations. These discourse relations determine another level of structure for a DRS for a discourse. This structure is imposed on top of its logical structure. This structure, which I call a segmented DRS or SDRS, consists in the simplest form of a set of DRSs and a set of conditions on these DRSs.l4 These conditions assert that certain discourse relations hold of certain DRSs; these DRSs are constructed from segments of the text whose content they determine. To distinguish these DRSs from those structures created by the basic construction procedure of chapters 2-5, I shall call them constituents of SDRSs or simply constituents. Discourse structure should, as many have suggested, be defined recursively.l5 So some of the constituents of a segmented DRS may themselves be segmented DRSs. Below is the full definition of an SDRS and an SDRS condition by simultaneous recursion, which presupposes the usual DRS and condition definition, as well as a stock of primitive discourse relations, Discourse Relations. DEFINITION

(SDRS and SDRS Conditions): If ()J, ... , ()n are DRSs, Con a set of

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SDRS conditions on those DRSs, then <{~h, ... , ()n}, Con> is a SDRS; If aJ, ... , an are SDRSs or DRSs, Con is a set of SDRS conditions on aJ, ... , an, then <{ aJ, ... , an}, Con> is an SDRS. If al and a2 are SDRSs or DRSs and R E Discourse Relations, then R(aJ, a2) is an SDRS condition on al and a2. If K is a DRS, the simplest SDRS K = <{K}, ¢> is simply equivalent to K, and I shall write it as such. SDRSs add discourse structure to DRT's account of the content of a discourse. The parts of an SDRS are the propositions defined by the text. Discourse relations hold between elements of an SDRS; the conditions of an SDRS state which discourse relations hold between these propositions. Thus, it is not surprising that besides DRSs, propositional discourse referents are part of the propositional structure and are counted as constituents. An SDRS K for a discourse D has a straightforward relation to the DRS K derived from D using the construction procedure of chapters 2-5. K contains a subset of the conditions in the result of removing all the hierarchical structure in K. The precise relation is given in the appendix. To develop the notion of an SDRS, we need some more definitions and notation. Many of these will be found in the appendix to this chapter, which contains a complete list of definitions introduced here. Constituents are the theory's reconstruction of the intuitive notion of the propositions defined by a text. The structure of an SDRS for a discourse reflects the propositional structure of a text. DEFINITION

A constituent a of an SDRS K is an SDRS K' such that a E W

K. I shall assume that the constituents of a constituent have a canonical order--the order in which they were introduced into the SDRS. I will make use of this ordering in defining SDRS updating in the sections below. As notation, '<' stands for the constituenthood relation; Shadow letters with primes or subscripts (e.g., K, K', K, K 2, etc.) denote SDRSs. Greek letters, a, /3, 'Y, (), etc., range over constituents--DRSs or subDRSs. I will also refer to the transitive closure of the constituenthood relation,
3. DISCOURSE RELATIONS AND THEIR SEMANTICS Discourse relations are the glue that bind simple constituents together to make

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more complex constituents. Discourse relations hold between abstract objects or related eventualities; thus, their semantics should be one that can be explored within a framework like the one developed in the previous chapters. But discourse relations are a diverse bunch. Some discourse relations segment a discourse on the basis of the rhetorical function of particular propositions in relation to propositions already established in the structure. These relations are called rhetorical relations. A Comment relation for instance distinguishes between two propositions, the proposition being commented on and the proposition containing the comment. Similarly, Generalization is a two place relation distinguishing two propositions-one the generalization and the other containing the subject matter generalized. Other examples of rhetorical relations appealed to in the literature are Parallel, Contrast, Purpose, Reason, Instance, Generalization, Summary, Opposition, Concession, Explanation, Elaboration, Support, Continue, Narration, and Consequence.1 6 In virtue of the fact that rhetorical relations in particular are relations over propositions, the list of possible rhetorical relations seems openended: potentially any such relation can be a rhetorical relation. Nevertheless, there seems to be a certain stock of "useful ones," ones that are suggested by the sort of simple texts I am going to look at--though why this list should be singled out, I don't know. These useful rhetorical relations are: Elaboration, Explanation, Instance, Purpose, Elaboration, Continuation, Consequence, Generalization and Contrast. 17 There is of course a wide variety of rhetorical functions--some like Parallel or Continuation depend on the structure of the constituents while others like explanation and consequence depend wholly on the semantic content of the constituents. Other discourse relations segment the discourse on the basis of relations between the eventualities introduced within the constituents. 18 These relations are called coherence relations. 19 They are often defined on world immanent entities like eventualities, but also facts may occur as terms of such relations. Examples of such relations are Cause, and the temporal, and the spatial and thematic event-paths that are used in the principles of event collection. These relations offer a convenient means of representing world knowledge and are suggested by what the reader knows about the subject matter. As with rhetorical relations, just about any relation between eventualities or facts can serve as a coherence relation in principle. Rhetorical relations and coherence relations may, though need not, be explicitly signaled by some expression in the text. They often result from an inference on the part of the interpreter. 2o Here are examples from Dahlgren (1989) that show that these relations need not be lexically realized:

Presumably, readers infer, after reading the first sentence of (S.a), that John was arrested for some reason. The next sentence of (S.a) gives the reader a plausible reason for his arrest, and so the reader concludes that John was arrested because he broke the law. The reader also concludes that given that this seems a plausible reason, the constituent introduced by the second sentence functions as an explanation of the first. The causal and explanatory link inferred in (S.a) is made explicit in (S.b). Similarly in (S.c), readers infer a rhetorical relation of purpose and of explanation between the constituents constructed from the two sentences. The link is made explicit in (S.d). A number of factors determine discourse relations. Clearly the content of the constituents is relevant. Sometimes tense and aspect are also important in determining discourse structure. 21

264

(S.a) (S.b) (S.c) (S.d)

John was arrested. He broke the law. John was arrested, because he broke the law. John robbed a bank. He wanted to get rich quick. John robbed a bank in order to get rich quick.

(S.e) (S.f)

John slipped. It had rained. John slipped. It rained.

In (S.e) the second sentence introduces a constituent that can serve as an Explanation of the first clause, but not in (S.f); (S.f) must be read as a narrative in which the raining follows John's slipping.22 The fact that one sentence uses a pluperfect tense where the other does not is decisive concerning which discourse relation is to be used in these examples. In many cases there is widespread agreement about what sort of discourse relation obtains between two segments. This is presumably so in virtue of the meaning of these relations. Yet most researchers in discourse theory have used rhetorical and coherence relations without providing any semantics for these relations or for their constituents. A semantics for discourse relations is needed, if only to make precise one what means by using them. A further reason for supplying a semantics for discourse relations is that they may add to the truth conditional content of the discourse; typically the relations of purpose and explanation do. Indeed, the principal difference between rhetorical and coherence relations is semantic; rhetorical relations always have a truth conditional content about the discourse. Unlike rhetorical relations, which are paradigmatic ally abo u t constituents and only sometimes directly contribute to the truth conditions of these constituents, coherence relations like Cause typically directly contribute to the truth conditional content of the constituents themselves. The semantics of discourse relations is often complex. A full story must await much more detailed work in a variety of areas. Relations like Instance, Generalization, and Support encode a notion of evidential support and "common sense proof" within SDRS constituents. The precise explication of such a notion seems still a ways off. Relations like Elaboration and Summary require an extensive theory of topic to get their semantics right. Finally, relations like Explanation have a very complicated semantics, which philosophers of science have been studying for a considerable length of time. Luckily, the SDRS framework allows us to draw on the work of philosophers to

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elucidate the meanings of some discourse relations. The theory of SDRSs provides a framework in which this semantic aspect of these relations can be aptly explored. For in characterizing discourse structures as SDRSs, we see discourse relations as relations between objects characterizing abstract entities, whose semantics philosophers have already explored in other contexts. The discourse relation Explanation, for example, ought to have the same meaning as the propositional relation EXPLANATION; roughly as Bromberger (1962) and van Frassen (1980) have argued, EXPLANATION(p, q) just in case q holds and p serves as an answer to the question, Why q? There are several types of explanation on such a semantics. We can distinguish at least two kinds--ex'planations that appeal to causal connections or "causal explanations" and explanations that appeal to plans and purposes of agents or "intentional explanations." The different sorts of explanations hinge on the different sorts of answers to why-questions; there are causal answers, telic answers and so on. SDRSs are structured propositions; and the semantics for the rhetorical relation is just that of the propositional relation of explanation.23 Consider, as another example, the coherence relation, Cause. The truth conditional meaning of the discourse relation, Cause in no way differs from the meaning of the causal relation, CAUSE. CAUSE is a relation between facts. Cause is a relation between constituents, but of course such constituents, or at least the DR-theoretic union of the leaves of those constituents under
domination. I'll write a .. /3 to denote that a discourse dominates /3. D-domination does not affect the truth conditional content of the discourse; 'a .. /3' means that a is a semantic label for /3; it holds just in case a acts as a summary or topic statement of /3. But it is a very important structural notion for discourse and for information in genera1. 24 It affects anaphora and the process of discourse segmentation. .. is defined precisely in the appendix, as is a measure of complexity of constituents. The measure has to do, roughly, with how many events are introduced in the constituent. The definition of Elaboration exploits the measure of complexity of constituents, the" relation and a more narrative-oriented relation in which one event is part of or a subevent of another event. Me(a) is the collection of "main events" introduced in a; this notion is defined in the appendix. Since a DRS K may be formed from a compound sentence, there may be several main events for K.

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DEFINITION: Elaboration(a, /3) iff ( a" /3 v (for every e E ME(/3) there is an e' E

ME(a) such that e is a part of e') & /3 is more complex than a.

Continuation is a complementary relation to Elaboration. Intuitively, a constituent a continues a constituent /3 just in case a and /3 have the same topic. But to use this as a definition would make our definition of topic circular. Continuation is quite weak and many other relations are compatible with it, as long as they do not introduce a discourse domination. Continuation is incompatible with discourse domination. Also it requires that its terms have the same relations to anything that dominates them. A Continuation must not only "continue" the same content; it must also "continue" the same rhetorical function. I formalize these properties of Continuation with axioms in the appendix. With an understanding of Continuation, I am ready to define topic. Topics do not contribute generally to the text's content about its subject matter. Their principal function is to contribute an important structural component of SDRSs. Topics are summary constituents for a group of constituents. A topic is a proposition that summarizes the content of a constituent in an SDRS, and it bears a particular structural relation to that constituent. The topic structure is a way of organizing the content of the text. One constraint on topics then is that they be simple; they should summarize not repeat. So one constraint on topics is that they be simple constituents with only one main event. It is useful to distinguish explicitly and implicitly represented topics.

= a iff a is simple and either (i) a" /3 in ]I{ (in this case a is an explicitly represented topic); or (ii) -,3y < /3 (Continuation(y, a) or Continuation(a, y) or Background(a, y)) and Vo < /3 3R E Discourse Relations R(a, 0) or R(O, a) in]l{ (in this case a is an implicitly represented topic).

DEFINITION: Let a, /3 be constituents in]l{. Topic(/3)

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The notion of topic naturally yields a notion of "topic trees," a structure consisting of a partial ordering imposed on a set of topics to help segment discourse according to content. 25 I will refer to the topic of a constituent /3 as "topic(/3)" and I shall define a discourse relation Topic* to capture the partial ordering. Topic *(a., /3) iff (i) a. is a topic of /3 or, a. is a topic ofy and 30< y 0 is a topic of /3 or (ii) a. is a topic of 8 and Topic*(8, /3).

DEFlNfTION:

Let us now put our investigations together. The general semantic interpretation of SDRSs is relatively straightforward and familiar from DRT. Because constituents may share discourse referents with other constituents in an SDRS, we must define the semantics relative to an embedding of the SDRS in which they occur. But in this, the semantics of SDRS conditions is no different from the definition for the semantics of DRS conditions. Satisfaction conditions for the discourse relations discussed here are given in the appendix to this chapter; other relations in the appendices to chapters 8 and 9. The satisfaction definition shows that most discourse relations are not different in kind from relations defined on propositions, facts, and other abstract objects. Many simply exploit the content of a constituent, which is simply the sum of the contents of its DRS leaves. For relations like Cause, for instance, the discourse structure of the constituents is simply unnecessary. For other relations like Explanation, the pure exploitation of content is probably an oversimplification; we probably need to take account of the discourse structure of the constituent as well if it is to properly explain. Structural relations like Elaboration and Continuation exploit the form and content of constituents. The satisfaction of all of the non structural discourse relations entails that the DRS constituents are properly embedded; we have, for instance, Cause(a., /3) -+ True(Una.) & True~n/3). This means that the proper embedding of an SDRS a. typically (though not always) entails the proper embedding of una., which is what we should expect. To make clear the semantic import of discourse relations, I define an SDRS to be coherent, just in case a particular discourse relation is satisfiable relative to that SDRS. To say that an SDRS OC is coherent is to say that the form and content ofOC must be consistent with the satisfaction of all its conditions. An SDRS OC is coherent just in case every condition

DEFINITION:

For each discourse relation introduced, I shall define satisfaction conditions or at least make some attempt to discuss them. For some conditions like parallelism or contrast, an appropriate form and content of the SDRS is all that is required for conditions using such relations to be satisfied. Other conditions like those that use coherence relations, for instance Cause or Purpose, may be satisfied relative only to a proper embedding of the constituent terms. Coherence is a constraint on SDRS construction.

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The SDRS update procedure should produce a coherent SDRS output whenever possible.

CONS1RAINT:

4. PRINCIPLES OF DISCOURSE SEGMENTATION AND SDRS CONSTITUENT CONSTRUCTION With the basic notions concerning SDRSs, discourse relations, and their semantics introduced, I can now say how to construct a new SDRS from a given (potentially empty) SDRS and some new information encoded in a DRS. SDRSs do not result from the process of DRS construction described in chapters 2-5. But like DRSs, they are built up incrementally from the processing of each sentence in a discourse. As sentence Sn+l is processed, the information it conveys combines with the SDRS produced from the processing of the prior n sentences to produce a new SDRS. The construction of an SDRS for a discourse requires that the new material be attached somehow--i.e., to some point in the previously built up SDRS by means of some discourse relation. The process of adding new information is the process of segmented DRS update or SDRS update. This process has four parts: (1) Determining the Basic Constituents (2) Constraints on Possible Sites for Constituent Attachment (3) Rules for Attaching at an Attachment Site (4) Revision of Basic Constituents After Attachment I will look at each part of the process. The first problem involved in SDRS updating is deciding what to take as basic constituents. What should be the basic units of information? The theory takes DRSs to be the basic constituents of SDRSs, but it leaves open whether those DRSs correspond to a particular sentence, a clause, or several sentences. As noted by Grosz and Sidner (1986), purpose plays an important role in determining the individual segments. But sentences might generally correspond to basic purpose units; sentence boundaries have important effects for anaphora and semantics in many areas, which might support this contention.26 On such a view, the full stop punctuation marks the basic complete unit of communication--a thought--which is communicated with,a particular purpose or intention on the part of the author. But it also seems that to some extent the basic units are context and discourse function dependent. Question-answer pairs or turn taking, as suggested by the work of Guindon et al. (1986), seems very useful for analyzing dialogue. On the other hand, for the simple texts and newspaper articles in the commentary genre that will be the centerpiece of study here, it seems that as a default each new sentence should introduce a new basic information unit and a new constituent. A trademark of default, or non-monotonic, logic is that a certain conclusion that holds given certain

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information may be reversed by more comprehensive information. ThuS, in some cases the default may be overridden and clauses or larger stretches of text may furnish basic discourse constituents.

This complicates my task to define openness and related notions precisely. The SDRS predicate, .. and the notion of d-domination are essentially involved in these definitions. • relates a topic and what it subsumes. It has the function of closing off constituents in an SDRS and rendering them unavailable as attachment points. • and the relation of being a constituent define a notion of subordination on discourse structures very similar to and more general than the notion of subordination defined by the logical structure of a DRS; discourse subordination or d-subordination includes "ordinary" or semantic subordination and is defined below.

DEFAULT AXIOM FOR CONSTITUENTS: Typically, every sentence introduces a

new leaf into an SDRS. In specifying the basic information units, our default axiom constrains us to update an SDRS built up from previously processed discourse with a DRS constructed from the next sentence.

DEFINITION: Let a,

4.1 Constraints on Attachment A dynamic theory of SDRS construction must constrain the possible sites for attachment and offer precise algorithms for attachment of new constituents to given structures. The first constraint is formulated as a rule ofrelevance:

Rule of Relevance: Given an SDRS a for an initial segment of a discourse D, any new constituent derived from further processing of D must be attached to some constituent of a, if D is coherent. So newly processed constituents must be attached to antecedently constructed constituents, if there are any and if the discourse being processed is coherent. But now the question is what constituents may serve as attachment points? To answer this question and to formulate the constraints on attachment, I introduce some terminology. The open constituents of an SDRS K will tum out to be the constituents of K which are available candidates for entering new information. The current constituent is the constituent DRS containing the information from the previous sentence. The position of the current constituent in an SDRS is essential for determining the possibilities for attachment of new material in the SDRS. Grosz and Sidner (1986), Polanyi and Scha (1984), and Polanyi (1985) have observed that only some components of a discourse structure are "open" in the sense that one may add new material to them as the processing of the discourse proceeds. Certainly, one may add material, or attach a new constituent, to the current constituent. Further, one may add material to the SDRS in which the current constituent occurs, and to any SDRS that encloses that. This corresponds roughly to Polanyi's observation, noted also by Webber, that the "right frontier" of a discourse structure is "active." But it is more general, since nothing specifies that the current constituent need be on the right frontier. In the next chapter we shall see current constituents that are not on the right frontier.27 Previous research has not examined how attachment interacts with the internal structure of constitutents. I must do this, however, because I am interested in completing anaphoric equations inside constituents by exploiting discourse

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p be constituents, DRSs, or proposition discourse referents.

a is d-subordinate to Piff (i) a:5; te Por a is subordinate to p or P• a or a is declared in U~; or (ii) (a
d-subordinate to

p.

D-subordination allows us to define openness, which generalizes Polanyi's and Webber's right frontier constraint, and the more restricted notion of d-freedom.

A constituent a
DEFINITION (Openness):

a • Pis a condition of K and a or some constituent not discourse subordinate to a is the current constituent, then Pis not an open constituent ofK.

FACT: If

DEFINITION (D-Freedom): A constituent a

Together the constraints of D-freedom and openness single out those nodes in a discourse structure that are not discourse dominated and that are superordinate to the current constituent. Since domination has much to do with topic, these constituents correspond either to topic constituents or to the last entered constituent. D-freedom and Openness determine where new constituents are to be attached. Both concepts are needed to get a satisfactory theory of discourse structure combined with an adequate analysis of anaphora. To resolve anaphora of the ordinary variety in a discourse like A man walked ill; He bought a coke. we have to look inside SDRS constituents. But when we attach to complex constituents, we should not be able to look inside the constituents that are "closed off." The present theory avoids this potential difficulty by distinguishing between two types of updating--topic-based updating and SDRS updating using discourse

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SEVEN relations that do not appeal to a notion of topic. Which type is used to attach the new material to the antecedent structure determines which attachment point is available; the use of a non-topic-based relation requires a D-free and open attachment point, while a topic-based relation like Continuation requires only an open attachment point. Further, each type will yield slightly different relations between constituents in the updated SDRS. Now whether a discourse referent or structure a may be anaphorically linked to another discourse referent z will depend upon whether a occurs in a constituent that bears a discourse relation to the constituent in which z occurs. The way updating proceeds and the restrictions on updating will insure that closed off constituents do not yield potential antecedents.

4.2 Inferring Discourse Relations The rules for attachment depend on the type of discourse relation used to attach the new information to the given structure. In distinction to the discussions of attachment by Polanyi and Scha, Mann and Thompson, Grosz and Sidner, or Webber, I define attachment in SDRS theory such that it affects the constituents being attached. These effects are sensitive to the type of discourse relation being used to attach the new material to the given structure. So to determine the effects of attachment, one must also determine the choice of discourse relation given an attachment point. I turn now briefly to a sketch of how one might go about determining a discourse relation within the SDRS framework. It is a genre relative matter and a matter of stylistics how the presence of a particular discourse relation is signaled, if it is explicitly signaled at all. As we have seen above in the section on discourse relations and in particular with examples (5), discourse relations may be present in a text without being explicitly signaled by cue words. When inferred, discourse relations often appeal to world knowledge suggested by the text. Sometimes the semantics of the discourse, in particular the semantics of discourse particles (as we shall see below), forces us to introduce certain discourse relations or indicates their presence. But it is usually the interpreter's knowledge of the subject matter (and of the style) that tells him what the appropriate rhetorical relation is in a particular case. 28 The interpreter's knowledge base is an essential parameter in the task of segmenting a text. All this complicates the problem of inferring discourse relations. Without going into the details of a knowledge base, we need a way of organizing the various sources of this knowledge so as to be able to see at least in principle how to conclude the right discourse relation given an attachment point. In many of the discourses that serve here as examples, a simple heuristic based on a search for key or clue words is quite successful. 29 But in any robust algorithm designed to find such rhetorical relations, other sources of information must be used. We need to understand how these various sources of information interact; more importantly we need to understand the underlying logic of discovery of discourse relations.

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As argued in Lascarides and Asher (1991), the appropriate setting for investigating this problem is a nonmonotonic logic. An interpreter must infer the presence of a discourse relation between two constituents using partial information, since he is unable to see directly into the speaker or writer's mind. Moreover, the inference is sensitive to the amount of information in a nonmonotonic way; if an interpreter has limited information about two constituents a and p, he may conclude that one sort of discourse relation holds between them, but with more information he would conclude that a different discourse relation holds between a and p. Let us examine some simple but telling examples,3° Consider the contrast between: (6.a) (6.b) (6.c)

John took an aspirin. John ate dinner. John took an aspirin. John was sick. John took an overdose of aspirin. John was sick.

By the rule of relevance, each new constituent must be attached to some point in the SDRS constructed to date. There are only two constituents for each of these discourses, according to my default principle governing the individuation of constituents. The second constituent can only be attached to the first. So in these examples, there is only one possible attachment point, and we can concentrate on the inference relation in virtue of which the two constituents are to be attached. Let us turn to the examples in (6). In (6.a), intepreters do not apparently infer any causal or explanatory connection between the constituent introduced by the first sentence and that introduced by the second sentence. They simply infer a narrative connection, a continuation of the first constituent together with an ordering of the main events described in the constituents. In the second discourse, however, they infer a causal and explanatory connection between the second constituent and the first; the fact described by the second constituent yields a cause and an explanation for the obtaining of the first. In the third, interpreters infer the causal and explanatory relation in the opposite direction. The explanation of this inferential behavior goes as follows. First, we take as assumption that we are to attach the second constituent to the first, and that this attachment must proceed by means of some discourse relation. I will express the assumption that a is to be attached to p as . This premise is significant, because the putative attachment of a to p implies some relevance of p to a. We have a general relevance rule to the effect that if a is to be attached to p, it must be so in virtue of some discourse relation. If no other information obtains, we assume a Continuation. The language in which the axioms used to infer discourse relations is a quantifier free language with names for constituents and predicates about constituents among the nonlogical symbols together with truth functional connectives and a nonmonotonic implication operator, >, whose logic I have made precise elsewhere and which is a propositional version of the generic quantifier Gen of this fragment,3! The default for Continuation uses the operator, >:
P> >Continuation(a, P)

A THEORY OF DISCOURSE STRUCTURE It is just this axiom and the fact «x, ~> that allows us in the case of (6.a) to conclude defeasibly Continuation between the fIrst and second constituents. In some cases, we infer, in virtue of the presumed relevance of ex to ~ and the assumption that both constituents obtain, some other sort of relation. There is a large list of axioms that depend on the content of ex and ~ supporting these inferences. But the general form of these follow the schema:

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obtaining at the same time. Another thing to note is that these rules do not alwyas determine a unique discourse structure. The simple examples above yielding SDRSs with two basic constituents have unique discourse structures because there is only one possible attachment point for the second constituent. But often many different attachments are possible. We shall see examples of this in the next chapter and also in the next section.

4.3 Rules for Attachment In the relevant instances of (S),

, then one may defeasibly conclude that ~ was a Cause of ex, and from this one may conclude that ~ is an Explanation of ex or Explanation(ex, ~). Although the defeasible law about Continuation also holds in the case of (6.b), the more specifIc law about Cause will be used to conclude Explanation(ex, ~) and will defeat the incompatible conclusion that Continuation(ex, ~). In a nonmonotonic logic like the one generated by>, more specifIc laws always hold over more general ones when there is a conflict. In (6.b) this licenses the conclusion that Explanation(ex, ~). Finally, in (6.c), the particular content of ex and ~ and the assumption that they are relevant to each other gives us another instance of the schema, in which the interpreter concludes Cause(ex, ~). These axioms yield three different discourse structures for (6.a-c). As the examples (S.e-t) repeated below show, we must also integrate knowledge about cues and tense within our defeasible laws for attachment. (S.e) (S.t)

John slipped. It had rained. John slipped. It rained.

The axioms relevant to calculating the discourse relations for such discourses will again exploit specific information about ex and~. They are instances of the schema (S), like the causal rules above; but the predicates '1'1 and '1'2 applied to the constituents ex and ~ to be related contain information about the tense of the main verbs in ex and~. These laws combine with the nonmonotonic logic for> to give us the right results, as is shown in Lascarides and Asher (1991). Such axioms allow us to derive in some cases that more than one discourse relation obtains between two constituents. For instance, we may have a Continuation and a Parallel relation

The principles of constituent attachment are both principles for updating SDRSs and principles of summation for constituents. As principles of summation, they furnish principles of comprehension, in the sense of chapter 1, for what propositions a text may be thought to give rise to. These principles will affect proposition anaphora. But in the next chapter we shall also see how discourse principles of summation help account for what plural sums may serve as anaphoric antecedents. The principles for attaching constituents of an SDRS might proceed in two ways. If K and K' should go together according to the principles, then in updating ]({ with K, we simply might "merge" K with K', and set the current constituent to K U K' in the new SDRS. Alternatively, we might take K and K' to be constituents of a new SDRS ]({', which is itself a constituent of ]({. This preservers antecedently built up structures; and as we shall see, it is this way of thinking about propositional sums that is most fruitful. Principles of attachment exploit the presence of discourse relations, and their exact definition depends on the type of discourse relation used to relate the new information to the antecedently built up SDRS. There are two principle kinds-those principles that have to do with the manipulation of topic and that exploit particular kinds of rhetorical relations like Elaboration and Continuation--and those having to do with other discourse relations between extant segments. The topicbased relations are more complex and much less studied in the discourse literature, perhaps because their analysis demands a close connection between the semantic theory and the discourse theory. Thus, most of this section and the next will be devoted to topic-based updating. Topic-based Updating. Topic-based updating exploits two sorts of discourse relations--Elaboration and Continuation, which,as we saw, are intimately linked to the notion of topic; if the new constituent to a given SDRS is attached with Continuation or Elaboration. Other relations may also give rise to topic-based segmentation, although I will not pursue that issue here. Topic update affects not only the SDRS as a whole but also the topic of the constituent in which the new information is entered; topic update may even replace a topic in the old SDRS with a new topic. Thj.lS, the notion of updating is not purely additive. Constraint on Attachment for Topic-Based Updates: Suppose that a DRS K.i+l must be attached somehow to an SDRS ]({j. It may only be attached to an

A THEORY OF DISCOURSE STRUCTURE open constituent Pin llCj when using topic-based updating. As topic-based updating attaches constituents either as topics (such that the constituent they dominate is an elaboration) or as continuations, the constraint above is restricted to attachments that use the Continuation or Elaboration relation. Any attachment using a relation other than Continuation will be restricted to a d-free and open constituent. The topic-based update operation is a complex substitution operation. Its precise formulation is to be found in the appendix to this chapter. The definition is complex, because the addition of material using topic-based updating may require a modification the topic or other parts of the SDRS structure. There are six cases of topic-based updating. Principle (i) governs summation under same topic. Cases (ii) and (iii) are "topic introduction rules." They stipulate configurations that require the introduction of topics. Case (ii) says that one may introduce a topic for an open constituent p, when the new constituent a is a summary of P(or Pis an elaboration of a). (iii) says that one must, when using topiC-based updating, introduce an explicitly represented topic d-dominating both Pand the newly attached constituent if P lacks a topic. Note also that (iii) implies that topics inherit the relations of the constituents they d-dorninate, when the relations have terms that are not ddominated by the topic. Case (iv) deals with the case of summation in which we generalize, and form a new explicitly represented topic. In effect this is a type of constituent revision--a case of topic revision. Generalization of topics proceeds by sUbsumption, defined on hierarchies of concepts or event-types. The topic of two constituents with topics t, t' and t *- t', would be the most specific proposition that entails t and t', where most specific could be defined by entailment. But simply conjoining t and t' would not give us a topic, because the resulting proposition would not be simple. Case (vi) tells one how to begin an SDRS using topic-based segmentation, while case(v) deals with implicitly represented topics (more on this later). These cases exhaust the possibilities of topic-based discourse segmentation. The topic rules entail certain relations between some of the discourse relations I introduced earlier. To wit: FACT: (Continuation(a, a') & a, a'

< y)

---+

3p Elaboration(p, y)

A problem with topic-based updating as stated is that it may often not be clear what the topic of a segment is. Topics may have to be constructed in the course of building an SDRS. But the definition of topic places few constraints on what a possible topic for a constituent might be. Typically the main clause or a generalization thereof gives us the topic of a constituent, but this area requires more careful linguistic work, especially in languages that grammaticize topic like Japanese. Let's look at an example of topic-based updating on the following discourse: (7)

Kathleen is five feet 5 inches tall. She has brown hair and green eyes.

277

She teaches at a university. According to our first principle of SDRS construction, we begin with the DRS for the first sentence,

Kathleen(v) s,-5' 5" tall (v)

s, • n

and we attempt to add it onto some open constituent. But there is no prior SDRS, so according to clause (v) for topic-based updating, just this DRS forms our SDRS llC,. Only topic-based updating is relevant in this case here, because we have no antecedent constituent to use as a term for any discourse relation that the first sentence might suggest. We now process the second sentence. This yields the DRS, n, x, y, s, s' z=? s' n

s-have(z, x) brown hair(x) s" n s-have(z, y) blue eyes(y) How do we integrate this second DRS together with the first in a coherent SDRS llC2? The presence of an anaphoric relation and the use of the same present tense as in the first sentence are good though not infallible clues that this DRS is a Continuation of the topic introduced by the first DRS.3 2 Also no other discourse relation incompatible with Continuation and based on the particular content of these two constituents suggests itself. So by our basic default axiom concerning attachment, we attach to the previous constituent with Continuation. Attaching the new DRS with the previous DRS is essential to discourse coherence, but is also essential if we are to resolve the anaphoric pronoun--more about anaphora resolution in the next chapter. Our rules, in particular clause (iii) of the Topic-Based Updating definition, now require us to pick a topic that summarizes both of these DRSs. 11- only requires topics for constituents with continuations and hence multiple constituents. A plausible topic of the two constituents above is Kathleen. By clause (iii), we now construct an SDRS t, containing k, and k2 as constituents with their topics; the topic of the whole segmented DRS t, is k o. I will assume that the discourse referent introduced in the topic statement, for instance, is accessible to the discourse referent introduced by the pronoun in k 2. This gives us the following then for llC 2.

278

A THEORY OF DISCOURSE STRUCTURE

A more complex example of topic-based updating is (8), in which occurs what is known as a discourse pop. A discourse pop happens when new material is entered into a d-superordinate constituent to the current constituent. 33

ko:=

(8) n, x, y, s, s'

t .-

v,

279

Sit

I ate a lovely dinner. I had quenelles de brochet. I had salmon. I had duck. I had a nice wine. I then went for a walk around the old city. I slept well.

z=v

n

kl := 1 - - - - - - - 1 Kathleen(v) sl-5' 5" tall(v)

so n

s-have(z, x) brown hair(x) s' n 0

s-have(z, y) blue eyes(y) Continuation{klt k 2) Elaboration(ko,t ) The graphic picture makes clear the constituents and conditions of the SDRS. Notice the effects of SDRS accessibility on anaphora resolution. The third sentence essentially continues the same story that we have seen already. We have three possible attachment points, and the theory does not tell us which one to pick; the obviously, sensible reading is to attach the new information to t. The only difference is that we must appeal to clause (i) to add another constituent to an open SDRS. l.I{3 then looks like this:

The reasoning concerning discourse relations and the general construction of an SDRS for (8) goes as follows. The first sentence introduces a constituent, kit which stands by itself--a very simple SDRS. The second sentence yields a constituent k2 and it must be attached to kl by the SDRS construction procedure. By the rule of relevance, we assume that there must be some relation between kl and k 2. Given this assumption of relevance, world knowledge leads us to conclude defeasibly that the main event of k2 is a part of k l . The axioms for discourse relations allow us to conclude that when the main event of a is a part of the main event of ~, we may conclude that a is an elaboration of~. Since no other information contradicts this choice of relation, we defeasibly conclude that k2 is an Elaboration of k l . Now what about k3' the constituent derived from the third sentence? There are two possible attachments--a high attachment to kl and a low attachment to k 2. We intuitively want to say that k3 is a continuation of k 2. But we must check that k3 is also an Elaboration of k l ; for by attaching k3 to k2 we imply by the semantics of the discourse relations that this is the case. That we must do so follows from (A *), which is a consequence of an axiom for Continuation, (C4). (A*)

(a' ~ & R(a,~) & .R(a,

W» -. .Continuation(~, W).

ko:=

n, x, y, s, s'

t ._ kl := I--_v_,_sl_,_n_-i Kathleen(v) sl-5' 5" tall(v) Sl ° n

Continuation(k lt k 2) Continuation(k 2, k3) Elaboration{ko, t)

z=v

k 2 := son s-have(z, x) brown hair(x) s' on s-have(z, y) blue eyes(y)

Zl =z e-teach(zl) at(e, w) university(x)

noe

Using the same reasoning as with k2' we establish that k3 is an Elaboration of k l . By (A*), however, since kl is not an Elaboration of itself, we cannot have Continuation(k lt k3)' (A *) is a hard axiom, whereas the basic Continuation attachment axiom is a default axiom: if ~ is to be attached to a, infer Continuation(a, ~) by default. The hard axioms always take precedence over the default rules. 34 Since no other relation for attaching k3 to kl is suggested, k3 cannot be attached to k l . On the other hand, since Elaboration(k lt k 2) and Elaboration(k lt k 3), the low attachment of k3 to k2 is possible. Since there are no other relations we infer for k2 and not for k3, (A*) does not preclude Continuation(k 2, k3)' Since no other relation suggests itself, we conclude Continuation{k2, k3)' We conclude similarly that k4 and k5, the constituents introduced by the fourth and fifth sentences of (8) above, are Continuations. Thus, to this point we have constructed the following structure.

280

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A THEORY OF DISCOURSE STRUCTURE

281

coherence relation, of which it is a tenn. With updates using non-structural relations, in which one is given a new constituent 13 and a discourse relation R whose other term is some element y of ex, one simply adds 13 to the set of constituents in ex and the condition R(y, 13) to the condition list of ex. 35 The precise definition is in the Appendix. The problem with updating is to find an appropriate other tenn for the relation.3 6 As with topic-based updating, there is a constraint as to which constituent may be the other tenn of a non-structural discourse relation.

k2' k3,~, kS OC:= Continuation(k 2, k3) Continuation(k3, k 4) Continuation(k4 , kS) Elaboration(k 1 , OC)

Constraint on Attachment for Non-structural Discourse Relations: Suppose that a DRS Kj+l must be attached to an SDRS OCj and that with Kj+l is associated a rhetorical relation R other than Continuation; the other argument of R must be some con~tituent 13 that is ei~her d-.free and open in OCj or an implicitly represented tOpIC of an open constItuent In OCj-

Now we have to integrate k6--the constituent about going for a walk. World knowledge tells us that going for a walk is not part of having dinner. If that is the case, we will conclude that k6 is not an Elaboration of k 1 • By an instantiation of (A *), we conclude that k6 is not a Continuation of k5. But since we have no further infonnation that would allow us to attach k6 to k5 by some other discourse relation, we do not attach k6 to k5 but instead to k 1 • We have no special infonnation concerning the relation between kl and k6 that would allow us to infer some relation other than Continuation, so we attach k6 using Continuation. By the topic construction rules, we must now construct by subsumption a topic ko to this new complex constituent. Now when we process (k7) , we have only two open attachment points--(k o) or (k6). Presumably, (k7) continues the topic of what happened that evening. The finished discourse structure for (8) looks like this if we attach (k7) to (k6):

The constraint on attachment requires some discussion. The conditions on the antecedent term of a discourse relation 13 imply that topic constituents are special. The reason for this is that a particular event or occasion in a single constituent may be the subject of several commentaries, may have a cause and effects that are ea~h described in separate constituents. These separate constituents, howeve~, may st~ll all have as their common topic the event or occasion and would thus be Included In one topic based constituent. One thus wants attachments and SDRSs of the form (OC) to be possible. (OC) .-:--------,

ko

•

OC :=

Continuation(k 2, k3) Continuation(k 3, k 4) Continuation(k4 , k5)

If none of the Ri involving k is a Continuation and if k is not a Background to. any constituent, then according to my definition, k is an implicitly represented tOpIC of all of the other elements and indeed of the constituent as a whole, although k ddominates neither the constituent nor kb k2' k3' etc. On the other hand, the antecedent term of non-structural discourse relation must be d-free. Together with the topic-based update procedure, this ensures that discourse relations always attach to implicitly represented topics (the case just discussed), to explicitly represented topics, or to local (i.e. single) constituents. . It is an important characteristic of discourse relations that whenever there IS a condition of the fonn ex • 13 and a discourse relation R one of whose terms is e ~nd the other of which is intuitively 13 as a completed constituent, then the relatIOn always attaches to the d-superordinate constituent ex. ex summarizes 13 and gives, as it were, its "external features." Attachment to the dominating constituent ex, where

Elaboration(kl> 1IQ Continuation(k b k6) Continuation(k6, k7) Elaboration(ko, OC 1) Updating Using Non-Structural Relations: Topic-based updating concerns itself with just two relations, Continuation and Elaboration. The other two structural relations, Parallel and Contrast also affect SDRS constituents in quite particular ways. But sometimes a constituent suggests a specific, non-structural rhetorical or

..-l-

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A THEORY OF DISCOURSE STRUCTURE

a Jj. ~, has the same content as attachment to ~; the difference is that in attaching only to the superordinate constituent, we constrain how the discourse structure is to be updated. By attaching to the topic, completed constituents are not reopened and do not become available as new attachment points for subsequent material. That certain constituents become closed off and unavailable as attachment points is a central feature of discourse structure. The requirement that updating using non-structural relations may take as an argument only a d-free constituent in the built up SDRS, forces us to consider what to say about an SDRS like (K.) depicted a paragraph ago, which has an implicitly represented topic. Because of past choices in the formalism and our goal of a general explanation of anaphoric constraints, we must say that such an SDRS itself is not d-free. We must suppose that when a complex SDRS a with an implicitly represented topic is "closed off" under the uP9ating process, an explicitly represented topic is given to it, and then topic based updating. will attach new constituents to a's topic, not a itself. This requirement is encoded in clause (ii) of the definition for updating using non-structural relations and clause (v) of the topic based updating definition in the appendix. An example of a simple discourse for which the process of building an SDRS appeals to rhetorical relation updating:37 (9)

Brazil suspended debt payments yesterday. panicked.

Banks and investors

We start out as before with the DRS for the first sentence to get an SDRS Jl(l. The first sentence yields by topic-based updating a very simple SDRS with just the DRS for the sentence. When we process the second sentence, we get a DRS that must be related to an open constituent of Jl(l. The task of finding the other argument of the relation is simple here; there is only one constituent--the DRS constructed from the first sentence. There are no clue words here to suggest a particular relation, but our method of inferring discourse relations will rely on an axiom of the form,

«a, ~> & suspend-debt-payments(a) & investors-panic(~»

> Cause(a,

u,e,X Brazil(u) e-suspend(u, X) debt-payments (X) yesterday(e)

283

Z,W,e' k 2:=

banks(Z) investors(W) e'-panic(Z+W)

Let us consider now a narrative example, in which we have multiple attachments to an implicitly represented topic: (10)

Alexis fell down. Stephan had pushed her. She hurt her knee. She cried a little. She told her friend Ev. Ev kicked Stephan.

The discourse structure for this narrative looks like this. We have the event of Alexis's falling described in kl' which forms by topic based updating a simple SDRS with just one DRS constituent The cause of this event is described in k2 and hence kl and k2 are related by Cause. k3 describes one result of her fall--so Result(k 3, k 1 ). The next sentence--she cried a little--also describes resulting actions of Alexis's fall. This just continues the same segment and so an SDRS is created containing the two constituents k3 and k4 related by Continuation, as prescribed by clause (iii) of topic-based updating. Clause (iii) also requires a topic, k o. Finally, the fifth and the sixth sentences yield constituents, k5 and k6, at a higher level. k5 describes a result of the entire pushing episode, and k6 describes a result of k5. But it also describes a result of the entire episode as well. So we have Result(kl> k6). The following SDRS for the discourse emerges, in which we have a plausible example of multiple attachments to the topic of the SDRS, where topic is defined not in terms of Elaboration and discourse domination, but in terms of the other discourse relations.

~),

where a = suspend debt-payments(Brazil) & ~ = panic(banks + investors and where + is the plural sum forming operation. Of course, we also have the axiom > Continuation(a, ~), but since Cause and Continuation have incompatible temporal properties on the main events in the constituents they relate, we cannot have both Continuation(a, ~) and Cause(a, ~),38 In virtue of the fact that a good nonmonotonic logic will exploit the axiom with the more specific antecedent (which is encoded in the system of Asher and Morreau (1991) by the so-called Penguin Principle), we conclude that Cause(a, ~) and not Continuation(a, ~). So we infer that a Cause relation holds between the two constituents. By our principles of discourse relation updating, we end up with the following SDRS.

It is probably a genre-relative matter as to whether methods of segmenting discourse prefer certain discourse relations over others. Segmenting texts according to topic--on which constituents with similar content are grouped together and those

CHAPTER SEVEN

A THEORY OF DISCOURSE STRUCTURE

with a distinct content are separated--will often work together with the more specific discourse relations like those of Explanation or Commentary. Moreover, change of rhetorical function often accompanies a change of topic. Presumably, good writing should reinforce content-driven segmentation with cues and devices indicating rhetorical patterns that dictate the same sort of segmentation.

Another important clue to the presence of these relations is the occurrence of discourse particles like but and too. But appears to be one way in English of setting up a contrasting discourse connection. A particle like too signals the presence of a parallel between two constituents. Parallelism and contrast may be present even when the particles are not, however. Parallelism involves a pairing of constituents in an SDRS and their parts such that each pair contains two semantically and structurally similar objects. Contrast also involves a pairing between constituents and their parts, in which at least some pairs contain structurally similar but semantically dissimilar objects. Given a pragmatic constraint of novelty or informativeness, no two constituents can be perfectly parallel, for this would mean that they had exactly the same structure and content. Consequently, the constituent introduced later into the SDRS structure would be not informative, and the pragmatic constraint would be violated. Each distinct constituent must contain some amount of new information. Echoing the distinction between topic and focus or given information and new, I shall isolate for each constituent a theme. Parallelism between two constituents is maximized when there is a common theme and it is as maximal as is compatible with informativeness. Contrast is maximally plausible when themes are complementary or even contraries. Developing a notion introduced in Anscombre & Ducrot (1983), I will suppose that a constituent may be assigned a "polarity feature" (plus or minus) relative to some other constituent. These polarities determine parallelism or contrast. As Ducrot (1980) remarks, some predicates have often an "implicit negation" relative to other predicates. For example assert and prove in isolation may both have a positive argumentative force, but in a structurally parallel construction, if the node in which the condition assert(x, q) is entered is paired with a node which contains the condition prove(y, p), then it is clear that a contrast is being made and the constituents that are arguments of these conditions should be assigned different polarity values. The assignment of polarity features is partial; if one cannot conclude that there is a common theme or two complementary or contrary themes, then no polarity value is assigned. For instance, two constituents that discuss the attitudes of agents--one agent's doubts and the other agent's beliefs--can be assigned polarity values, whereas it is quite difficult to assign polarities to completely unrelated conditions--e.g., cause and believe.4o Here are a pair of simple examples, in which discourse particles make evident the intended parallelism or contrast and in which the presence of common or contrasting themes is easy to see.

284

5. REVISION OF CONSTITUENTS AFTER UPDATING The last stage in SDRS construction is the revision of newly attached constituents and other basic constituents in the SDRS. We have already seen one sort of constituent revision--the revision of topics dictated by the procedure for topic-based update. We will see some detailed examples of this in the next chapter. Here I will investigate constituent revision based on the discourse relations, Parallel and Contrast. Parallelism and Contrast are structural discourse relations that exploit the semantic and syntactic structure of a discourse. 39 They not only furnish a means for attaching a new constituent to another constituent in a given SDRS, but they also specify very particular rules for constituent revision of the constituents that they relate. These rules have pronounced effects on the truth conditional content of constituents and, as we will see in the next chapter, on the resolution of anaphora. Such relations yield an interesting case study of constituent revision. A principal motivation for postulating a revision of constituents related by Parallel or Contrast comes from some examples of Rob van der Sandt's. In these examples, the truth conditional content cannot be explained in terms of the semantics for DRS constituents built up so far. (l1.a) If Fred drinks, half the bottle is gone. If Sam drinks too, the bottle is empty. (l1.b) If the King opens the exhibition, the newspapers will comment on his speech. But if the Queen opens it, they will comment on her robe. In (l1.a), the content of the second sentence is dependent upon the first: it says that if Sam and Fred both drink, then the bottle is empty and not just half-gone. But this meaning cannot be derived simply from the DRS construction algorithm or any compositional semantics concerning the two clauses. Similarly with (11.b), the meaning of the second sentence also depends on the meaning of the fIrst; the second sentence says that if the Queen opens the exhibition and the King does not, then the newspapers will comment on her robe. My hypothesis is that in both of these examples, the semantics of the relations of Parallel and Contrast force a very particular interpretation on the second constituents. The presence of Parallel and Contrast force us to revise the content of the constituents they relate. Parallelism and Contrast Defined. To understand these examples, we must define Parallel and Contrast precisely. The semantic content and structure of constituents offer clues as to whether they are terms of Parallel or Contrast relations.

285

(12.a) A girl that I met envies Sam. I envy him too. (12.b) A girl that I met dislikes Sam. But I like him. The parallelism between the two clauses in (12.a), as well as the contrast in (12.b) is fine, and there is clearly a common theme between the two constituents in (12.a)-envying a particular individual, while in (l2.b) the themes of liking Sam and

rr---~~=~-~~~~~---------"'-)~lJ#-'"~-~--"-286

A THEORY OF DISCOURSE STRUCTURE

CHAPTER SEVEN

disliking Sam are plausibly complementary. This allows us to assign unequal polarities. Without such complementary or common themes as in examples (12.c-d) below, we cannot set up Parallel or Contrast discourse relations. Since the presence of the parallelism or contrast particles like too or but require such relations to be present,41 the resulting SDRSs for these examples are incoherent. (12.c) #A girl that I met envies Sam. I find him amusing too. (12.d) #A girl that I met envies Sam. But I find him attractive. Notice that it is the lack of connections between the conditions derived from the main verbs that prevents us from determining polarities for these simple constituents. The presence of a common or contrasting theme determines the polarity of two paired constituents. So to define polarities and Parallelism and Contrast, then, we must make sense of the talk of pairing constituents and their parts. An embedding tree for a constituent of an SDRS ~ is the ordered structure determined by the dsubordination relation on 0. in~. It is defined in the appendix. The basic idea is that two constituents will stand in a Parallel or Contrast relation just in case there is a bijection from the embedding tree of one to the embedding tree of the other such that the nodes of the trees that are paired together have the appropriate polarity (same polarity in the case of Parallel relations and contrasting polarity in the case or Contrast relations). The definition of tree isomorphism is given below. As we shall see, however, Parallel and Contrast may obtain when there is no fully parallel structure. We must define Parallelism and Contrast with respect to subtrees of embedding trees in which part of the structure is disregarded. I call these modified embedding trees or ME trees. 't* = , is a modified embedding tree of an embedding tree 't = iff (i) A* S A, (ii) root('t*) = root('t), (iii) d-6 A * S d-6 A, (iv)Vx (x is a leaf of 't* iff x is a leaf of 't).

DEFINITION:

Let't = and 't' = be two trees. 1'}: 't -+ 't' is a tree isomorphism from A onto A' iff 1'} is a bijection and V0., ~ E A (0. 0-6 ~ iff 1'}(0.) d-6 1'}(~).

DEFINITION:

To get a feel for the notions of embedding trees and modified embedding trees (ME trees), consider the sentence, (13) John doubts that Mary believes that Susan likes him. This yields a DRS with several embedded structures.

!

x,s john(x) s-doubt(x,

u, s' Mary(u) s'-believe(u, v, Z, S" Susan(v) z=x s"-like(v, z)

287

) )

Since d-subordination incorporates the semantic notion of subordination defined in chapter 2, the embedding tree and modified embedding trees for (13) will reflect to some extent the embedded SubDRSs in the DRS above. The embedding tree for (13), which is also an ME tree, is the structure on the left. On the right is another ME tree for (13). Given the definition, there are only two ME trees for (13). 'tJ 't2

To see how we may pair constituents in different ME trees, consider (14) as following (13): (14) John doubts that Susan believes that too. (14) has two ME trees as well--each one isomorphic to an ME tree for (13). Thus, two tree isomorphisms are easily defined--the natural ones between the pairs of isomorphic ME trees of (13) and (14). With ME trees, we have a new tool with which to investigate polarities. Because of the way the DRS construction procedure is devised, a constituent never o~curs more than once in another constituent. We must always introduce new discourse referents even when processing the very same verbal material. So we can isolate uniquely the condition in which one constituent occurs in another as an argument or term. I shall call such conditions matrix conditions; these are defined precisely in the Appendix. Note that the matrix condition of a constituent 8 in 8' may b~ complex if there are elements 'Y such that 8 is d-subordinate to 'Yand 'Y is dsubordinate to 8', as happens in the ME tree 't2. Given a tree 't and a node 0. in 't, the matrix condition of a in 't is the matrix condition of 0. in the node immediately superordinate to 0. in 'to In a ME tree, the matrix condition of a node may be complex. The matrix condition for k2 in't2 ( or equivalently for k2 in k o) is:

A THEORY OF DISCOURSE STRUCTURE (13.1)

doubt(x,

u, s' Mary(u) s'-believe(u, k 2)

A theme of a constituent always contains at least a part of the matrix condition and always the predicate or operator of which the constituent is an argument. Consider again the discourse where (14) follows (13). The discourse particle too makes clear that Parallel should hold between the constituents ex and ~ derived from (13) and (14). But the parallelism between ex and ~ is that in both, John has a doubt toward someone's believing that Susan likes him. It is this common theme that licenses the assignment of common polarity and hence the parallelism. The common theme abstracts away the information in the matrix condition for k2 in (13.1) who is doing the believing. Two nodes paired under a tree isomorphism will have the same polarity if they have themes that are necessarily equivalent or one is a subsort of the other relative to the background fixed knowledge base. They will have distinct polarities if they have themes that can be shown to be typically complementary, relative to the knowledge base. 42 Since subsumption may be at a more or less abstract level and since themes may cover more or less of the matrix condition for a constituent, polarity assignments are scalar and may vary in strength. Theme and polarity are defined precisely in the Appendix. With these definitions we can define Parallelism and Contrast, as well as their generalizations Parallelism* and Contrast*. Because of the scalar nature of polarities, Parallel and Contrast will be scalar relations as well. Constituents may support many different Parallel or Contrast relations, and some are stronger than others. The maximization constraint for Parallel and Contrast relations requries that we maximize the strength of the polarity assignment and so pick the maximally strong Parallel or Contrast relation, when picking a pair of ME trees, a tree isomorphism, and themes for paired constituents. I predict that there always is one such maximally strong relation in a coherent discourse. It can happen that one pair of constituents may support both Parallel and Contrast relations. Consider for instance (15.a-b): (I5.a) Mary is a gourmet. She loves that restaurant. Although not a gourmet, I love it too. (I5.b) Hank likes Susan. But I like her too. Given our investigations of the previous sections, we can build an SDRS for (15). The first two sentences yield constituents kl and k 2. We must attach k2 to kl by the relevance rule. Given that is a gourmet is a dispositional predicate that might explain or serve to put in perspective people's tastes in restaurants, world knowledge suggest sBackground(kb k 2), and perhaps also Explanation(k 2, k 1).43 Hence kl and k2 form a constituent ~ with such discourse relations obtaining between kl and k 2.

289

k 2. k2 serves as an implicitly represented topic of ~. Now we process the next constituent, k 3, which contains particles indicating both contrast (although) and parallelism (too). The relations Parallel and Contrast are often clues for topic continuation. Since these are structural relations, they must be used with Continuation and the topic based updating rules. There are two possible open attachment sites--~ and k 2. Since k2 is an implicitly represented topic in ~ and we wish to continue the topic of ~ itself, we must close ~ off with an explicilty represented topic, topic(~), and attach k3 there. Since world-knowledge yields no other candidate discourse relation, we conclude either Continuation(k 2, k3) or Continuation(topic(~), k3). The relation between topic(~) and k3 maximizes both the Parallel and Contrast relations. So far we have seen ME trees only of simple constituents. But the notion of an ME tree extends to complex constituents too. The constituent structure of complex constituents may be diagrammed in a similar way to embedding trees. I will call the picture of the constituenthood relation over an SDRS a constituent graph. Of course embedding trees are defined also for SDRSs since the constituenthood relation is part of d-subordination. Constituent graphs are a partial representation of a full embedding tree. We have the following ME trees for k3 and topic(~) showing the tree isomorphisms necessary to define parallelism and contrast. The arrows show the isomorphism. The sharp cornered rectangle shows the collapsing effect of the ME tree for topic(~); the rounded rectangles show the scopes of the parallelism and contrast relations.

parallelism

contrast The final constituent graph for the discourse in (I5.a) looks like this. Attaching k3 to ~ yields a new constituent Wby Continuation and thus a new topic k o' by the rules for topic attachment.

As the discussion of (I5.a) reveals, Parallel and Contrast have a scope as well as

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A THEORY OF DISCOURSE STRUCTURE

a degree. We may easily depict the scope relations and the Parallel and Contrast relations themselves graphically using the modified embedding trees. The enclosed areas in the rounded rectangles show the scope of the parallelism relation in the graphic depictions of what the definitions permit as scopes for a Parallel or Contrast relation.

Roughly, the concept anaphor that picks up the complex property of John defined by the entire previous sentence. The presence of the particle too forces a parallelism relation to be drawn so that the property defined by the root of the attachment point is identified with the discourse referent introduced by the leaf of the constituent to be attached. Finally let us briefly look phenomen of "nested" Parallel and Contrast relations. In (I5.a) the parallelism and contrast relations "overlapped" in that both relations involved the root of the embedding tree of the constituent to be attached. Given the constraints on scopes just discussed, however, it is possible that a given pair of constituents support a Parallel relation "nested" within a Contrast relation; Parallel would have narrow scope and not encompass the root of the ME tree t# of the constituent to be attached, while the Contrast relation would have scope over all of t#. Graphically, we would have in this case:

290

Minimal Parallelism tl

~

+~

/~

+

contrast subtree

+

7\

Maximal Parallelism

subtree

L

tl

/\

+ subtree

p allelism

+~+

/\\ The diagrams make evident that the subtrees for which Parallel and Contrast relations are defined must cover certain bits of the modified embedding trees; the subtree t# of the new constituent ~ to be attached must cover the leaves of the embedding tree of ~, while the subtree t* of the attachment point a must cover the root of the embedding tree of a. This asymmetry is related to the scope of these relations. If the constituent ~ to be attached comes with a Parallel or Contrast relation, this relation must have scope over at least some simple DRSs in~. On the other hand, the attachment site a is the other term of the relation and so all of a must fall within the scope of the relation. The asymmetry shows up in analyses of anaphoric connections like the one in the discourse below: (16)

291

[If John goes to the party, he always sings the bluest. Thatj's true of Judy too.

This sort of nested parallelism and contrast occurs in (I5.b). SDRS theory can analyze (I5.b), if we use the embedding trees for the two constituents extended by the predicative DRSs that are the translations of the VPs; I call these extended embedding trees. The contrasting and the parallel elements have different scopes in the second sentence; the contrastive element but extends over the DRS constructed from the whole clause, while the scope of too extends only over the predicative DRS introduced by the verb phrase. Graphically we get a nested picture, similar to, though simpler than, the one above. Extended embedding trees will be used in chapter 9 in connection with concept anaphora. Examples like (I5.b) also motivate the generalizations of Parallel* and Contrast* found in the Appendix. Parallel* and Contrast* generalize the definitions of Parallel and Contrast to subtrees: Parallel*(y, 0) holds just in case some discourse relation R is such that R(a, ~) and Parallel(y, 0) and y < a and 0 < ~--similarly for Contrast*. With these relations, we can attach two constituents by means of Contrast and have subconstituents related by Parallel*. This is precisely the situation in (I5.b); the contrast extending over the DRS constructed from the whole clause contains within it an instance of Parallel* between the two predicative DRSs

CHAPTER SEVEN

A THEORY OF DISCOURSE STRUCTURE

introduced by the verb phrases. I will make use of these relations throughout section, as well as their variants in which the relevant tree isomorphism is explicitly mentioned--Parallel*(a, ~) (Contrast*(a, ~»with respect to 'i}. Parallel* and Contrast* introduce yet another parameter of variation in parallel and contrasting relations. The degree of the Parallel*/Contrast* relation depends roughly on the size of the ME tree relative to the embedding tree of the constituent, as well as on the scope and the strength of the polarity assignment. Discourse Particles and Revision. Discourse particles (e.g., but, also, too) mark a particular constituent as being a contrast, parallel with some other constituent. The other constituent is determined in the process of attachment. Contrastive particles signal a necessary contrast of structures, while parallelism-indicating particles like also and too signal a necessary parallelism in structures. Parallelism and Contrast may obtain in discourses where the particles like too, also, but, anyway do not occur. But such particles are often present when such relations obtain. What is the function of these particles and what is their semantics? Under the construction procedure, a discourse particle a introduces a DRS predicate over a certain constituent 0, which contains at least one leaf of the embedding tree of the constituent derived from the discourse in which a occurs. a may even introduce a predicate over parts of DRSs or predicative DRSs. While there are a variety of parallelism and contrastive particles, I will suppose that under the DRS construction procedure any parallelism particle yields a condition, too(~) and that any contrast particle yields a condition, but(~). The semantics of these conditions is straightforward. Too(cp) is satisfied in an SDRS l!{ only ifParallel*(a, cp) holds for some a in l!{. Similarly, but(cp) is satisfied in an SDRS l!{ only if Contrast*(a, cp) holds for some a in l!{. Since parallelism and contrastive particles for the presence of certain discourse relations, they enable us to analyze how Parallel and Contrast affect constituent revision. The semantic effect of a parallelism particle forces us to read a discourse as containing a parallelism, if it is to be coherent, and the condition it introduces also marks the scope of the Parallel relation. Similarly for a contrastive particle. I shall call the constituents that are arguments to the conditions but(cp) and too(cp), designated scope elements relative to the tree isomorphism used to define the maximal Parallel * or Contrast* relation. Designated scope elements are those elements that are transformed by revision. The constituents that are arguments to parallelism or contrast particles have thus a special importance in the constituent revision procedure. To specify the constituent revision procedures using Parallel and Contrast, I define a join-like operator /\ for constituents with the axioms (/\ 1-/\ 4) in the appendix. Suppose that too(o) occurs in a constituent K that is being added to an SDRS l!{, and attached in particular to some constituent~. The presence of the condition too(o) in a constituent requires a Parallel* relation and licenses the rule for constituent revision using Parallel* found in the Appendix. The effect of Parallel* is to add the contents of the constituent in the designated scope to the contents of the other parallel constituent. Similarly, a contrastive particle introduces

a DRS predicate of a constituent, over which it has scope, as well as a Contrast* relation. It licenses a rule of revision using Contrast*, which is also defined in the Appendix. The truth conditional import of but is to add to the content of each constituent A that is in its scope and that has an unequal polarity with the constituent it is paired with under the tree isomorphism necessary for Contrast* the negation of the content B of the contrasting constituent. This is so at least if -,B and A are consistent; if this is not the case we add to A the negation of the implicature that only B. Constituents that are candidates for revision may be either topic or non topic constituents. As we saw before, topics play a very special role in discourse structure, and the same is true here. When we join a topic node a to a node 0 that is in the designated scope say of a Parallel* relation, we must join with 0 the content of all the constituents a dominates. Axiom (/\4) reflects this. The rules of constituent revision supply revised constituents to be added to the SDRS. Thus, the general SDRS-UPDATE produces a set of new SDRSs from a previously given SDRS a and a constituent ~. It is defined using the attachment rules on ~ and a possible attachment point y in a; given the attachment point, the rules determine a function ATTACH that yields a new SDRS.

292

293

= {a': there is a constituent y < a such that y is a possible attachment point in a and a' = ATTACH(a, y, ConstituentRevision(y, ~».

DEFINITION: SDRS-UPDATE(a,~)

It is easiest to understand the rules of constituent revision by means of some examples. First consider the case with Parallel and Van der Sandt's example (ll.a) again.

(ll.a) If Fred drinks, half the bottle is gone. If Sam drinks too, the bottle is empty. The truth conditions of (il.a) are: (F --+ H) & ((S & F) --+ E). We are now in a position to account for these truth conditions. (I 1. a) requires for its interpretation first an identification of a relevant Parallel relation. Consider the following ME trees, isomorphic with the original embedding trees. The - indicates the operator between the two DRSs. I also indicate the tree isomorphism by means of arrows. The maximal scope of too is the antecedent K2 1 of the second conditional, shown by the rounded box around K 21 . I suppose that it contains only K2 1, for the discourse also contains an element of contrast--the two consequents mapped onto each other are plausibly of opposite polarities.

294

CHAPTER SEVEN 'tl

Now let us build the discourse structure for (I1.a). The presence of a parallelism particle signals that if the discourse is felicitous, Parallel(K b K 2) or Contrast(K b K 2). Since Kl2 and K22 have conflicting polarities, we may in virtue of the tree isomorphism ~, which pairs these two nodes togheter, have Contrast(K 1, K 2). By the procedure for attachment, we infer by default that Continuation holds between Kl and K 2. The rounded square shows the scope of the too discourse particle and of the Parallel* relation it i~n·order for our SDRS to be coherent, we must ensure that Parallel*(~K21)' K 21 ). But this is so since ~(K21)' which is K ll , and K21 have a common theme constructed from the VP that is maximal with respect to any other common theme that one might construct by pairing K21 with some other constituent (e.g., K I2 ). So the condition too(K 2 b K ll ) is satisfied in this SDRS, and the parallelism is maximized. The extended constituent graph below for the whole discourse shows the effect of the discourse relation Continuation linking Kl and K by the presence of a topic node, which is required when we update using Continuation. The ellipse shows the extension of the discourse relation.

A THEORY OF DISCOURSE STRUCTURE

295

add only the negation of the implicature that the bottle was only half empty. This gives the right truth conditions for (Il.a), if we take the truth conditional import of an SDRS to be simply the truth conditional import of the DR-theoretic union of its elements (and this seems perfectly justifiablesince /\ is a summation operator, and DR-theoretic union is the natural way of construing the content of a sum of constituents).

x,e Fred(x) e-drinks(x)

k

x,e Fred(x) e-drinks(x)

I

y, e'

I

"*

I half the bottle is gone

I

I

k'i Tom(y) ~ "* the bottle is empty e'-drinks(y) ..., I only half the bottle is gonel

parallel(k, k')

Let us now turn to another case of constituent revision using Contrast. Comparing (Il.b) with (ll.a) is instructive in seeing the difference between too and but. Note that but has scope over the whole sentence in (ll.b). (ll.b) If the King opens the exhibition, the newspapers will comment on his speech, but if the Queen opens it, they will comment on her robe. The desired truth conditions for (ll.b) are these: (K -> S) & ((Q & ...,K) -> (D &..., S)). This is what the procedure for Constituent revision based on Contrast supplies. Consider the SDRS for (l1.b). The contrasting relation is determined by the bijection defined on the components of the conditionals. The bijection is the same as that given for (ll.a). Only the polarities are different for K21 and K ll • Here is the relevant constituent graph of the whole SDRS.

Let us now turn to the effects of constituent revision. ~ maps the two antecedent clauses of the conditional onto each other. The constituent revision procedure now dictates that the second conditional must be updated so that the designated scope element and its image under ~--i.e., two conditional antecedents-are summed together, as indicated by the SDRS for (ll.a). The negation of the first consequent is added to the consequent of the second under the Contrast* constituent revision procedure but since the bottle is empty entails that the bottle half empty, we

i! I I!

%T "''''1\

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296

,y,"

I The tree isomorphism guides the constituent revision procedure--joining the appropriate leaves of the tree with opposite polarities that fall within the sc~pe of the discourse particle--in this case again K2 I and K I I . Contrast does not sImply conjoin the two constituents; it conjoins the new one with the negation of the antecedently given one, if this is consistent. In this case it is. The procedure of updating here is then the same as sketched above and we get the following result. Below I identify two discourse referents in different constituents; this is permissible in this case, as we shall see in the next chapter. u,x King (u) kl exhibition I l e Ie opens (u, k~ v,z Queen (v) k2 z=x L e' I Ie' - open (v, z)J

=*0 =* ~ ...,S

Contrast (k 1, k2) So far we have looked only at those contexts where we have particles marking parallelism or contrast. What happens when the indicating particles are not there? (12)

If Mary likes John, he is happy. If Susan likes John, he is ecstatic.

(12) seems ambiguous to me. We could maximize either Parallel or Contrast relations. If (12) is interpreted as containing Parallel constituents, then constituent revision will produce an SDRS similar to that for (ll.a); if (12) is interprete~ as involving Contrast, then the resulting SDRS will look like that for (ll.b). My intuitions accord with these results. If these intuitions are right--and they seem to me to be reasonably robust--then this indicates that the updating strategies in cases where parallelism or contrast are present but not explicitly marked should not be treated as different in kind from those in which it is explicitly marked. Even without explicit, parallelism or contrast particles, the interpretation of the discourse assumes a maximal scope element when a Parallel or Contrast relation is present between two constituents a and ~; this typically is assumed to be the most dsuperordinate constituent 8 ~ tc ~ that falls within the Parallel or Contrast relation. Nevertheless, without explicit marking of parallel or contrast structures by discourse particles, there seems to be more leeway for interpretation, both of .what sort of relation is suggested and what the maximal scope elements are. The fmal structure

A THEORY OF DISCOURSE STRUCTURE

297

will depend on other factors too--e.g., the content of the constituents as wholes.

6. TAKING STOCK Let us take stock of the machinery that I have developed for elucidating discourse structure within DRT. The SDRS KD for a discourse D, in comparison with the DRS KD derived from D using the standard construction algorithm first of all adds assertions about the discourse relations that parts of KD bear to each other. Further, KD displays the partial ordering < of the parts of K, together with the various discourse relations whose relata determine the parts of K. SDRSs don't destroy the logical structure of the discourse. But the use of SDRSs commits us to a view of DR-theoretic structures beyond that of just determining dynamic truth conditions of discourses. The divisions in an SDRS are needed to make sense of the anaphoric data, but even this tie to truth conditions is sometimes only indirect. The machinery of discourse relations, the procedure by which the segmentation comes about, may not have a truth conditional import concerning the subject matter of the discourse. The discourse dominance hierarchy does not appear to have any truth conditional import for the content of what is said. Neither do many other rhetorical relations, though coherence relations do sometimes have a truth conditional import and all of these relations have a truth conditional content concerning the relations of segments to each other. There are precedents within the DRT-framework for such indirect ties to truth conditions. Many of the distinctions made by tense and aspect that are reflected at the level of the DRS, such as the positing and manipulations of the various reference and temporal perspective points, do not affect truth conditions except by serving to determine temporal anaphora. The structure of an SDRS is close to that of a delineated DRS (DDRS). This is no accident. Our structuring of a discourse depends upon our beliefs about how the speaker/writer intended to organize the material, and in order to do this interpreters must assume that they and the speaker/writer share many beliefs about how the world is structured. DDRSs must also have some sort of a topic structure which determines its constituents, and this topic structure presumably also affects discourse structure. Finally, they will share many discourse relations. The process of DDRS construction and the process of SDRS construction are clearly also closely related; they are perhaps two sides of the same coin. As part of the interpretive process, SDRS construction may give a segmentation that makes it easier to update one's belief structure. SDRS and DDRS construction are both part of a complex interpretive process of verbal messages that is not even foreshadowed in ordinary truth conditional semantic theories. Both also have a truth conditional content: the DDRS conditions tell us the mode of a constituent, or about the evidential relations between constituents, in the DDRS. Conditions in an SDRS do something similar. They express discourse relations between constituents. Some of these may also be of an evidential and hence attitudinal nature. Future work should reveal a closer connection between these two sorts of structures.

298

SEVEN

The parallels already mentioned between DDRSs and SDRSs point to a more metaphysical moral. They are both in effect cognitive structures of an interpreter and intelligent agent. The SDRS is a function of an interpreter and a text; the interpreter brings a structured knowledge base and a particular set of interests that determines what SDRS he comes up with in interpretation; but in general, different interpreters with different skills and interests may very well segment texts differently. I am not committed to the view that there is one correct interpretation or discourse structure for a text. This is welcome, since people often disagree what discourse relations a text exhibits and also what are the boundaries of the subDRSs that are the terms of those discourse relations. 44 Finally a word about the relation between my theory of SDRSs and previous theories of discourse structure. My theory of discourse segmentation leans heavily on insights of others like Kintsch and Van Dijk, Grosz and Sidner, Mann and Thompson, Polanyi, and others. I have used many of the discourse relations discussed by Mann and Thompson (1987), and the dynamic aspect of SDRS construction has strong similarities to Polanyi's ideas about discourse syntax construction. I have elaborated a dynamic process of SDRS construction and sketched in several cases how one could build up an SDRS for a whole discourse in processing a discourse sentence by sentence. I have also formulated principles of summation and separation of SDRS constituents based on topic and on rhetorical relations and showed how these could be used to build SDRSs. I also investigated certain ideas about topic construction. My account gives a bottom-up SDRS construction procedure that yields a semantically motivated and semantically based discourse structure, rather than one based on the idea of a discourse syntax like Polanyi's. This gives me quite different discourse trees from Polanyi's. I also treat in a relatively precise fashion a much wider class of relations than she does. Mann and Thompson have a much wider class of relations than I but they do not, as far as I could figure out, really provide a formal or formalizable procedure for building discourse structures. Also my theory is directed toward the explanation of abstract entity anaphora; thus, I have provided a much tighter fit between semantics and syntax than these other theories achieve. Finally, insofar as the semantic construction procedure is mechanizable and heuristics for topic and rhetorical/coherence relations are forthcoming, the entire procedure for SDRS construction is perhaps more clearly mechanizable. The principal difference with these other theories, however, is that my theory of discourse structure is fully integrated with and fully interpretable by a semantic apparatus. As we have seen already, this integration predicts that discourse structure may have effects on the truth conditional content of constituents through constituent revision. Constituent revision is triggered by structural discourse relations like Continuation and Elaboration (for topic revision) or Parallel and Contrast. The idea of constituent revision is novel and can only be articulated if the integration between semantics and discourse is thoroughgoing. We shall have opportunity in the next two chapters to test the effects of constituent revision and SDRS updating in general on anaphora.

A THEORY OF DISCOURSE STRUCTURE

299

Another consequence of the integration of semantics and discourse structure is that I have used a level of semantic information to develop discourse structure. The discourse structure itself is defmed out of semantically meaningful constituents; the elements of a discourse structure or SDRS are propositions, and the terms of rhetorical and coherence relations are propositions, or events. This permits us to draw on information in the lexicon and in the knowledge base about relevant events and objects in order to construct SDRSs. The fact that our discourse structures employ semantically meaningful constituents allows us to reason about our structures and elements of them using ordinary logic. It also allows us to state constraints and axioms about discourse structures in a declarative rather than procedural way.

7. APPENDIX OF DEFINITIONS AND CONSTRAINTS IN CHAPTER 7 7.1 Basic Definitions for SDRSs and their Constituents:

SDRS Conditions): If 0" ... , on are DRSs, Con a set of SDRS conditions on those DRSs, then < {Ol, ... , On}, Con> is a SDRS; If aJ, ... , an are SDRSs or DRSs, Con is a set of SDRS conditions on a" ... , an, then <{a" ... , an}, Con> is an SDRS. If al and a2 are SDRSs or DRSs and R E Discourse Relations, then R(a" a2) is an SDRS condition on al and a2.

DEFINITION (SDRS and

NOTATION: Shadow letters with primes or subscripts (e.g.,][, ][', ][" ][2, etc.)

denote SDRSs. Greek letters, a, subDRSs.

~,

y, 0, etc. range over constituents--DRSs or

DEFINITION: A constituent a of an SDRS ][ is an SDRS ][' such that a

E

UU][.

DEFINITION: a is a tc-constituent of ~ iff a < ~ or a is a tc-constituent of yand y < ~. NOTATION: a is a constituent of~: a <~. NOTATION: a is a tc-constituentof~: a
=

=

FACT: The SDRS ][ for a discourse D and its tc-constituents form a tree under <.

The Relation of SDRSs to DRSs: DEFINITION: A

part of a DRS K is a DRS K' such that UK' !: UK and ConK' !:

ConK DEFINITION: A leaf of a constituent a is a constituent ~ that is
300

CHAPTER SEVEN

DEFINITION:

A THEORY OF DISCOURSE STRUCTURE

una = ~ {p: P is a leaf of a}, where ~ represents DR-theoretic union.

DEFINITION: Contingent(K) iff K " AXIOMS FOR CONTINUATION:

Let K be the DRS derived from D using the standard construction procedure and lI{ the SDRS for D. Then K is a part of ~nlI{.

FACT:

(Cl) (C2) (C3) (C4)

7.2 Axioms and Meaning Postulates for Discourse Relations

FACT: FACT:

AXIOMS FOR DISCOURSE RELATIONS:

(SI) (S2)

(S3) (S4) (S5) (S6)

Instance(a, P) .... Support(P, a) Explanation(a, P) .... Support(a, P) Causal-Explanation(a, P) ..... Explanation(a, P) & Cause(a, P) Intentional-Explanation(a, P) ..... Explanation(a, P) & Purpose(p, a) Instance(a, P) ..... Generalization(p, a) Causal-Explanation(a, P) .... -,Result(a, P)

Continuation(a, P) .... -,(a .. P) & -,(p .. a) (R(a, P) & P" y) .... (-,Continuation(a, y) & -,Continuation(y, a)) Continuation(a, P) .... 3y ( Contingent(y) & y" a & y" P & simple(y)) (a" P & Continuation(p, y)) .... \7'R (R(a, P) ..... R(a, y)) Elaboration(a, P) .... -,Elaboration(p, a) Elaboration(a, P) .... (-,Continuation(a, P) & -,Continuation(p, a))

Let a, P be constituents in lI{. Topic(P) = a iff a is simple and either (i) a" pin lI{ (in this case a is an explicitly represented topic); or (ii) -,3y < P (Continuation(y, a) or Continuation(a, y) or Background(a, y)) and \7'0 < P 3R E Discourse Relations R(a, 0) or R(o, a) in lI{ (in this case a is an implicitly represented topic).

An eventuality discourse referent e is a main event in a DRS K iff there is a predicate cp such that e-cp E ConK and for no predicate 'JI is it the case that e'-'JI(it, e) E ConK.

Topic*(a, P) iff (i) a is a topic of P or, a is a topic of y and 30< yo is a topic of P or (ii) a is a topic of e and Topic*(e, P).

DEFINITION:

The Definition of i: The definition of i assumes a sort hierarchy in which there is a subsort relation that is a partial ordering on the set of sorts. The sort hierarchy will cover both event types and object types. The sort hierarchy is part of a fixed knowledge base, in which is to be encoded common sense world knowledge.

Satisfaction Definition for Discourse Relations: I will write' (M, w, t) ~ g cp' just in case g verifies a condition cp at a model M in a world wand a time t. The usual notion of DRS validity (written simply as ~) carries over to SDRSs. Here are satisfaction definitions for the most common of the discourse relations that I will use: As is familiar from chapters 3-5, the models will contain DR-theoretic structures--in particular the SDRS derived from the discourse itself; this structure is exploited by the structural relations.

Let A be a background knowledge base with a sort structure S. A constituent a subsumes relative to A a constituent P iff for each e' E ME(P) there is an e E ME(a) and for each condition 'JI such that e'-'JI(Ylt ... ,Yn) E Con~ there is a condition e-cp(x 1, ••• , Xm) E Cona. such that (i) 'A.e'A.ye-'JI(Y) is a subsort in S of 'A.eH e-cp(x); (ii) if Yi has the same a-role as Xj' then Yi is introduced by a DP whose head yields a predicate that is a subsort in S of the predicate introduced by the head of the DP in which Xj is introduced.

DEFINITION:

DEFINITION: a

J.. and K " T.

DEFINITION:

DEFINITION:

I1-

301

DEFINITION:

(M, w, t) ~f lI{ iff for every condition C in lI{ (M, w, t) ~f C. (M, w, t) ~f Cause(a, P) iff (w, M) ~ f CAUSE~na, ~np). (M, w, t) ~f Purpose(a, P) iff for some x E UK, K
i P iff a subsumes P or (P entails a and not a entails P).

[{e'}, {e'-do(x, cp)}) P is more complex than a iff either I{e: e is a main event in UnPlis larger than I{e: e is a main eventin~na}1 or I{y. y< P}I > I{y. y< a}1. DEFINITION: A DRS K is simple iff it contains at most one main event and no dsubordinate structures.

~

una}])

DEFINITION:

Elaboration(a, P) iff ( a i P v (for every e E ME(P) there is an e' ME(a) such that e is a part of e') & P is more complex than a. DEFINITION:

(M, w, t) ~f Explanation(a, P) iff (M, w, t) ~ f EXPLANATION~na, ~np). (M, w, t) ~f Comment(a, P) iff for some x and some attitude predicate cp, 3 g ~n~ f (M, w, t) ~ g cp(x, ~ P) and3 g ~na. f (M, w, t) ~ g ~na. (M, w, t) ~f Elaboration(a, P) iff relative to the (fixed knowledge base) A, P or for every e E ME(P) there is an e' E ME(a) such that e is a part of e') & P is more complex than a and 3 g 2(~na.~~n~) f (M, w, t) ~g ~na) U (

a"

E

vnP)· (M, w, t) ~f Continuation(a, P) iff (M, w, t) ~ (Cl)-(C4) instantiated to a and P

I IIi

i

L

~

rr-------30-2~~~~'="'-=-~=~~='~--~CHAP-~TE~R-S-E-VE=-~N~~-~------~----""'"'I1fJ... 'r"c..,."---~--"------A'~T-H-E-O-R-y-O-F-D-IS-C-O-U-R-S-E-S-TR-U-cr-u-RE---- ~~-30-3-----

and 3 g ~~na\,d \,d"~) f (M, w, t) I=g ~na) V (1d"~)

I

a entails ~ iff for all w, t and given the intended model M, if M, t, w 1=[ a, then 3g ~~ f (M, w, t) 1= g ~.

(Eat-dinner(a) & eat salmon(~) & Part of(Me(a), Me(~»

DEFINITION:

7.3 Basic Definitions and Axioms for SDRS Updating Rule of Relevance: If a is a constituent to be incorporated in an SDRS must be attached by some discourse relation to a constituent in ~

~,

then it

DEFAULT AXIOM FOR CONSTITIJENTS: Typically, every sentence introduces a new

leaf into an SDRS.

a, ~ be constituents, DRSs, or proposition discourse referents. a is d-subordinate to ~ iff (~~ a::;; tc ~ or a is ~ubordin~te to ~ or ~ • a or a is declared in U~; or (n) (a
FACT: If a • ~ is a condition of lK: and a or some constituent not discourse

subordinate to a is the current constituent, then ~ is not an open constituent of lK:.

Axioms for Inferring Discourse Relations: These are the axioms over and above the general axioms about discourse relations that are needed to nonmonotonically infer the desired conclusions in the examples. They exploit world knowledge but also the structure of the text--viz. that two constituents with a certain content are to be related to each other in the SDRS for the discourse. For (6.a-c): > Continuation(a, ~) (John-take-aspirin(a) & John-sick(~) & Explanation(a, ~) (John-take-overdose-of-aspirin(a) & John-sick(~) & Result(a, ~) For Example (8): > Continuation(a, ~) (Eat-dinner(a) & have quenelles(~) & Part of(Me(a), Me(~» (Eat-dinner(a) & have duck(~) & Part of(Me(a), Me(~» (Eat-dinner(a) & drink wine(~) & Part of(Me(a), Me(~»

General Operations Needed to State the Updating Rules: To define updating precisely, we need some general operations on SDRSs. We will want to add constituents to SDRSs as well as merge SDRSs together--this is the function of the operation add*. Also we need a contraction operation for SDRSs, because sometimes updating forces us to revise the structure built up by previous processing. a \\ ~ is the SDRS that results when the constituents and conditions in ~ or elements of ~ are removed from a; if al> ... , an are constituents of ~, then ~ ~ {al> ... , an lis the SDRS that results from removing aI, ... , an from ~ as well as all conditions involving al> ... , an. Finally I define a substitution operation: R#(a, y, ~) is the set of those conditions that are derived from a condition in ~ containing y by substituting uniformly a for y. DEFINITION: Let Con and Con' range over sets of discourse relations. Ifais a single DRS, then a add*[~, Con'] = <{a,~}, {R(a, ~)}>.

If a

= <{ al> ... , an}, Con> is an SDRS, then

add*[~, Con'] = <{al> ... , an, ~}, Con UCon'>. DEFINITION: If a = [A, Con] and ~ = [B, Con'] are constituents, then

a

(3\\0.:= . DEFINITION: Suppose ~S; Ie Kj. Then ~~ [al> ... , an] = ~ \\ [{al> ... , an}, ({R(a;, y): 1::;; is; n & y
E

Conw}.

Topic-based Updating: Topic-based updating exploits topics. But also important for topic-based updating is the notion of a subtopic. I will use the following, naive definition of subtopics: t is a SUbtopic of t', which I'll write as t Crt', just in case the interpreter's knowledge base KB entails that t --> t', or the text establishes independently a discourse relation like summary or elaboration that entails a subordination of topic. Recall that for me topics are propositions, or more specifically DRSs, so such a definition makes sense. I'll say that t ~ t' iff t = t' or t c't t'. I will assume that when there is no explicitly given topic for [3, topic(~) = ¢ and for all t ¢ C,; t. In the definition below, I abbreviate 'Elaboration(a, ~)' as 'E(a, ~)'; R ranges over discourse relations: DEFINITION (Topic-Based Update) Suppose we have decided to update an open constituent ~ of the SDRS Kj with Kj+l using the topic-based-updating to get the

updated SDRS lK:j+l. Let W be that constituent (if it exists) such that ~ < WS; tc Kj. For (i)-(iv), suppose that Kj ¢. Then: (i) Suppose that already topic(~) < Wand Kj+ 1 ~'t topic(~). Then lK:j+ 1= lK:j,

*"

1

m .j i ~

304

CHAPTER SEVEN

I

f

I

It

II

1[1

r

II II il I

d 11

Ii

Ii 11

II fl

]i

Ii Ii q li

except that W is replaced with: (W\\P) add*[p add* Kj+l, Contination(last(p), Kj+l)] ]. (ii) Suppose topic(P) = Kj+l. Then Kj+l= Kj, except that W is replaced with: (W - topic(P)) add* [{Kj+l}, {Kj+l • P, E(Kj+l, P)} U R#(Kj+l, topic(P))]. (iii) Suppose not topic(P) < W and P has no implicitly represented topic but there is a 8 such that topic (P) S 8 and Kj+l S 8. Then Kj+l= Kj except that W is replaced by (W - P) add*[ {8, y}, {8.0. y, E(8, y)} U R#(8, P)], where y = [ P add* [Kj+l, Continuation(last(p), Kj+l)] ]. (iv) Suppose topic(P) < Wand P has no implicitly represented topic, but it is not the case that Kj+l ~ topic(P), but for some 8, topic(P) ~ 8, Kj+l S't 8 and 8 S topic(W). Then Kj+l= Kj. except that Wis replaced wIth: (W - [p, topic(P)]) add* [{ 8, y}, {8.0. y, E(8, y)} U R#(8, topic P)], where y = [P add [Kj+l, Continuation(last(p), Kj+l)]] . (v) Suppose P has an implicitly represented topic in Kj- Then Kj+ 1= Kj, except that W is replaced with: (PO - P) add* [(topic(P), p, Kj+l}, [{topic(P) ,p, E(topic(P), P), Continuation(topic(P), Kj+l)} U R#( topic(P), P)]]. (vi) Suppose Kj = ¢, then Kj+l = Kj+l. FACT: (Continue(a, a') & a, a' < y)

->

3p Elaboration(p, y)

Definition(Updating using Non-structural Relations): Suppose that with Kj+l is associated a discourse relation R other than Continuation or Elaboration and whose other argument is some constituent p:::; tc K j • Then in updating the SDRS Kj with Kj+l to get the SDRS Kj +1: i) Suppose P < a:::; Ie Kj- Then Kj+l= Kj, except that a is replaced by: a Add*[ K~+J, R(P, !S+I)]. ii) if P = Kj, lIrj+l = <{topic(P), P, Kj+l}, {R(topic(P), Kj+l)' topic(P).u. P, Elaboration(topic(P), P)} >.

,.

A THEORY OF DISCOURSE STRUCTURE

r·"

305

For any a the leaves of the embedding tree of a contain no complex conditions.

FACT:

matrix condition of a constituent 8 in 8' is the condition or operator in 8' of which 8 is an argument or term. DEFINITION: 't* = , is a modified embedding tree of an embedding tree 't = iff (i) A * SA, (ii) root('t*) = root('t), (iii) d-6 A * S d-6 A, (iv) Vx (x is a leaf of 't* iff x is a leaf of 't).

DEFINITION: The

Themes and Polarities To define a theme of a constituent, note that the most important part of a simple constituent 8--Le., a constituent without d-subordinate constituents--is the condition derived from the main verb or main verbs of the text that yields 8. If we take away the conditions contributed by the verb's arguments, we have the constituent's skeleton--it is a DRS containing just those conditions introduced by the main verbs and their logical structure. We may apply the same thinning procedure to matrix conditions of constituents in modified embedding conditions where those conditions are complex. Note that the skeleton of an atomic condition cp is just cpo We also need a generalized part of relation, c*. I will symbolize part of as C. DEFINITION: If K is simple, then a c* P iff aC p. If K is complex, then a c* P iff a C P and for any 8 d-< a there is a y d-< P such that 8 c* y. DEFINITION: If 8 is a simple constituent, a theme of 8 is any DRS K such that the skeleton(8) c Kc 8. If 8 is not simple, a theme of 8 is any DRS K such that for any y d-< 8, the skeleton(matrix(y)) c* K c 8. DEFINITION: Let 't = and't' = be two trees. 1'}: 't -> 't' is a tree isomorphism from A onto A' iff 1'} is a bijection and Va, PEA (a d-6 P iff 1'}(a) d~ 1'}(P). DEFINITION: Polarity Assignment with respect to a Tree Isomorphism and a Pair of

7.4 Constituent Revision Embedding Trees and Tree Isomorphisms DEFINITION: For any constituent a d-subordinate to P in some SDRS K the embedding tree ofP down to a is the tree , where B = {x: x dsubordinate to P and a d-subordinate to x} and d-6 is the partial ordering determined by the d-subordination relation on B.

a the embedding tree of a = , where A = {x: x is d-subordinate to a} and d-6 is the partial ordering determined by dsubordination on A.

DEFINITION: For any constituent

Embedding trees are finite and well-founded, so we may without difficulty speak of the leaves of a tree (it's minimal elements).

Themes Let 1'}: 't -> 't' be a tree isomorphism and suppose 8 < 'to (a) If there are conditions P and P' and some substitution of discourse referents ':P such that (i) P is a theme of 8, (ii) P'(':P) is theme of 1'}(8), (iii) P is plausibly equivalent to P'(':P) or one is a subsort of the other in the background knowledge base, then: polarity(8, P) = polarity(1'}(8), P'). (b) If there are conditions P and P' and some substitution of discourse referents ':P such that (i) P is a theme of 8; (ii) P'('¥) is a theme of 1'}(8); (iii) P and P'(':P) are plausibly complementary, then: polarity(8, P) # polarity(1'}(8), P'). Remark: There are several degrees of freedom to the definition of polarity assignment. First, two constituents may have several themes; some may suggest

CHAPTER SEVEN

306

parallelism; some may suggest contrast. Since themes can be more or l~ss comprehensive, and more or less close, the definition allo",:s for degrees of polanty assignment. Some themes cover much more of the constltuent than others; some themes are very close in the sense that under a substitution of discourse referents, the two themes are identical and the themes subsume each other. The closer the themes are to each other, the stronger the assignment of same polarity. The strongest same polarity assignment to ex and ~ occurs when we have two identical themes for ex and~. Similarly with contrasting polarities, some are clearly much more striking than others. What the interpreter believes the speaker may have intended appears to make some contrasts and commonalities much more salient than others. Finally, plausibility is a matter of context; certain contrasts ma~ be implausible only because a discourse suggests others that are much more plaUSIble. These remarks suggest that a nonmonotonic logic might be appropriate to determine polarities.45 Proto parallelism with respect to 'I'l-: For ex, ~ < K o, Proto-Parallel(ex, in K ° with respect to 'I'l- iff 3't#, 't* such that 'I'l-:'t# ..... 't* is a tree isomorphism and: (i) 't# is a subtree of a modified embedding tree of ~ in Ko; (ii) 't* is a subtree of a modified embedding tree of ex in Ko; (iii) root('t*) = root('t); (iv) ¢c {O: ois aleafof't#} S {O: ois aleafof't}; (v) for any node 0 of't#, there are themes P and P' such that polarity('I'l-(o), P) = polarity(O, P').

DEFINITION: ~)

Contrast with respect to 'I'l-: For ex, ~ < K o, Proto-Contrast(ex,~) in Ko with respect to 't'} iff 3't#, 't* such that 'I'l-:'t# -+ 't* is a tree isomorphism and: (i) 't# is a subtree of a modified embedding tree of ~ in Ko; (ii) 't* is a subtree of a modified embedding tree of ex in Ko; (iii) root('t*) = root('t); (iv) ¢ c {O : 0 is a leaf of 't#} S {O: 0 is a leaf of't}; (v) there are some nodes 0 of't# and there are themes P and P' of 0 and 'I'l-(o) such that polarity(O, P) polarity('I'l-(O), P'), and for the rest of the nodes y of 't#, there are themes P and P' such that polarity(y, P) = polarity('I'l-(y), P').

DEFINITION: Proto

"*

DEFINITION: Parallel(ex,~)

Parallel(ex,

~).

DEFINITION: Contrast(ex,~)

with respect to'l'l- in Ko iff Open(ex, ~) in Ko & Protowith respect to 't'} in Ko iff Open(ex,~) in Ko & Proto-

Contrast(ex, ~). DEFINITION: Parallel( ex, ~) in Ko iff 3't'}(parallel(ex, ~) with respect to 'I'l- in Ko ). DEFINITION: Contrast(ex,~) in Ko iff 3'1'l-(Contrast(ex, ~) with respect to 'I'l- in Ko).

A THEORY OF DISCOURSE STRUCTURE

307

Parallel*(ex, ~) in Ko iff there are y, 0 such that ex ~ tc Y& ~ ~ Ie 0 & there is a discourse relation R such that R(y, 0) & there are ME tree 'ty and 'to s for y and 0 & there is a tree isomorphism 't'}: 'ty -+ 'to such that Proto-Parallel(ex, ~) with respect to 'I'l-). DEFINITION: Contrast*(ex, ~) in Ko iff there are y, 0 such that ex ~ Ie Y& ~ ~ tc 0 & there is a discourse relation R such that R(y, 0) & there are ME trees 'ty and 'to for y and 0 & there is a tree isomorphism 't'}: 'ty -+ 'to such that Proto-Contrast(ex, ~) with respect to 't'}. DEFINITION:

These definitions reflect the scope and the degree of the parallelism or contrast relation. A parallelism or contrast relation may be stronger or weaker depending on the degree of polarity assigned to the various nodes by the choice of maximal themes. The degree of the parallelism or contrast relation depends on the ease or degree to which the nodes can be assigned polarities. I will assume that plausible parallelisms and contrasts can be assigned a ranking such that the constraint below holds. Where 't* and 't# are subtrees of modified embedding trees of constituents ex and~, 't'}i: 't* -> 't# yields a maximally plausible polarity assignment compatible with Proto-Parallel(ex, ~) (Proto-Contrast(ex, ~)) iff for any'l'l-j if Proto-Parallel(ex, ~) (Contrast(ex, ~)) in virtue of 'I'l-i and 'I'l-j' then (i) for each leaf node 0, 0 and 'I'l-i(O) have themes P and P' such that for any themes of 0 and 'I'l-j(O) Pj and P/ are such that P entails Pj and P' entails P/ . (ii) for each non-leaf node 0 that dominates leaf nodes Vb ••• , Vm of the embedding tree of~, the polarity assignment between 0 and 'I'l-i(O) for P and P' is at least as plausible as the polarity assignment between 0' and 'I'l-j(O') for Pj and P/, where 0' also dominates VI> ••• , V m •

DEFINITION:

Suppose that for constituents ex and ~ there are more than one tree isomorphism that define Proto-Parallel(ex, ~) (Proto-Contrast(ex, ~)). Then one is defined through a maximally plausible polarity assignment.

MAXIMIZATION CONS1RAINT:

Another element in the definitions accounting for degrees of parallelism and contrast is that the subtree 't# used to define Proto Parallel or Proto Contrast may cover more or less of the modified embedding tree 'to The more it covers, the wider the scope of the parallelism or contrast relation in relation to ~; the less it covers the narrower the scope. Notice that if Parallel* or Contrast* holds of ex and ~ and ex~ tc Y& ~~ tc y, then the relevant tree isomorphism must be defined for the nodes corresponding to ex and ~. Thus, Parallel* and Contrast* have also maximal scope elements in a given tree. A maximal scope element ~ for a relation Parallel* (Contrast*) defined on a pair of constituents ex, ex' with respect to 't'} is a constituent such that for any

DEFINITION:

308

CHAPTER SEVEN

A THEORY OF DISCOURSE STRUCTURE

S::;; tc ~::;; a' there is a y::;; tc a such that Parallel*(y, S) (Contrast*(y, S» in virtue of t't and for every y such that a ~tc S' > ~ there is no y::;; tc a' such that Parallel*(y, S') (Contrast*(y, S'» in virtue of t't. DEFINITION: A Parallel* (Contrast*) relation on a and ~ is stronger than another just in case it is defined through a more plausible polarity assignment over more of the original embedding trees of a and ~. FACT: There is a partial ordering of all Parallel* (Contrast*) relations between any two constituents a and ~.

, DEFINITION: Suppose cp is a parallelism (contrast) particle. Then too(S) (but(S» is satisfied in an SDRS Jl{ just in case there is some constituent y such that Parallel*(y, 0) (Contrast*(y, 0» in Jl{.

Revision of Constituents using Parallelism and Contrast and SDRS Update Axioms for I\. Let a, and ~ be SDRS constituents. (J\ 1) (a J\ ~) J\ Y= a J\ (~ J\ y) = a J\ ~ J\ Y (J\ 2) a J\ a = a (J\ 3) a J\ ~ = < {a, ~}, ¢ >. (J\ yields a constituent that corresponds to sum). (J\ 4) If a in Con(lI{o); K is the current constituent in Jl{o, and there is a 0 ::;; tc K, y::;; tc ~ and t't such that Parallel*(y, 0) with respect to t't and 0 is a designated or maximal scope element of Parallel* on yand 0 in virtue of t't. Then: Constituent-Revision(lI{o, K) = Jl{o[a!K], where (i) a = ,

309

(ii) ConK* is the result of replacing in ConK each occurrence of n with an occurrence of n' for each node n of't(o) and where, (a) if n is a leaf node and an abstract discourse referent, n' = n J\ t't(n) (b) if n is the maximal node in 't(S), n' = n J\ t't(n) Rule for Constituent Revision Using Contrast: Suppose <~, K> in Con(lI{o); K is the current constituent in Jl{o, and there is a 0::;; tc K, y::;; tc ~ and t't such that Contrast*(y, 0) with respect to t't and S is a maximal or designated scope element for Contrast* on yand S in virtue of t't. Then: Constituent-Revision(lI{o, K) = Jl{o[aI K], where (i) a = (ii) ConK* is the result of replacing in ConK each occurrence of n with an occurrence of n' for each node n of't(S) and where n' is defined as follows: (a) if n is a leaf node and an abstract discourse referent, n' = n J\ t't(n); n' = n otherwise. (b) If n is the maximal node in 'to and the matrix conditions cp(x) and cp'(y) of t't(n) and n have the same argument structure and polarity(n) =F polarity(t'}{n», then: n' = f[ni'/n] & -,t't(n)[cp,[x/y)/cp], if this is consistent; n' = n J\ -,Onlyt't(n), otherwise. DEFINITION: SDRS-UPDATE(ex, ~) = {ex': there is a constituent y < a such that y is a possible attachment point in ex and a' = A TT ACH( ex, y, ConstituentRevision(y, ~». 1Fllfl!1er, it has often not been <;lear what data or ~acts studies of discourse structure are attempting to explam; everyone knows that discourse structure IS out there but there is often a dearth of material that might distinguish between one way of looking at discourse structure and another. Anaphora offers a f~us for the ~tudy of discourse s1!Ucture; it is certainly an area in which discourse structure makes an Important difference. It also POInts to a need for a discourse structure of a certain kind. 2See Allen (1987). 3See Polanyi (1988), Polanyi and Scha (1984). 40ne possible exception to this claim would be fictional individuals. Characters in a fairy tale or a novel '!light, some would argue, have their properties determined wholly by the text at least in the follOWIng sense: wh!lt. was. asserted about such individuals in the text constituted all of the InformatIOn ~bout. therr IdentIty. But this sense of being determined by the text is still distinct from what I have In mmd for abstract objects. The problem with abstract Objects is that the structural properties of the text, its thematic ana rhetorical organization, may determIne which abstract objects are being talked about. This is never true of fictional individuals. 5S omew hat doctored from an article in the New York Times about the launch of the Discovery on September 29, 1988. 6Notice t~at so alsosignals art anaphoric relation, between the VP of the previous sentence and the ~honologlcally null VP node In the 5th sentence. More on this in chapter 9. In postulating such a discourse structure for (3), again I am following the ideas of Mann and Thompson, but also of Fox (1987) as well as earher work by Reichman (1985) and Grosz and Sidner (1985). The repetition of the words in the fourth sentence in their terminology is to effect a pop back to the theme of the discourse. 8Cf for ins~nce Grosz (1977), Joshi, and Weinstein (1981). The thematic and rhetorical organization may determIne more than one such structure. But I shall only use one in my analyses. 9S ome of these areas have received much attention in artificial intelligence research. See (Grosz P977), Altennann (1982), Hobbs (1985), and Grosz and Sidner (1985». °This is not to preclude that there aren't anaphors to bits of text or speech acts or other entities

.-----------------_._----------

311

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A THEORY OF DISCOURSE STRUCTURE

related to but distinct from contents. See for instance Webber (1988). llFor example see Mann and Thompson (1987). 12 Here is a first shot for instance at a working definition of the relation, comment: one proposition or semantic content p, for instance, is a Comment on another q just in case p entails for some agent x and attitude B, B(x, Q). 13The DR-theoretic union or update of K and K' is defined in chapter 2 as : K l"i K' = <(UK U UK')' (ConK U ConK'» 141 am indebted to discussions with Kathy bahlgren and Barbara Partee who persuaded me that this was the best way to go. 15See Gros.z & Sidner (1986), Polanyi (1985), Polyani & Scha (1984), Polanyi (1985) (1988), Scha and PolanYI (1988), and Dahlgren (1989). 16For definitions of these relations, see Lockman & Klapholtz (1980), Klapholtz and Lockman (1983), Matthiessen & Thompson (1986), Mann and Thompson (1987), Hobbs (1985), Reichman (1985), Cohen (1984), Fox (1987), Dahlgren (1988). Certain proposals indicate that there may even be a hope of using the various sorts of clues in a program to discover with a reasonable probability of success the underlying rhetorical relations. Wingnart (1986) has suggested using a blackboard architecture with various types of clues to figure out the rhetorical structure. Dahlgren (1989) has suggested that a combinatIOn of using tense mformation, world-knowledge, clue words and other factors might succeed in being a reliable predictor. But to examine details of proposals in this area would require a large world kriowledge database, which is beyond the scope of this book. 17There seems to be considerable debate about what are the appropriate primitives for texts. But this ~i11 probably vary with genre. Commentary newspaper texts make use of the relations that I have Cited. Narrative for instance is not often found. One of the difficulties, however, is that without a clear semantics, it is often impossible to decide what the primitives are: one person's elaboration may be another's summary. 18 See for ~xaml!le Alterman (1982) and Hobbs (1985), Mann & Thompson (1986, 1987). For the use of a qUite different strategy see Garnham (1990) who reports on some jomt work with Mason. Garnham believes that interpreters' recognition of complex, stereotypical sequences of events in texts are almost completely responsible for their segmentation. For Garnham there are no discourse relations as such, independent of these stereotypical event types. Segmentation approaches based on story-lines or complex event types go back to earlier work in AI, such as that by Scbank and Abelson

321 owe this point to Tanya Reinhart. 33Discourse pops have been discussed frequently; see for instance Fox (1984, 1987), Mann and Thompson (1987), Polanyi (1988), and Grosz and Sidner (1985). A similar example to the one above is also worked out in detail in Lascarides and Asher (1991), although there the counterpart of the SDRS updating strategy is very simple. We were interested in very Simple temporal anaphora in that paper and so tlie full complexities ofSDRSs ware not needed. They are needed to handle pronominal anaphora and VP ellipsis. 34See Lascarides and Asher (1991) for details on the axioms used in this case. 35This reflects procedures for building discourse structures employed for instance by Dahlgren (1988), Fox (1987), and Mann and Thompson (1987). But this principle is not recognized as such, except by Polanyi (1988), for whom discourse structure is not guidea just by content but rather by difference in content with the previous segment. The particular statement here enables us like Scha and Polanyi to have a discourse structure constructed on line. For a discussion of this point, see Dahlgren (1989). 361 assume here for simplicity that there are only two place rhetorical relations. 37This discourse simplifies an actual story in the Wall Street Journal. 38S ee Lascarides and Asher (1991). 39S ee Mann and Thompson (1987), who acknowledge these as discourse relations, or Polanyi ~1988), who uses parallelism to build up lists or topic chain segments. Oaf course, context can do wonders for making otherwise crazy pairs get sensible polarity assignments. 41For more on this see below. 42The use of a knowledge base in defining discourse relations is already familiar from the discussion of Elaboration and Continuation. 43Notice that since we are using relations other than Elaboration or Continuation, no topic need be introduced to dominate ~. k2 is the implicit topic of~. ~here is a real range of detail in the literature. Grosz and Sidner postulate only two relations, while Mann and Thompson postulate a large number (around twenty or so). I'll have more than two, but I am certainly not committed to such a large number-- at least not unless forced by the data. The limited set of examples that I have looked at and come up with don't appeal to a large array of discourse relations. 450ne might set this up as follows. Rules whose antecedents paired nodes a and ~ under a tree isomorphIsm would defeasibly imply a certain polarity assignment (or none at all). This assignment again could be overridden by more specific, contextually supplied information.

310

P977).

~he term coherence relation is due to Hobbs (1979, 1985). 20]: owe this observation to K. Dahlgren. 21A discussion of this example can be found in Lascarides and Asher (1991). 22The pluperfect does not always have this effect. Consider for instance, John fell. Mary pushed him. John fell. Mary had pushed him. Here bo.th texts allow for th~ constituent introduced by th.e second clause to serve as an explanation ~f the frrst. In languages like French, however, the chOIce of tense does seem to be the deciding fif,ure. In English, chOIce of tense and verb aspect, seem to be decisive. 2 It should be noted that the context sensitive analysis of the attitudes in DRT seems well suited to pursue Achinstein's pragmatic view of explanation, on which an appropriate answer to a why ~uestion depends on who is doing the asking. 4A similar notion of domination finds its way into knowledge bases in isa-hierarchies, for instance. The presence of such dominances may be essential for efficient reasoning with large amounts of information. Certainly many knowledge-based systems employ various forms of reasoning based on some sort of dominance principle. 25According to Garnham (1990), topic structure depends upon knowledge of the subject matter. 26See for instance studies by Dahlgren and Lord (1990). 27This occur in discourses with "resumptions" (polanyi 1988) or "discourse return pops" (Mann and Thomps~m 1986, Fox 1987); texts (3) and (4) in the introductIOn of this chapter provide examples of resumptions. 28 See for instance Dahlgren and Lord's (1990) discussion of Comment and Evaluation in Wall Street Journal articles. 29S uch work has been pursued in a computational setting by Cohen (1984). 30rhese examples come from Lascarides and Asher (1991). 31See .Asher and Morreau (1990, 1991) for a development of the non-monotonic logic. See Lascandes and Asher (1991) for a discussion of the various axioms and the application of the nonmonotonic formalism to a simpler sort of discourse structnre than the one developed here. One could p!lrsue th~ ~sk of inference .of 4iscourse relations in a dif~erent setting-- viz., prioritized crrcumscnptlon or default logiC With ordered defaults. For adlscussion of the > formalism in comparison to other candidates, see Asher and Morreau (1991) and Lascarides and Asher (1991).

ANAPHORA AND DISCOURSE STRUCTURE CHAPTER EIGHT accessibility constraint needs to be restated to take account of SDRS structure. This is easily done:

APPLYING THE THEORY OF DISCOURSE STRUCTURE TO THE ANAPHORIC PHENOMENA

The last chapter developed SDRS theory, a theory of discourse structure using DR-theoretic structures for the purpose of imposing constraints on anaphora. I elaborated several phases of SDRS construction: determining basic constituents, constraints on attachment, rules for attachment, and rules for constituent revision. This chapter introduces the constraints on anaphora, in p~icular abstract. entity anaphora, and investigates the predictions of the theory. I wIll wO:k o.ut a vanety of examples of abstract entity anaphora and look at two other apphc.atlOns Of. SDRS theory: event anaphora and anaphoric relations between abstract objects of dIfferent types. l

1. CONSTRAINTS ON ABSTRACT OBJECT ANAPHORA DERIVED FROM

AN SDRS: AVAILABILITY AND WELL-FOUNDEDNESS My task here is to add two new constraints, availability and wellfoundedness, to the DRT account of anaphora. These exploit SDRS structure and will supplement accessibility and the intrasentential syntactic constraints. Here is a table of the various constraints on anaphora in my account, as well as their level of application: Type of Constraint

Constraint Name

Level at which defmed

Syntactic Constraints

Disjoint Reference grammatical features

Syntactic Structure

Semantic Constraints

Accessibility

DRS

Discourse Constraints

Availability Wellfoundedness

Segmented DRS (SDRS)

While SDRS theory is designed to mesh with the general DRT analysis of anaphora, developed in chapter 6, the additional level of structure in SI?RS theory because of SDRSs forces us to modify that approach of anaphora resolutIOn. SDRS construction is the output of the DRT interpretive component and that anaphora resolution takes place at the level of SDRS construction. The syntactic, constraints on anaphora resolution are intrasentential and so do not need any generalization. The 312

DEFINITION: x is SDRS accessible to y in][C iff x

E

UK, Y E UK', K, K'
& x is accessible to y in ~][C. Only a discourse referent or structure that meets the syntactic constraints, is accessible and is available is one that can be identified with a discourse referent introduced by an anaphoric pronoun. The identification will use the relation'" on which a discourse referent is characterized by a DR-theoretic structure. With the possibility of referring anaphorically to SDRSs, we now admit the possibility that a discourse referent may be characterized by an SDRS. Availability: Availability functions similarly to the accessibility constraint in D RT discussed in chapter 2. Accessibility is a constraint that is defined relative to the configurational (and truth conditional) properties of DRSs and their constituent conditions. Availability exploits the hierarchical structure of SDRSs. Availability is an absolute constraint, like accessibility and unlike salience, on the felicity of discourses. Principle of Availability: A structure or discourse referent e may be felicitously identified or otherwise related to a discourse referent z in an SDRS ][C during the process of anaphora resolution, only if e is available to z in ][C. The constraint on abstract object anaphora (with pronouns) is roughly the following: only a discourse related constituent in ][C or the current constituent of ][C and its discourse referents or subDRSs are available as antecedents. Here is the full definition of availability. Let e range over abstract object discourse referents, or DRtheoretic structures, and let R range over discourse relations. DEFINITION (Availability): Suppose that z is introduced by an anaphoric pronoun

into UK, K~ ~~tc][C. Suppose further there is a constituent a and a discourse referent or structure e such that: (a) either ....,::Jll~ ][c::Jy (a. y E Conll and e is introduced in a or e = a); or (b) ::Jll~ ][c::Jy (a. y E Conll) and e is introduced in a or e = a Add* y. Then e is available to z in ][C iff R(a, ~) or a = ~. Given the relation of Topic * defined in chapter 7, the notion of availability is similar to Webber's (1991) idea that the acceptable anaphoric antecedents must be introduced by the textual elements on the right frontier of a discourse structure. Availability predicts that the topic of any open constituent or any d-free and open constituent will yield available anaphoric antecedents. Since Webber does not specify what those elements are especially for nodes dominating a complex of other nodes, however, it is difficult to say in detail what the differences between the right frontier idea and

ANAPHORA AND DISCOURSE STRUCTURE availability are. Open constituents alone, according to availability, will not yield available antecedents. This is all to the good, for otherwise we would be able to refer to any constituent in an open constituent, and this would violate the right frontier observation made by Polanyi and Webber. It is precisely to deal with the anaphoric potential of complex constituents that I restrict discourse relations to attach only to dfree and open constituents or implicit topics. The constraint of availability together with the procedures for constructing SDRSs defined earlier are intended to capture the effects of discourse structure on abstract object anaphora, and proposition anaphora in particular, like those noted in examples (1), (2) and (3) of chapter 7. I will test this definition in later sections. But it is worthwhile to make some connections with what is known about discourse effects on individual anaphora. While it has long been recognized that discourse segmentation may aid the reader in determining the intended antecedent of an anaphoric pronoun,2 research to date has almost exclusively concerned itself with individual anaphora alone. Fox (1987) has shown that discourse structure places a limit on the list of potential, individual antecedents by restricting search to the "active" or "controlling" discourse segment to use Mann and Thompson's terminology.3 The active segment is the one to which one attaches a new constituent, and the controlling segment is roughly the topic segment. In our new DR-theoretic terminology, this means that a discourse referent may find an antecedent either in a constituent that is connected by a discourse relation to the current constituent or in a constituent that is the topic of the current constituent. But the partial ordering induced on discourse structure is just Topic*. So availability together with the account of discourse structure gives us the findings of Fox (1987) and also predicts that one can find antecedents within the current constituent and also in higher topic statements. Both of these seem necessary additions. 4

,;

1

1 ',",,'.,1

"1

,I

; I, ,I i I ,I

Well-Foundedness: By taking DRSs and even SDRSs themselves to be antecedents, abstract object anaphora makes possible a variety of forms of selfreference, with all the well-known, accompanying, logical difficulties. Interestingly, self-reference does not seem to be possible with abstract object anaphora in which the pronouns that or it are used or where null anaphors are present as in VP ellipsis. This implies that abstract entity anaphora and its interpretation imposes a very general constraint on discourse structure, which has not been noticed in previous work. The way I have set up a SDRS and the principles of summation allow a discourse referent introduced by a pronoun to be identified with the constituent that characterizes it. Suppose that in processing a pronoun, an abstract object discourse referent is introduced in the following DRS. (Ko)

k

I

I Now according to the availability constraint, if we have some ex such that K is d-

'I

315

subordinate to ex and if S is introduced in ex, then we may identify ex with S. Suppose that ex is an SDRS which contains Ko as a constituent. Then nothing stops us from characterizing k with the very same structure in which k is introduced: k

k '"

I----=k'----I

..~'",1kI ~ There is something quite peculiar about this structure. The anaphoric resolution routine would yield, in an attempt to resolve the anaphoric equations, an infinitely descending chain of subDRSs, each one contained as part of a complex condition of the next. Such a DRS has non-contradictory embedding conditions, though a proper embedding does require the use of an embedding function with an infinite domain. 5 Nevertheless, such infinite structures appear to be unintelligible when one tries to express them in a natural language using anaphoric pronouns to refer to abstract objects. The following sentences all tum out on my analysis of anaphora to yield such infmitary structures. (La) (I.b) (I.c) (I.d) (I.e) (I.f)

*John [believes that Mary does ¢i]i. *John believes that [Mary believes thatil. *John [forced Fred to do itJi *John wants [for Mary to believe that i (iti)l. *[Sam agreed ¢Ji. * [Mary yelled at me. Thati is really true.]i

A general constraint on abstract entity anaphora, well-foundedness, forbids this sort of self-reference and infinitary structures. Well-foundedness: Suppose Z E UK. Then for any constituent 13 such that K is either a constituent of 13 or a subconstituent of 13, Z may not be identified with 13 by the anaphora resolution process. Well-foundedness prevents a non well-founded structure from resulting from the process of anaphora resolution. The data for anaphors like that, it and the null elements of VP ellipsis indicate that a constraint like this holds. Well-foundedness holds for all abstract entity anaphors that I know of, including null complement anaphors (7.d) and V' and VP ellipses. It implies a syntactic constraint commonly applied to VP ellipsis--namely the constraint that the VPs not C-command each other. But it is much more general than this syntactic constraint. Well-foundedness dictates certain constraints on SDRS updating too. It cannot be

ANAPHORA AND DISCOURSE STRUCTURE

CHAPTER EIGHT the case that a newly fonned DRS K is entered into K and for some Z E UK, Z is identified with K during anaphora resolution. That would violate well-foundeness. Perhaps the contrapositive is a bit more perspicuous: if Z E UK, then Z = /3, only if K is not a subconstituent of /3. This provides an important constraint on the configuration of SDRSs and precludes certain attachments of new material. Wellfoundedness also explains the incompatibility of Continuation and discourse relations like Elaboration, Result, Explanation or Comment: insofar as these relations say something about a constituent's content, they cannot be part of that content. Here is an example from the Financial Times that shows the constraints on anaphora at work: (2)

Moscow is to broaden collaboration with Fiat by making a version of Fiat's Panda small car instead of a vehicle of its own design. This means Fiat may be involved in all three phases of Soviet plans for raising output at the Yalabuga plant, 1,000 miles south-east of Moscow, by 900,000 units by the end of the 1990s.

The boldfaced pronoun introduces a discourse referent z of abstract type (either factlike or proposition-like). The discourse structure of (2) is quite simple, consisting of two constituents--call them kJ and k 2. k 2, introduced by the second sentence, contains a condition on z that indicates that it is giving a Result or Consequence of another constituent's obtaining--presumably the available constituent or discourse referent that is assigned to z. There is only one constituent in the structure, kJ, and so k2 is attached to kJ by the relation Result. kJ is clearly available to z and so we have the identification of z with k J. Well-foundedness forbids z being identified with the SDRS containing kJ and k2' which is an available constituent as well. The well-foundedness constraint precludes self-referential propositions that would come about from a particular way of filling in the equations introduced by anaphoric pronouns. But it applies only to equations constructed in anaphora resolution, and there are other ways of forming self-referential propositions: (3.a)

There is a proposition that says of itself that it is not true.

p, s proposition(p ) s-say (p, z z""p

)

'~ true(z) Note that while the DRS for (3.a) above asserts the existence of a self-referential proposition and it has an anaphoric link, it does not violate well-foundedness. There are also other ways of constructing self-referential propositions that make use of the

317

demonstrative adjective--viz. (3.b-c). (3.b) (3.c) (3.d)

This sentence is false. This claim is true. This is false.

The well-foundedness constraint does not rule out the self-referential deictic interpretations of the complex demonstratives in (3.b-c); deictic interpretations are accomplished by means of external anchors, not links between discourse referents and DR-theoretic structures within a DRS. This also applies to demonstrative uses of pronouns, as in the case in which someone points to (3.d) written on the blackboard and says: This is false. Again, it is the external anchors not some use of the anaphoric equations that capture this deictic referential use. I will analyze such uses in more detail in chapter 10, when I discuss self-reference, and I will argue that these complex demonstratives are used deictically to pick out in the non-verbal context a proposition, by picking out a more concrete object like the sentence or utterance used to express the proposition. Event anaphora follows the constraint of well-foundedness as sell. One cannot use the pronouns that or it to refer to the event in which the event discourse referent introduced by the pronoun plays a part. Consider the following examples: (4.a) (4.b)

That was fun. This is fun.

In principle one might identify the discourse referent introduced by the pronoun with the state introduced by the inflection node for the whole sentence given the semantic and syntactic constraints of accessibility and disjoint reference, the latter of which applies only to NPs. Nevertheless, this identification seems to be impossible, or rather unintelligible. Even this, which for propositional contexts has a deictic selfreferential reading cannot refer to the state in which one predicates being fun of this. It seems that the well-foundedness constraint applies to all uses of pronouns. The DRS construction algorithm or group fonnation operations have explicitly demarcated all the propositional antecedents of anaphors discussed so far. But as examples (1), (2) and (3) from the beginning of chapter 7 suggest, there are many antecedents for abstract entity anaphora that are not explicitly demarcated by the DRS construction algorithm. A study of the proposition anaphora in these examples suggests that certain summation and separation principles operate on the propositional content expressed by a text. These principles of separation and summation, stated in chapter 7, yield new constituents of segmented DRSs that can act as anaphoric antecedents. These summation and separation principles serve as comprehension axioms for propositions; they state what propositions exist in a given discourse context. Availability and accessibility constrain which of these propositions can be anaphorically related to a discourse referent in a particular discourse context. In this section I will investigate the interaction of the principles of SDRS construction and

~---~~~~~-----~:='::"~~~---~--~~----.-~~~~----------------------------

318

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ANAPHORA AND DISCOURSE STRUCTURE

availability within anaphora in more detail. I will also investigate another type of constituent revision--topic revision.

Now we must decide where we should put KS, the DRS for the last sentence. Ks involves an evaluation, so it should be attached to some open and d-free constituent by means of Commentary. Since the state it describes involves a different agent from any of those previously mentioned, it cannot be entered simply as a constituent in K. 1. Thus, there are two possible attachments for KS. We may take the other term of the Commentary relation to be Kl--i.e. the whole story so far; or we may take it to be K4. These are the only two open constituents. In the latter case KS is a comment or evaluation on the deployment of the satellite; together with K4, Ks will be constituents of a new SDRS K2 < K 1. Well-foundedness then precludes taking either K 2, KS or Kl as antecedents for the discourse referent x introduced by the pronoun in KS. If KS is attached to Klo then only KS or Kl /\ Kl will be available antecedents according to the definition of availability. Well-foundedness precludes the whole SDRS for (1) as an anaphoric antecedent. So on the low attachment of KS to K4, we predict that only K4 is an available antecedent; on the high attachment to Klo only Kl /\ Kl is an available antecedent. Let u~ now compare the SDRS and predictions made for example (2) of chapter 7, repeated below as (6):

2. SOME EXAMPLES OF PROPOSITION ANAPHORA

To test the constraints articulated above, I begin with some examples that motivated my account of discourse structure and DRT to show how the m~chinery deals with them. In so doing I will add one more wrinkle to the story about discourse structure. First, consider again example (1) of chapter 7. It is a text with a proposition anaphor and no ready-made DR-theoretic structure from the DRS construction procedure to refer to. (5)

After thirty eight months, America is back in space. :he sh~ttle Discovery roared off the pad from Cape Kennedy at 10:38 this mormng. The craft and crew performed flawlessly. Later in the day the TDRS shuttle communications satellite was successfully deployed. This has given a much needed boost to NASA morale.

One salient interpretation of the anaphoric pronoun in boldface in (5) is that it refers to a fact characterized by the sum of all the DRS constituents introduced by the second, third and fourth sentences. This interpretation as well as one other is predicted by the anaphoric constraints and the SDRS construction procedure. ~fter pro~essing the second sentence to yield a DRS k2' we must attach k2 to k 1. Smce k2 mvolves an event that is subsumed under kJ. we conclude defeasibly by the apparatus of chapter 7 Elaboration(kJ. k2).6 The third and fourth sentences yields DRSs k3 and k4, which also are interpreted as elaborating upon k 1. By the axioms for Elaboration and Continuation we also infer Continuation(k 2, k 3), Continuation(k 3, k4). Since Elaboration i~troduces a discourse domination, the SDRS of (5) looks like this prior to the processing of the last sentence.

kl

kt

x, S America(x s-back in space(x) after 38 mos.(s) k2

I

Y,e I k3 the Shuttle~) Discovery~ [e- y mare off... ]

Continuation(k2, k3) Elaboration( kt, k 1)

k1.u. k t

z,W,e' k I u,e" the Craft(z~ 4 [later that dac;~")] the crew( theTDRS ... u] e'-perform(zEBW) e"-dwloy(Z, u flawless( e') Z= Continuation(k 3, k 4 )

I

(6)

319

The shuttle Discovery roared off the pad from Cape Kennedy at 10:38 this morning. Later in the day the TDRS shuttle communications satellite was successfully deployed. The craft and crew performed flawlessly. After thirty-eight months, America is back in space. This has given a much needed boost to NASA morale.

Each sentence contributes largely the same DRS to the SDRS for (6) that it does to the SDRS for (1). Nevertheless, they have a quite different effect. The sentence that gives us the topic statement, K 1, for the story comes after its elaboration. By our rules for topic updating--in particular clause (ii), Kl replaces whatever provisional topic has been built for the first four sentences. Thus Kl is the current constituent for the SDRS built up from the first four sentences, and by the updating procedure for discourse relations, Kl is the only open and d-free constituent. According to the definition then, KS may only be attached to K 1. The availability constraint and wellfoundedness will allow only the link between the discourse referent introduced in Ks by the pronoun and the join of K1and the SDRS K\ formed from the first three sentences to be felicitous. 7 This accords with intuitions. There is a question about the interpretation of proposition anaphora now that we may characterize discourse referents using SDRSs. How are we to interpret the link between a discourse referent introduced by a pronoun and an SDRS? It is inadvisable to interpret that link as identity. For if we do, we may commit ourselves to the view that all discourse structure is integral to the information content of the discourse itself, and that seems wrong. For instance, then, the interpretation of the anaphor in (5) would entail that the successful launch, the return of America to space and the particular discourse structure the text--namely, that one subDRS constitutes an elaboration of another--was a boost to NASA morale. This is intuitively not part of

ANAPHORA AND DISCOURSE STRUCTURE

321

the content of the discourse. Discourse relations serve to determine what are the possible propositional antecedents for the discourse referent but at least sometimes are not constitutive of their content. 8 So we cannot understand anaphoric relations involving SDRSs in just the same way as we do the paradigm cases of individual anaphoric relations. A natural alternative is to take an SDRS to determine a proposition--the proposition that is the sum of its leaves--and to take this proposition as the anaphoric referent. I'll argue in section 3 that such anaphoric relations are best understood along the lines of the DRT analysis of plural anaphora. Here is another text from the Wall Street Joumal,9 in which there is proposition anaphora and which does not start off with an explicit topic statement. But the problems of discourse (6) with topics do not arise.

(7)

For a new TV series, "Tattingers" had more going for it than most. But because of the strike by television writers last summer, "Tattingers" couldn't get on the air until late October. By the time ... NBC shot down "Tattingers" after only seven episodes. So it goes for the networks in this dismal post-strike season. This is taking place while television watching in general is on the rise.

Two paragraphs, with a total of eight sentences, detail the TV networks' loss of viewers and revenues. Presumably, we constructa topic statement Ko to this effect or take our cue from the title of the article, TV Networks lose Viewers and Revenues. We then come to the sentence, So it goes for the networks in this dismal post-strike season. This sentence introduces a DRS KJ and a rhetorical relation, Commentary (the word dismal should tip us off to that effect), one term of which is DRS K J. KJ may easily be attached to the topic statement Ko built up in the usual way for the SDRS Jl( containing the contents of the eight sentences. By the definition of availability, the discourse referent introduced by the anaphor so could be identified with Ko /I. Jl( without difficulty. The next sentence of (7) This is taking place while television watching in general is on the rise marks a new segment about television watching in general, call this Jl('. This sentence introduces a DRS K2 and a coherence relation giving the background of the previous topic. The rest of the segment continues and elaborates upon K 2 ; hence, we introduce a topic dominating structure for K2 and its Elaboration, Jl('. There are two places K2 might be attached to the SDRS Jl(* containing KJ, Ko and Jl(.10 K2 might attach to the topic statement Ko, since we permit multiple attachments of discourse relations to topic statements, or to the topic statement K" of Jl(* as a whole. Thus, the constituent graph for (7) and ensuing text might be either one of these structures:

On either of these attachments, the theory predicts plausible anaphoric readings for the discourse referent z introduced by this ; z may either be identified on the first with Ko /I. Jl( or on the second with K" /I. Jl(*. These are plausible, if we think of K" /I. Jl(*, for instance, as determining a content that is the sum of all of the leaves of Jl(* joined together with K".

3. A V AILABILITY, ANAPHORA AND CONSTITUENT REVISION

3.1 A vailability and Parallelism and Contrast SDRS theory has some initial success with the anaphoric phenomena. Availability, however, appears to be at odds with some examples of abstract entity anaphora from chapter 6, in which anaphoric reference was made to embedded DRtheoretic structures. The examples are repeated below. (S.a) (S.b) (S.c)

John does not believe that [Mary is treating him fairlY]j. But Fred is certain of itj Sam doubts that John believes that [Mary is treating him unfairlY]i. Fred doubts that John believes that i too. If Al believes that [Pedro beats donkeys]j, he will yell at him. But Al doesn't believe thatj, so Pedro will escape with hearing intact.

(S.a-c) aid the reader to make the intended anaphoric connection in a variety of ways. In (S.a) the discourse particle but serves to set up a contrast between a negated positive attitude in the first clause and a positive attitude in the second clause. This contrast helps the reader to find the antecedent. l1 In (S.b) a very close parallelism between the semantic content and the syntactic structure of the two sentences serves to alert the reader to the intended linkage. The SDRSs for these discourses are simple to construct. There are only two constituents and they must be attached to each other. Because of the presence of the discourse particles, we will infer that Parallel or Contrast hold between the

CHAPTER EIGHT

322

ANAPHORA AND DISCOURSE STRUCTURE

constituents. Unlike many other discourse relations, however, Parallel and Contrast do not preclude Continuation as an attachment. The axioms for attachment imply a Continuation between the two segments, since no more specific attachment axiom fires whose conclusion is incompatible with Continuation. (8.c) again exploits a semantic and syntactic contrast between two SDRS constituents to alert the reader to the intended antecedent. Here too we infer both Contrast and Continuation. Of course in choosing Continuation, we also must come up then with a topic-dominating node. I will suppose then the following constituent (a) dominated by an appropriate topic for the SDRS for (8.c). Without using constituent revision, we would have the following SDRS:

I

x, s AI(x) s-believe(x,

z,w e---lV_ _ _ _---i )

Pedro(y) [beats donkeys(y)]

[z will yell at w] z=x w=y

x

AI(x) x, s, P s-believe(x, p) P"" ?

[So Pedro will escape with his hearing intact]

FACT: Suppose Contrast*(a, ~) in lK o. Let <'t, 't'>lo ... <'t, 't'~ be pairs of ME

trees for a and ~ and ~i be the tree isomorphism maximizing Contrast* from a subtree 't# of't\ onto a subtree 't* of'ti such that some terminal node n of't# is a proposition discourse referent k that falls within the scope of a contrast particle and that ~i(n) = 'Yb for each 1 ~ i ~ k. Then 'Ylo ... , 'Yk may be identified with k and they are the only constituents in lKo that may be identified with k. FACT: Suppose Parallel*(a, ~) in lK o• Let <'t, 't'>lo ... <'t, 't'>k be pairs of ME

trees for a and ~ and ~i be the tree isomorphism maximizing Contrast* from a subtree 't# of't\ onto a subtree 't* of'ti such that some terminal node n of't# is a proposition discourse referent k that falls within the scope of a contrast particle and that ~i(n) = 'Yb for each 1 ~ i ~ k. Then 'Ylo ... , 'Yk may be identified with k and they are the only constituents in lKo that may be identified with k. These facts follow straightforwardly from the SDRS updating and revision procedure, which merges terminal nodes of embedding trees or modified embedding (ME) trees under the given tree isomorphism~. The merging procedure identifies abstract entity discourse referents with their images·under~. Let us work through some examples. With a contrastive particle, the two constituents of (8.c) support a relation of Contrast. The diagram of the ME trees for the two sentences of (8.c) below indicates the obvious tree isomorphism on a subtree of kl (by definition it must include the root), which pairs p with its intended antecedent, the subDRS constructed from that Pedro beats donkeys:12 kl •

The availability constraint predicts that the subDRS introduced by the that clause, that Pedro beats donkeys is not available. But it is obviously the intended antecedent. The observations about the anaphoric potential of discourse referents introduced by pronouns in such contexts show that availability, though an important constraint, does not tell us the whole truth about abstract entity anaphora. Something like the following seems on the right track: Z E UK, e < a, a is d-subordinate to 0, ~ is d-subordinate to 'Y, and K~ ~~ tc lK. Then e may 'be identified with z in lK only if the relation Parallel or Contrast holds of 0 and 'Y, and the relation may be extended in a suitable way to z and e.

Provisional, Descriptive Constraint (A): Suppose that

Constraint (A) is suggestive and seems to capture a generalization of not only the data on proposition anaphora but various forms of concept anaphora as well. . We can actually derive not only a precise version of (A) but also its converse from the effects of parallelism and contrast on constituent revision and SDRS updating.

323

k2

Kll "* K12 -------------

I I~K21

K 13 _ _ _ _ _ _ _

1

p

What does our constituent revision procedure predict? The two sentences yield constituents that are attached by means of Continuation and Contrast. If we take the Contrast relation to be determined by the tree isomorphism ~ indicated with arrows above with as its designated scope element the entire second constituent, then the constituent revision procedure tells us that we must update the leaves of the tree that abstract entity discourse referents by merging them with their images under ~ in the other tree. This means that we must identify the discourse referent introduced by the pronoun it with the subDRS introduced by that Pedro beats donkeys. In this case, there is just one leaf that must be so updated. We now perform the substitution of the subDRS for []. We also have to add the contrasting matrix condition for the new leaf. But by the idempotence of 1\, this is just the same condition as we already have. We

324

ANAPHORA AND DISCOURSE STRUCTURE

CHAPlER EIGHT (9)

thus get the SDRS below.

x s AI(x) s-believe(x,

ffi AI(x)

'Cl

'C2

Kl~

K2

I

s,p s-believe(x, p)

Kll~

I

P~EB So the theory predicts the intended reading of (8.c). Now recall the constraint of maximization of the appropriate Parallel* or Contrast* relation. Since there are a variety of ways one might realize a Parallel* or Contrast* relation in a given SDRS, there is a constraint to maximize Parallelism* or Contrast*, whenever one attaches two constituents by means of the appropriate relation. The SDRS constituent revision procedure for two contrasting constituents is always defined relative to the relation that maximizes Contrast*, and similarly for two Parallel* constituents it is defined relative to the relation that maximizes Parallel*.13 Maximizing Contrast* requires choosing three things: (i) the largest modified embedding trees or ME trees 'C and 'C' for the constituents relative to their embedding trees compatible with contrast, (ii) the largest subtrees for 'C and 'C' compatible with contrast and (iii) the most plausible polarity assignment compatible with Contrast*. Similarly, to maximize Parallel*, we must pick (i) the largest modified embedding trees 'C and 'C' for the constituents relative to their embedding trees compatible with parallelism, (ii) the largest subtrees for'C and 'C' compatible with parallelism, and (iii) the most plausible polarity assignment compatible with Parallel*. Because we follow a maximization constraint for Contrast* and Parallel* relations, the update procedure predicts that (8.c) has only the desired reading in a intonationally neutral reading; l'} is a tree isomorphism between maximal subtrees, and there appears to be only one group of maximally contrasting themes defining the maximal, contrasting polarities. Another example of contrasting constituents in which an anaphoric link is given shows how the constituent revision procedure may also add content.

John thinks that Mary claimed that the conjecture was false. But he thinks Joan proved it.

The maximal subtrees for which an appropriate tree isomorphism can be defined are just the embedding trees for the two constituents, both of which are simple linear structures with three nodes. The tree isomorphism is defined on the total embedding trees and pairs z, the discourse referent introduced by the pronoun it, with the subDRS that results from the conjecture was false. The constituent revision procedure then must identify z with K12 .

x

contrast( kl' k 2)

325

K12~

I

K21

I Z

But since the contrasting nodes under the scope of the particle are Kll and K2 1. the revision procedure predicts that (9) implies that Fred thinks that Joan proved and Mary did not prove that the conjecture was false. Parallel constituents also give rise to similar predictions concerning anaphora. Given the maximization constraint for Parallel and Contrasting constituents, the method of updating parallel constituents also predicts that an example like (8.b), repeated below, has only one possible reading--the intended one: (8.b)

Sam doubts that John believes that Mary is treating him unfairly. Fred doubts that John believes that too.

The SDRS construction procedure yields two constituents kl and k2 for (8.b), and two embedding trees that again are isomorphic. The second condition contains a discourse particle too. The scope of too could be syntactically and semantically the entire clause; I will suppose that we have tOO(k2) as a condition. Thus maximal and designated scope elements will in this case coincide. Parallelism is maximized using the tree isomorphism defined between the two embedding trees for kl and k2' and the constituents have same themes derived from the VPs. The constituent revision procedure now dictates that the discourse referent introduced by that be identified with the subDRS introduced by that Mary is treating him unfairly. Relative to the constraint of maximization, no other anaphoric antecedent for that can be found. This approach works equally well with other propositional anaphors like so: (10)

John thinks that it's a great idea for Mary to go to Hollywood. I think so too.

Only by identifying so with the translation of that it's a great idea for Mary to go to

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Hollywood is parallelism of structure and polarity maximized. Then the constituent revision procedure forces the identification of the discourse referent introduced by so with the DRS derived from it's a great idea for Mary to go to Hollywood. These unambiguous examples just examined are not always representative. Sometimes there may be no clear way to maximize parallelism or contrast. In those cases ambiguity and awkwardness results. Consider these examples where the parallelism/contrast extensions are difficult, perhaps even impossible, to construct.

parallelism or contrast is signaled. 14 For instance, (11.c) contains no helpful particles like but or too, but it's structure does have a conditional that corresponds to the structure of the first antecedent. Both subDRSs of the conditional in the second constituent have anaphors, and there is a strong preference to identify them with the same antecedent. Constituent revision might suggest taking the subDRS antecedent of the conditional as a whole as the antecedent. But it seems very bad style to express one's disgust at Pedro's possible activities with farm animals in this way. (l1.d-e) seem to me completely hopeless, and the intended reading cannot be salvaged with any discourse aids. The logical structure and discourse structure interact in (11.d-e) in a peculiar way, making such salvaging impossible. How does the theory handle these marginal cases? To get an appropriate bijection in (l1.b) for instance, we must choose a modified embedding tree on which the DRS KI2 introduced by Mary is treating him fairly has as its matrix condition in the top DRS KIthe property, AP Sam doubts that John believes that p. So the respective ME trees for the two constituents constructed from (l1.b) with a possible bijection between them are:

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(ll.a) It's false that John believes that [Mary is treating him fairly Ji. But Fred is certain that iti is true. (l1.b) ?? Sam doubts that John believes that [Mary is treating him unfairlY]j. But thatj is true. (ll.c) ?If Al believes that [Pedro beats donkeys] j, he will take steps to protect his herd. Thatj is disgusting, if true. (l1.d) *?If Al believes that [Pedro beats donkeys]j, he will take steps to protect his herd. Thatj is disgusting. (11.e) *If Maria believes that [Pedro beats donkeys]j or he steals chickens, she will take steps to protect her animals. Thatj is disgusting, if true. (I 1. a), though logically equivalent to (8.a), doesn't work nearly as well. The contrast here is naturally read as between the falsity of the claim that John believes that Mary is treating him fairly and Fred's certainty of this claim. So a natural antecedent given the availability constraint for the pronoun is the subDRS derived from that John believes that Mary is treating him fairly. Of course, constituent revision does not rule out other possible antecedents, if the relevant extension of the Parallel/Contrast relation can be constructed. One might take in (11.a) the intended contrast to be between the lack of John's belief and Fred's certainty. Then one can extend this relation to identify the object of John's belief and the object of Fred's attitude. If we do not count the predicate true as giving us a real embedding, which seems reasonable from the point of view of contents or propositions, then one could get an extension of the Contrast relation that takes the interpretations of the anaphor and intended antecedent as terms. Nevertheless, this relation is, intuitively, more difficult to construct. For instance we do have to ignore the first embedding; the contrast is not perfect in this case. The most felicitous anaphoric reading is one which exploits the maximal and most exact extension of a Parallel or Contrast relation. This would explain speakers' preference for the first of the readings discussed for (l1.a). In the reading we are attempting to force, we have not maximized the match in the two structures by pursuing this extension of the Contrast relation. With sentences like (l1.b), however, it is almost impossible to extend the indicated parallel or contrast relation to the intended antecedent. It is not as though the example involves some sort of category mistake or logical error; it is just that it appears impossible to say, for instance, that it is likely to be true that Mary is treating John unfairly by means of (11.b). Even worse and almost unprocessable are variants of (l1.c-e) in which the intended antecedent is embedded but no discourse relation or

327

- - - - - K2

I

The rectangle indicates that the modified embedding tree of'tl chosen keeps KI and KI2 as elements but collapses KII into part of the matrix condition for KI2 in K I . The difficulty with this embedding tree is that the appropriate polarity assignments are difficult to make; much more plausible than the contrast between truth and Sam's doubts about John's beliefs is the contrast between truth and Sam's doubts. Thus, this example does not work, because the strength of the polarity assignment is not maximized. With (11.c), we have a different difficulty. Here we may define a bijection based on the original embedding trees, but the question is, what sort of relation is defined? A contrast is suggested between the truth of Pedro's beating donkeys and AI's believing that, but the consequences do not attribute properties of the same type. The two nodes are not assigned a polarity when they are paired together. So it is impossible to assign either a contrasting or parallel relation. But without some such relation, the SDRS for (l1.c) cannot support the indicated anaphoric connection. (ll.d) and (I I.e) have this problem--it is impossible to define a modified embedding tree that makes a contrast or parallelism possible and gets the intended anaphoric links right after SDRS update; and they also suggest much more plausible Contrast or Commentary relations than the ones that the anaphoric readings would require. So the

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theory predicts correctly that in these cases the intended anaphoric link is not possible. Between the straightforward and impossible examples, there lies a large middle ground. Since parallelism and contrast come in degrees, embedded subDRSs become available as antecedents even when a perfect correspondence between two embedding trees is lacking. Consider for instance,

"accommodates" the intentions of the speaker in this way, then the theory would predict that the discourse would be felicitous. The discourse is awkward perhaps, because this sort of accommodation is not a natural one. With a few changes to (12.a), however, a better discourse, (12.b), results, in which the pronoun can easily pick up the proposition that Mary goes to Hollywood. I5 Given the presence of the particle but, the interpreter attempts to maximize contrast between the semantic environment of the anaphor and the environment of the antecedent. The following ME trees for the constituents in (12.b) suggest themselves, on which KI and KII collapse as indicated by the rectangle below.

(12.a) John is certain that Fred thinks that it is crazy for Mary to go to Hollywood. But it's a great idea. (12b) John is certain that Fred thinks that it is crazy for Mary to go to Hollywood. But I think it's a great idea. (12.c) John is certain that Fred thinks that it is crazy for Mary to go to Hollywood. But I know that Susan thinks it's a great idea. (12.d) John is certain that Fred thinks that it is a disaster for Mary to allow Jane to go to Hollywood. But I think it's a great idea.

329

'tl

Let us go through each of these at least cursorily. Most speakers find (12.a) not terribly good, even though it is obvious that the intended referent of the pronoun it in (12.a) is the proposition that Mary goes to Hollywood. The contrast must pair the two evaluative predicates crazy and great. But then one must take an ME tree to construct the maximal, contrasting bijection between the two constituents on which John's certainty about Fred's belief is a matrix predicate for the DRS formed from it is

crazy.

Here is a guide to the diagram above: Kb K 2 : outermost DRSs K l l : John's certainty K 12 : Fred's belief K 13 : Mary goes to Hollywood The matrix of KI3 in KI does not serve well with the matrix condition for z in K2 to define the appropriate polarity. To make this discourse work, one supposes that there is some other attitude--for instance, the speaker's belief--that attaches to K 2 • If one

The tree isomorphism now pairs K2 with KI and K21 with K 12 • The presence of the contrast particle indicates that we must construct a maximal Contrast relation. Clearly, the bijection above gives us a tree isomorphism between two maximal subtrees. Further, the pairing of the constituents makes Contrast plausible. The matrix conditions for z in K21 is an evaluative predicate as is that in K 12 , but they are contrasting, incompatible predicates. The matrix conditions of KI2 in KI and K21 in K2 are positive attitude predicates that do not contrast. 16 This then forces the anaphoric antecedent of the discourse referent introduced by that to be the subDRS constructed from for Mary to go to Hollywood. Some speakers do not like (12.b) and insist on yet more rigid parallelism or contrast being realized in the syntactic construction between the environment of the antecedent and the environment of the anaphor. Such speakers rate (12.b) not as good as (12.c) or (12.d). In order to maximize contrast, the pronoun that in (8.d) must anaphorically refer to the proposition that Mary allows Jane to go to Hollywood; it cannot refer to the proposition that Jane goes to Hollywood. The prediction seems correct to me, though once at this level of embedding I find my intuitions beginning to waver.

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3.2 Availability and Topic Revision

type of action they suffered. Here we can also exploit the parallelism between the patients and the contrasting information about what happened to them.l7 Thus, we will sum the individual plaintiffs into a group, and subsume the events they suffered under a general event type. K o would then contain information to the effect: plaintiffs unjustly treated. We will declare the plural discourse referent u + v in Ko, where u and v are the discourse referents introduced by the DPs one plaintiff and another in KI and K2 respectively. According to the rules for group formation sketched in chapter 2, one construct the group XI+ ... + Xn discourse referent in UK, if XI. ... , Xn are all accessible from K. The discourse referents introduced by the plaintiffs are all SDRS accessible from Ko, so we may proceed to introduce the u+v in UK o• Parallelism affects the updating of SDRSs in two ways. After the construction of Ko, this is the constituent graph of the SDRS constructed from the first two sentences of (13).

Parallel and Contrast are not the only discourse relations that furnish instances of constituent revision. So do Continuation and Elaboration. They license topic revision. Here is a first, simple example: (13)

One plaintiff had never received his full pay. Another had been passed over for promotion three times. Yet another had been denied a job because of his race. But the jury didn't believe it.

The preferred antecedent for the pronoun in (13) appears to be the proposition expressed by the first three sentences, especially if one reads the last sentence as equivalent to the jury didn't believe any ofit This antecedent is not available from the principles of DRS construction. It must be derived from the principles for SDRS construction and the availability constraint. It also appears very difficult for most speakers to get either the first or second of the plaintiffs claims as individual antecedents, and impossible to get an arbitrary subset of the whole collection as an antecedent. The possible antecedents are a quite restricted set in comparison to the space of all propositions that could be formed from the content. These restrictions derive from the interaction of the principles of SDRS construction and the availability constraint. To see how the theory handles (13), let us construct its SDRS. The first sentence yields a DRS K I . The second sentence yields a DRS K 2, about another plaintiff and more unfair treatment. K2 has a parallel structure and content to K I; these are important clues that this DRS continues K I. World knowledge allows us to conclude no other discourse relation besides Parallel(KJ,K 2), and so we conclude Continuation(KJ, K2)' The update procedure thus yields an SDRS ][{Icontaining KI and K2 as constituents. Note that the components are added together also according to the algorithm for treating the semantic effects of parallelism. The semantic effect of parallelism is that if K is parallel to K', then K should be incorporated into the discourse context of K'. Parallelism is a way of extending an open constituent with new material, though it is not the only way. Temporal and pronominal anaphora are also often important signs that two sentences should be included within a segment where those anaphoric connections can be resolved. By the topic updating rules, we must introduce a topic K o that subsumes both KI and K 2. Because topics must be simple, we cannot simply have KI A K 2. But there is a parallelism between KI and K 2, and we can use the tree isomorphism defining the parallelism to good effect. SDRS updating exploits parallelism in two ways--to sum across elements of ME trees as the algorithm of the previous chapter suggested and to build topic constituents. With parallel constituents, the constituent revision procedure using parallelism serves to sum across arguments to generate appropriate topics. Topic revision makes use of a strategy exploiting a particular discourse relation like parallelism whenever possible. So we must use subsumption and generalize over the common thematic roles--in this case the patients or the individual plaintiffs--and the

331

Continuing the process of SDRS construction, the third sentence yields another DRS K 3. K3 introduces a parallel relation to K 2; indeed K3 is parallel both to K2 and to K I. In pictorial terms using our constituent graphs and the arrow representations for parallelism relation from the previous section, we have the following picture:

The constituent revision procedure says that the leaves of the subtrees of the parallel constituents within the field of the bijection required for parallelism should be merged or added together. So this means given the parallelism relation depicted that we should in updating the SDRS simply replace K2 with K2 A K3 But if we think now what it means to have KI and K2 3 already as parallel constituents, we have KI A K 2; this merge is made by having KI and K2 constituents of][{I' So the prescribed replacement in the SDRS above simply nets us: KI A (K2 A K 3), which is KI A K2 A K 3, by the associativity of I\. This means in effect that we simply add K3 to the constituent ][{I, which follows from this general fact: FACT: add*([ {ab ... , an}, ¢], ~)

= alA a2 A ... A an A ~

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This is a welcome result, for now we see that relation based updating using Parallel and topic based updating using Continuation are not only consistent but yield the same results. Appealing to (iv) of the topic based update procedure from chapter 7, we add K3 to lI{1. But then we must also modify the topic constituent dominating lI{1. When a constituent is added to another constituent already dominated by a topic introduced by a previous constituent, then the SDRS update rules require that a topic for the updated constituent be found or constructed. K3 continues the general theme of the segment lI{J. but it has introduced new elements into the story as well,. Ko does not take account of these new elements. Again using subsumption and generalizing over the common thematic roles or the common parallel elements, we construct a new group discourse referent u+v+w, were w is the discourse referent introduced by another in the third sentence. The general event type subsumes the event that occurred to the third plaintiff. So the new topic constituent, Ko', looks like this:

attachment site must be open and D-free. There are two possible attachment sites then: Ko' or K 3 • Of these two possible sites, Ko' is preferred. Although nothing in my theory predicts this preference, there are certain clues that one could formalize within the theory so as to predict this preference. First there is a change in agent from plaintiffs to jury. Further, the plaintiffs are not mentioned in K4, nor are they anaphorically referred to. These are clues that the author might be introducing a new topic with 1«(.1 8 This suggests entering I«( as a separate constituent from Ko or its dominated SDRS lI{1 in a larger SDRS lI{2. By the principle of availability and the availability constraint, Ko '/\ lI{ 1 is a potential antecedent for the discourse referent z introduced by it in UK4.1 9 By the same principle and definition, however, the individual DRSs KJ. K2 and K3 would not be potential antecedents. There is in addition a contrastive particle with scope over 1«(. Maximizing the contrast here involves a tree isomorphism pairing the truth of the plaintiffs justices with the jury's unbelief. So this will force in the ME trees for K 2 ' and I«( a pairing of z with K 2 ' itself; and by the rules for constituent revision and updating we complete K4 by replacing z with K 2 ' /\ lI{b which is what is desired. For the less salient possible attachment of 1«(, the rules for non topic based updating would make I«( part of lI{1 by constructing out of K4 and K4 an SDRS lI{3.2 0 On this last attachment, well-foundedness precludes taking either lI{J. lI{3 or Ko' /\ lI{1 as antecedents. The principle of availability then entails that only K4 is available as an antecedent. So given the two attachment possibilities, there are two readings of the pronoun. This is also forced on us by the constituent revision required by the presence of Contrast. Here are the constituent graphs of the two possibilities.

u+v+w plaintiffs (u+v+w) unjustly-treated(u+v+w) Now the following constituent graph for the first three sentences of (13) emerges after this update: Ko'

• M

333

lI{t

We now update the SDRS depicted in the figure above with the content of the fourth sentence. The fourth sentence introduces a DRS I«( with contrastive force, as the discourse particle but indicates. I will again assume that there must be some relation between K4 and its attachment point. But I«( describes a state with a different agent, the jury. The interpreter is able to recover this fact, because he or she knows that the jury differs from and listens to and judges the plaintiffs. K4 also assigns a propositional attitude to the jury. Predicates of propositional attitude typically indicate the presence of a commentary relation. So in this case, the axioms of attachment suggest a relation other than Continuation; I«( introduces a commentary relation. Further the axioms for Continuation stipulate that since K4 introduces a Commentary relation, it cannot also be related by Continuation (these relations are incompatible). Since I«( is not a Continuation of the previous segment, it is entered as a separate constituent. We have now to figure out what is the other term of the contrastive Commentary relation. By the updating rules for discourse relations other than Continuation, the

The left constituent graph above for one SDRS of (13) forces us to identify the discourse referent introduced by the pronoun in (13) with the DRS union of an SDRS and its topic statement. This example is useful for understanding how this identification is to be interpreted. Is the SDRS to be thought of as just one DRS? If that were so, however, then the only possible reading of the anaphor would entail that the jury did not believe all of the testimony. This interpretation is compatible with the jury believing many of the things that happened to the plaintiffs. While one

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interpretation of (13) perhaps yields such a reading of the anaphor, it is not the only reading. In fact, much more salient is the reading of the pronoun which entails that the jury did not believe any of what happened to the plaintiffs. But this reading is only possible, if the "sum" of the individual facts is much more like a set than a mereological fusion. That is, the propositions about the different plaintiffs must be distinctly represented within the newly formed constituent. In order to get the two readings, we must interpret an SDRS as a collection or group. I will interpret an SDRS ][{ as a group of constituents. My interpretation of an anaphoric link between a discourse referent and an SDRS follows the explanation of plural anaphora in DRT. A condition of the form z "" ][{ is satisfied relative to an embedding function f, world wand time t just in case f(z) in w at t is a collection of DRSs, such that there is a bijection g from f(z) onto the set of DRS constituents
jury(Y) s, z, p --, s-believe(Y, p) p
These two interpretations of the anaphoric connection between a pronoun and an SDRS, together with the principles for SDRS construction and the constraint of availability, yield the three available readings for the pronoun in (13). Before leaving this example, let us retum for a moment to the topic revision in the SDRS updating. This yields a surprising principle about plural anaphora. In revising the topic after having added K3 to ][{h we created in Ko' a new plural discourse referent u+v+w but also eliminated another--u+v. We thus made a new plural sum available as a discourse referent but also eliminated another as a potential anaphoric antecedent for a plural pronoun. While the sum u+v was an available discourse referent after the first two sentences, it is no longer so after the second two sentences.

..

ANAPHORA AND DISCOURSE STRUCTURE

'*r·'" .

335

So SDRS theory predicts that in the following variants of (13), u+v is a possible antecedent in (14.a) but not in (14.b). (14.a) One plaintiff had never received his full pay. Another had been passed over for promotion three times. But the jury didn't believe them. (14.b) One plaintiff had never received his full pay. Another had been passed over for promotion three times. Yet another had been denied a job because of his race. But the jury didn't believe them. This discussion of my approach to topic formation and revision leads to the following hypothesis about sum formation: CONSTRAINT: Constituent Revision of Topics accounts for all summation of

discourse referents in cases where the summation is not guided by syntactic structure. According to our constraint, only updating of topic forces the construction of plural discourse referents when the plural sums are not licensed by a syntactic structure-e.g., conjoined noun phrases. Groups are thus, formed whenever the subDRSs have a common theme or topic. The constraint accounts for the observation that for the most part only maximal sums of "natural" or "socially recognized" kinds are given in a discourse. We shall study this prediction in the next more complex example and in section 5. It is almost right. The next example is purposefully very similar to (13), and will serve to reinforce my interpretation of SDRSs and dominating constituents. It is slightly more complicated than (13) and makes more demands on the notion of topic. (15)

One plaintiff claimed that he had never received his full pay. Another said that he had been passed over for promotion. Another was certain that he had been denied a job on the basis of race. But the jury didn't believe it.

In (15) the preferred antecedent of it is the sum of the claims of all the plaintiffs, although the last claim is also a possible antecedent. On the model of plural anaphora, the anaphoric referent would be a set or group of DRSs--call it X, consisting of the three plaintiffs claims. In order to get this intended antecedent given our proposed constraint on summation, the dynamics of topic must follow closely the parallelism in the three reports. Let us build up the SDRS for (15) step by step and see what our machinery yields. The DRS construction algorithm yields a DRS KI for the first sentence containing a subDRS K II . The second sentence yields a DRS K2 with a subDRS K2 I. Since K2 and KI are almost entirely in parallel, our semantic treatment of the parallelism relation dictates K2 may be attached to KI by Parallelism and, since the attachment and world knowledge axioms suggest no other incompatible relation, we get also Continuation. In the previous section, we saw also that parallel elements

~-~-~-~~~--------·~q~l1ll:r··.-.-----.--~--~------------CHAPTER EIGHT ANAPHORA AND DISCOURSE STRUCTURE "",-~,

336

should sum together using I\. The SDRS update procedure will yield an SDRS KI containing botlY KI and K 2. The SDRS construction procedure yields a topic statement Ko dominating K I. Parallelism says that we must merge the constituents at nodes consisting of abstract discourse referents introduced by anaphors and nodes introduced by maximal scope elements. In the absence of a designated scope element that would tell us to join the embedded clauses, we take the parallelism to hold as high up the tree structure as possible--viz., between KI and K 2. The SDRS gets further modified with the processing of the third sentence. It too yields another constituent K3 that is parallel to both KI and K 2. So we will add, following the same procedure as described earlier, K3 as a constituent to K 1. K3 also contains a subDRS K 31 , which represents another claim Let us now turn to the revision of the topic constituent. If the topic is the place in which plural discourse referents of various types are entered, then we should expect plural discourse referents for both common thematic roles--for the sum of the plaintiffs and for the sum of the claims in the topic statement for the SDRS. Summing over the claims and over the plaintiffs gives us a simple topic that capitalizes on the parallelism of the two constituents.

I

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processing of the last sentence looks like this:

r1 1 .,1

K2

I Ko'

•

Kl

~~K3 The fourth sentence in (15) introduces a Contrast relation, and once again the problem of attachment arises. One possible attachment is up high, to Ko '.

plaintiffs(u+v) Ko : = e-claim(u+v+w, KI d\ K21 ) The revised topic statement for KI with K3 added will exhibit also two sum discourse referents, one for the three plaintiffs and one for their three claims. By following the procedures for SDRS updating--in particular clause (iii) of the topic updating procedure and modifying the topic statement as we go along, we end up with the following topic statement, where u, v, w are the discourse referents standing for the plaintiffs:

plaintiffs(u+v+w) e-claim(u+v+w, KIIA K21 A K 31 ) K o·'.Once the sum of claims has been formed in (15), it is a discourse object introduced in the topic DRS. In order to account for the intended interpretation of (15), we needed to find the group of all the claims. The principles for topic revision have constructed such a group in the topic statement, Ko', for K 1. K2 says that a group of plaintiffs are making a group of claims. Which claims? Just those and all those that are described in KI--namely K II , K2 hand K 3I . To finish off the analysis of (15), the constituent graph of (15) prior to the

The availability constraint implies that with an SDRS for (15) as depicted above, the plural discourse referent KIIAK2 IAK31 in K2 is available to the discourse referent z introduced by the pronoun in ~, but none of the DRSs KI h K21 or K31 are available. We can explain. the two truth conditional interpretations of the anaphoric link in (15) by appealing to the cumulative and distributive readings of the plural anaphor. Notice that updating K5 on the basis of the Contrast relation between Ko and K4 will yield an even more determinate result; the maximal contrast results from pairing the plaintiff's claiming with the Jury's disbelief and hence z with KIIAK2IAK31' So we must identify z with K11/\K21AK31' Notice that once Ko has been updated to form Ko '--which occurs prior to the attachment of ~, only the maximal sum KII/\K21AK31 is available, not the sum K II /\K21.22 There is one other possibility for attachment for K5 in the constituent graph for (15). The other term of the contrastive relation could be K 3. This attachment would make K3 and K31 available to the discourse referent introduced by the pronoun in (15). But here the maximal contrast is given by a tree isomorphism that pairs z with ~l. This is the second reading most people notice for (15). Modulo the assumption about maximal contrast, there are only two interpretations for the pronoun in (15) according to my theory. In particular, the individual claims KII and K21 may not be identified with the pronoun on either attachment.

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3.3 The Limits of Availability

The fifth sentence of (15) introduces a contrast relation and a DRS K5 which informs the reader of the jury's attitudes to what they were listening to. The contrast can attach to K5 or to Ko'--since Ko' is an implicit topic in K 2. Our attachment rules will indicate that if , then Commentary(Ko', K5).25 But there is clearly also a Continuation between K4 and K5; K5 also constitutes a Result--in the sense of a consequence of the plaintiffs' testimony. Thus, we may also have Continuation(K4, K5). By the topic updating rules, we must now form a topic constituent for the constituent containing K4 and K5--call it K6. Presumably, the content of K() is something like: jury reacts to plaintiffs claims, where K 11 /\K 21!\K31 characterizes the claims and u+v+w identify the plaintiffs. By the rules for topic based updating, the topic node inherits those discourse relations of its constituents whose other terms are not d-subordinate to the topic. This yields the following discourse Structure:

338

The data concerning the possible antecedents in (15) suggests, and my SDRS constraints predict, that at least two out of three claims in the group are not available as antecedents. The asymmetry between the status of the individual claims and the sum of those claims becomes even more apparent, if we change (15) slightly. (16)

One plaintiff claimed that he had never received his full pay. Another said that he had been passed over for promotion. Another was certain that he had been denied ajob on unfair grounds. The jury listened politely. But they didn't believe it

The anaphoric pronoun introduced in (16) cannot refer back to the last of the plaintiffs' claims. The addition of the intervening material prevents the reading where the pronoun is linked to the last of the claims. Let us look at the constituent structure of the SDRS for (16) to see how the theory predicts this observation. The constituent graph of (16) is identical to that of (15), up to the fourth sentence. But upon processing the fourth sentence, differences emerge. The DRS K4 from the fourth sentence has a different agent, the jury, and it does not mention the plaintiffs or their claims explicitly. K4 indicates a shift in topic from the plaintiffs and their claims to another facet of the trial, how the jury reacted.23 There is, of course, a connection between K4 and the preceding discourse. A sophisticated lexicon would give the verb listen a semantic argument--typically, one listens to or for something. The jury presumably listened to the plaintiffs or to the plaintiffs' claims. A reasonable knowledge base should in any caseinfer that the jury is present to hear the plaintiffs case. Now one could take the jury to have listened to the last plaintiff politely. But that is not a salient attachment; if the author had intended this, he should have given us some clue that the topic of K4 was continued--perhaps by anaphorically referring to the last plaintiff, perhaps by using the peripheral pronoun that, or perhaps in some other way.24 In the absence of any such device, there is a very definite preference to attach K4 high via an appropriate discourse relation--perhaps Commentary but more likely something like Cause or Result. Result(a, ~) holds just in case un~ is a causal or logical consequence of un~. Here then is the constituent graph for the discourse.

Ko' ..

~

Result

Kl

~ K2 K3

Kl

Ko'

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Result

This diagram shows that K3 is not available to the discourse referent introduced by the pronoun in K5. Assuming that K6 or K4 has, as is plausible, a discourse referent standing for the plaintiffs claims, this is the only predicted antecedent for the pronoun in K5. On the other attachment where Commentary(K o', K5), the group of the plaintiffs claims is also predicted to be available.

4. DISCOURSE SUBORDINATION Typically as we have seen, SDRS updating builds up more complex structures by adjoining material to the current constituent or entering it in some superordinate SDRS. In fact my constraints on d-subordination so far force this strategy upon us. But there appear to be discourse contexts in which this strategy may be relaxed. This is similar to what happens to the DRS construction procedure in cases of modal subordination, a phenomenon discussed in chapter 2. Like those linguistic conventions that facilitate modal subordination, there are discourse devices that facilitate discourse subordination. In the discourse literature, this phenomenon is called a resumption or return pop.26 I have used the name discourse subordination, because the phenomenon is in effect a generalization of modal subordination. Example (2) of chapter 7, repeated here, offers an example of discourse subordination.

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CHAPTER EIGHT (19)

Human life expectancy gets longer and longer. At first glance this seems like good news. But hold it. Human life is not the only thing getting longer. So are television miniseries. Well you may say, it only proves that Parkinson's law also fits human life: the entertainment expands to fit the time.

Upon processing the second sentence to yield a DRS K 2, the anaphoric reference and evaluative terminology good news suggests that K2 is related to Kl> the DRS derived from the first sentence, by the discourse relation Commentary. Thus, the update procedure takes Ko as input and adds to it a new constituent K 2, related by the discourse relation commentary to Ko. Availability makes KI a possible antecedent and the only possible antecedent of the discourse referent introduced by this in UK2. The interesting question is what the third sentence contributes. It seems to say that the Commentary should not be taken at face value. Its DRS K3 contrasts with K2 but also continues the Commentary--modifying its content. Hence by the topic updating rules, we must introduce a topic node that now inherits the Commentary relation. At this point we have the following structure.

Notice that KI is no longer open in this SDRS. The next sentence, however, repeats almost verbatim the material that yielded K 1. This repetition has a specific purpose, as noted by Fox (1987). It forces the reader to return to expand the "closed-off" constituent KIP In the SDRS framework, the constituent from the fourth sentence, K4 is entered with KI in an SDRS K', which does not contain K 2. ~ is a Continuation of K1and so we construct a topic K', subsuming KI and~. K' is the topic--human life expectancy and TV miniseries get longer.

The next sentence of (19) yields a DRS Ks with a commentary on the topic

ANAPHORA AND DISCOURSE STRUCTURE

341

"Human life + TV. miniseries get longer.. " Thus, KS should be attached to K' with a Commentary relation. This is fme; K' is open, since ~ is the current constituent.

In Mann and Thompson's (1986) theory or other systems that appeal to resumptions or return discourse Pops, there is no account of this behavior. An advantage of the SDRS framework is that this curious behavior of resumptions comes about as a natural extension of the constituent revision rules suggested by parallelism and contrast. An explicit restatement of text is just another way of marking out a Parallel* or Contrast* relation between an already given constituent and new material as well as a maximal scope element. But unlike simple discourse particles, the explicit repetition of material forces us to accommodate the parallelism by extending the structure given by the current constituent so that we have a match and the maximal scope element can merge in the appropriate way already described. Let us apply this idea to (19). The repetition of the material forces us to extend the embedding tree for ~ so that the actual embedding tree for ~ can match under a tree isomorphism the appropriate substructure ofthe SDRS already built. Pictorially, we can represent this accommodation as follows:

Accommodated material

If ~ is specified as the maximal scope element, then the rules for constituent revision require us to merge ~ with K 1. But since ~ is a verbatim repetition of K 1, the rules for constituent revision entail that KI J\K.4 = K 1. The effect of the fourth sentence on the SDRS is to make KI the current constituent; it does not add any new information to the structure. This example of discourse subordination is yet another variation on the plaintiffs' story.

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(20)

ANAPHORA AND DISCOURSE STRUCTURE

One plaintiff claimed that he had never received his full pay. Another said that he had been passed over for promotion. Another was certain that he had been denied a job on unfair grounds. But the jury didn't believe any of it. A fourth plaintiff claimed that he had been denied a job because of his love for leprechauns. This the jury believed completely. The judge, on the other hand, still didn't believe any of it.

The fIrst four sentences give an SDRS familiar from earlier examples. The discourse referent introduced by it in the fourth sentence is identifIed with KI JlI\K 2 IAK 31 . The fIfth sentence introduces a DRS KS and a parallelism relation of the sort that we must accommodate somehow in the structure. Further, the strategy of restatement yields a resumption. Ks forces an explicit parallelism to a subtree of the whole structure, as depicted in the diagram below. We accommodate this parallelism by inserting Ks in the appropriate place; the entire superordinate structure is collapsed in a modified embedding tree and for what cannot be collapsed, we extend the structure given by Ks so that Parallel* is satisfied in the updated SDRS. Here are the relevant modifIed embedding trees. The sharp edged box shows the collapsing effect of the modified embedding tree, and KS is the maximal scope element.

343

plaintiffs(u+v+w+z) e-claim(u+v+w+z, KIIAK2IAK3IAKsl) The processing of the next sentence of example (20), This the jury believed completely, yields a Commentary relation and a constituent Kt; that is naturally to be attached to Kt;. It can only be coherently attached to Kt;, because K4 has already informed us that the jury did not believe the claims of the fIrst three jurors. With the processing of the final sentence in (20), The judge, on the other hand, still didn't believe any of it, we have telling evidence for this approach to discourse subordination. On one reading the judge doesn't believe any of the claims made by the plaintiff. So this example shows that we need to be able to collect together all the claims by the plaintiffs. This is of course what SDRS theory has in effect done for us with the construction of Ko". After we add K6 to the SDRS, Kt; is the current constituent. But then Ko" is open and d-free, and so we may attach K7, the constituent about the judge, to Ko ":

K2

~ Kl

~

L~K3 II I I

/

-----fjJJ

Accommodated material

~KS I

KSI

KII K21 K31 The algorithm for updating parallel structures dictates that the maximal scope element be merged to its image under the relevant tree isomorphism. So we should get K3 A KS· But since KIAK2AK3 and A is associative, we get the effect of adding KS to K I. This is just an application of the little fact about add* and A; parallelism in the context of a sequence of parallel constituents yields the consequence that the appropriate sort of addition is just add*(llCb Ks). In effect KS is a Continuation of K 3. Of course we must also revise the topic statement Ko' and get a new topic Ko" that subsumes the content of KS. As before, this is accomplished by summing the arguments in the same or similar argument places. Ko" looks like this (assuming that z is introduced by a fourth plaintiff).

This discourse and its SDRS introduce a dimension that was not evident in prior discourses in which discourse topics were constructed. While the discourse referent in K4 introduced by the anaphoric pronoun is identified with the sum KIIAK2 IAK31' which was available at the point at which K4 is attached, the SDRS construction procedure now makes only the maximal sum KIIAK21AK31AKsl available to be identifIed with the discourse referent introduced by the anaphoric pronoun in K7. The earlier sum is no longer available once the new topic Ko" has been constructed. Availability has a dynamic element unfamiliar from the account and implementation of accessibility. The SDRS construction procedure allows sums of propositions to be available at one stage of the processing of the discourse but not another. As we have seen, almost verbatim repetition or other explicit parallelism may trigger discourse subordination. But there are other ways of signaling discourse subordination--for instance phrases like speaking of X 28 (21)

Person 1: I have several friends who have dangerous hobbies. Jim likes

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ANAPHORA AND DISCOURSE STRUCTURE to hanglide. Susan skis the backcountry of Idaho all winter long no matter what the avalanche danger is said to be. Mary goes to El Paso whenever she can to talk her friends at NASA into letting her have just a little more time in T38s, and you can't get John out of his old W.W.II Mustang. Person 2: Speaking of Mary, she seems so quiet. No one would have believed it if you hadn't brought in those photos of her in a G-suit.

Phrases like speaking of x allow the speaker to access as a context for information a context that is generally unavailable. Such phrases indicate a species of rhetorical relation that doesn't just support a content-driven segmentation but allows the recipient to move about in the segmentation, to "subordinate" new incoming material to some context that would otherwise be closed off. Definite descriptions that refer to constituents may have a subordinating role as well--as in the following example: (22)

One plaintiff claimed that he had never received his full pay. Another said that he had been passed over for promotion. Another was certain that he had been denied a job on unfair grounds. But the jury didn't believe any of it. They found the first claim especially dubious.

The definite description in boldface can easily pick up the unavailable constituent. The content of the description is used just the way repetition of material is: to define an appropriate attachment site. Thus, we can expect definite descriptions when used anaphorically to behave differently than pronouns. Discourse subordination is a matter of having a particular device that forces the accommodation of a Parallel* relation with some constituent. The device also typically defmes a maximal scope constituent. Discourse Subordination: Suppose

345

interleaved structure. 29 In (23) is example 4 of chapter 7 again: (23)

There are two houses you might be interested in: House A is in Palo Alto, House B in Portola Valley. Both were built in 1950, and both have 3 bedrooms. House A has 2 baths, and B, 4. House A also has a kidneyshaped pool. House A is on a quarter acre, with a lovely garden, while House B is on 4 acres of steep wooded slope, with a view of the mountains. The owner of House A is asking $425K. The owner of House B is asking $600K. That's all I know about House A, and that's all I know about House B.

One might imagine processing (23) with a series of discourse subordinations, thus building up two constituents in a SDRS--one about house A the other about house B.30 The pronouns in (23) ostensibly each refer to one of these constituents. But these constituents might come about by exploiting the parallelism and contrast between the DRSs processed for each sentence. In either case, one could construct an SDRS for (23) that looks like this:

K2

[house A]

K' One might think that the SDRS for (23) has only one constituent within which are a number of contrast pairs--the first pair is about the location of house A and house B, the second is about their date and the number of bedrooms, etc. But then it would be a mystery: to what constituents the pronouns at the very end of the discourse anaphorically refer? On the proposed discourse structure for (23) there is no mystery; the appropriate antecedents are in plain view in the diagram above.

5. EVENT AND PLURAL ANAPHORA REVISITED The principles of SDRS construction have consequences not only for abstract entity anaphora but also for plural anaphora. 31 My hypothesis is that discourse structure, specifically the formation and revision of a topic, is responsible for the construction of non-syntactically marked sums or groups. These sums may be available when their individual members are not. The sums we have looked at are mostly sums of propositions, but we have also looked at a few examples of anaphoric reference to groups of individuals (14.a and 14.b). In this section, I test the "discourse hypothesis" about sum formation for events and individuals further. I provide at least one example that suggests that this principle alone will not be

346

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ANAPHORA AND DISCOURSE STRUCTURE

sufficient. Let us begin testing the adequacy of these hypotheses by looking at the example of event anaphora given in chapter 6, which I repeat here again. (24)

k 2 :=

T~e

Ashers were predictably short of groceries the day of the party. NIcholas Asher went out to get some, got lost and arrived back only after the party had ended. Because of this, the committee made sure that the Ashers never gave a party for the Society again.

In connection with (24), we saw that event anaphora shares a common trait with mass noun ana~hora, in that the singular pronouns this, that and it may anaphorically pick up a certam sum of events, which is itself considered as an event. These sums follow general principles for event summation of chapter 1; events that are temporally, spatially, causally or thematically connected may sum together to form larger events. 32 These may serve as anaphoric antecedents. In (24) the sum of the events and states befalling Nicholas Asher serves as an anaphoric referent for the pronoun. But what remained earlier unexplained about (24) was the impossibility of using some of the events that made up the sum as anaphoric referents for the pronoun. We can now account for these intuitions by examining the discourse structure of (24). According to our principles, (24) creates an SDRS ]I{I containing two constituents KI and K 3, related by Background, but perhaps also by Continuation. Nothing rules out our having both of those relations. Assuming that the latter relation also holds, the proce.dure for S~RS construction then generates a topic summary K2 for ]I{I. In constructmg the tOpIC for such a narrative, we may well appeal to slightly different principles from those in expository or commentary texts like the ones we have looked at to date. We may, for example, rely on principles about sequences of causally, temporally, and thematically related events. That is what I have done here in constructing the topic for ]I{I. The other constituent of the discourse is~, which describes the actions of the ~ommittee..Although this event is caused by the events in the preceding narrative, it mvolves a dIfferent agent (actor in subject place) and so suggests that the constituent describing it be distinguished from what came before. The phrase like because of this signals the presence of a Cause relation. ~ can attach either to the topic K2 or to K 3. The pr~ference is for a hig~ a~achment. A shift in the event narrative to a sequence mvolvmg another agent wIll m general create another constituent and a topic shift. The preference for pronoun to anaphorically refer back to the sum of the previous events helps confirm this preference. For that interpretation to be possible, we must attach ~ to K2 and that entails separating ~ from the rest of the narrative in ]I{1. 33 Here is the SDRS for (24). Some of the details relevant to SDRS and DRS construction have been omitted. 34

e*, u e* = s ED e ED el ED e2 preparations(e*) the party(u) for(e*, u)

e', z

f--:---=--~~~-

k 4 because-of(z, e') z=? e'-[the committee ... ]

•

1

kl

X,s,W,x the Ashers(X) s- X short of W groceries(W) the day of(s, x) the party(x)

Background(kb k3)'

347

k3

y, e, V, el e2, e3 Nicholas(y) e- y went out to get V el- Y got lost e2 - Yarrived back the party( x) erend(x) after(e3, e2)

Continuation(k h k3) Elaboration(k 2, ]I{ I)

Using this SDRS and the principles of availability, we predict the availability of e*,]I{ and KI as antecedents for z. There are two readings of the anaphoric interpretation of sums once again; we may read the anaphoric pronoun as referring to the mereological fusion of the events in e*, or we may take the anaphor to pick up the set and then to be interpreted distributively. The distributive reading is not really an option in (24) because the predicates of which z is an argument. 35 The discourse hypothesis also helps us predict some of the examples of plural anaphora. Consider this example from chapter 2: (25)

Suzie kissed John. Sam was wedded to Mary. They were both very happy.

The observations were that one could get as an antecedent to they in the second sentence the groups Suzie+Sam or John+Mary. But how does the discourse hypothesis account for this last reading? According to the discourse structure view, the first two sentences of (25) are related by Continuation, and so we must have a topic statement. Here the appropriate guide to topic formation seems to be topic/focus information; we sum over the objects in focus namely Suzie and Sam and then over the two not in focus. 36 The third sentence yields a constituent K3 that could be related by Result or perhaps Commentary to the topic statement. On this attachment, the groups Suzie+Sam, John+Mary would be clearly SDRS accessible and available to the discourse referent introduced by they in K 3. Thus, the discourse hypothesis predicts the possible readings for the anaphor in this example. Here is a more complex example which also supports the discourse hypothesis. In this example, the individual constituents of a plural group are not recoverable-though the group is--as our topic constrained theory of group formation would

CHAPTER EIGHT

ANAPHORA AND DISCOURSE STRUCTURE

predict. We cannot get the intended antecedent, even though gender information would appear to be enough to isolate it.

open constituent of the SDRS above. We could attach K4 to K 3 , Ko*, or Ko. Certainly Ko* is a possible attachment, in which case we predict that the group Bill+George or Alice+Shirley are possible antecedents. Attachment to Ko yields Alice+Shirley as a possible antecedent. Note that on none of the possible attachments do we get Alice+Bill, Shirley+Bill, or Alice+Shirley+Bill as potential anaphoric antecedents, which intuitions support. The sum Alice+Shirley+Bill+George, however, is not constructed in the topic position of either K or K'; further research on topics will have to determine whether we have in addition to sums formed by topic a principle that allows us to sum across all arguments mentioned in an available constituent. We shall see some more evidence concerning the discourse hypothesis in the next chapter.

348

(26)

A womanj from school had asked John to go to the movies. His brother wanted him to play basketball down at the Y. His father wanted him to clean up the garage. He didn't want to talk to any of them. He went down to the neighborhood bar for a beer. There, however, he saw herj again.

The intended anaphoric link for the singular pronoun in boldface is difficult to make, in spite of the discourse aids. The discourse hypothesis predicts this. The woman is just one of the many characters that make demands on John. The topic statement has summed over all of them, and she is no longer distinguishable.37 On the other hand, the intended antecedent of the plural pronoun in the penultimate sentence, the sum of the three people John talked to, is predicted to be available given the reasonable attachment for the constituent derived from that sentence A last example shows that the discourse hypothesis is perhaps not by itself sufficient to construct all nonsyntacticall y determined sums of individuals. (27)

Alice went out to eat with Shirley. Later they met Bill and went to the movies. Bill had brought George along. They had a nice time.

The pronoun in boldface does not appear to be able to pick up Alice and Bill, or Alice Shirley and Bill. It can refer to Alice and Shirley, George and Bill, or all of the individuals mentioned. Let us see how the constituent formed from the last sentence K4 attaches to the rest of the discourse structure. The DRSs Kl and K2 from the first two sentences seem to constitute a narrative, and they are hence linked by Continuation and have a topic statement K o, which is about Alice+Shirley's night out ostensibly. K3 contains a main verb in the pluperfect tense, and as Lascarides and Asher (1991) note, this tense form leads us to infer that K3 is related by the relation of Background to K 2. K2 is then an implicit topic of another SDRS K', which when closed off would have something like Alice+Shirley go to the movies with Bill+George as its topic Ko*. Ko continues t to serve as a topic for Kl and Ko*. Thus, the SDRS for (27) looks like this: Ko

•

K

K0Ko*

•

K'

K;" K3 The DRS

K4 from the fourth sentence seems to be linked by Continuation to some

349

6. ANAPHORIC CONNECTIONS ACROSS DIFFERENT ABSTRACT TYPES. In this last section I apply the theory of abstract anaphora and discourse relations to some puzzles about anaphoric relations across different abstract types, a difficult area that I mentioned already in chapters 1 and 4. We saw there how the anaphoric phenomena concerning abstract entities of different types was complex. The interaction between the constraint of availability and discourse relations discussed in the previous section offers us the tools to analyze some of those complexities. One puzzle is the strange "type leniency" in anaphoric relations across objects of various projective attitudes, those attitudes whose objects the semantics characterizes as sets of propositions. As noted in chapter 1, the typology of Asher (1987) predicts in general the impossibility of proposition anaphoric connections between the complements of pure propositional and projective propositional verbs. It appears generally impossible to quantify over or to refer anaphorically across objects of propositional and projective propositional verbs, as we saw earlier. This is what our typology predicts. The typology also predicts that pure propositional verbs and projective attitude verbs within the same category, like for instance rogative, buletic or permission verbs, may share complements through anaphoric linkage. It is curious, however, that proposition anaphoric relations appear to exist between the complements of different projective attitude verbs. While projective attitude verbs all take sets of propositions as objects, these sets may differ vastly in character. These verbs do not share complements in the sense of having the same set of propositions as complement. The set of answers to a question will only by chance coincide with the set of propositions that constitute the object of a buletic or a permission verb. Furthermore, the simple identification of a subDRS of the sort found in a buletic context with a discourse referent introduced in a question context threatens, in view of the analysis in chapters 3, 4 and 5, to produce nonsense at the level of the DRS. Nevertheless, consider the apparently acceptable anaphoric relations in (28.a-b): (28.a) John asked to go to the park. His mother allowed itj (refused ¢j, --i.e. i that John go to the park.

=

.~-~~-~~~~~----------~~~-~-~.~---------------------------------- ..

350

CHAPTER EIGHT (28.b) John wanted to go to the park. He asked his mother ¢i. She refused ¢i, (allowed iti, asked his father ¢i), where i = that John go to the park. (28.c) John asked to go to the park. His mother wanted iti . i = that John go to the park.

On the other hand, not all such links are equally felicitous--e.g., (28.c). What sort of mechanism is suggested by such anaphoric connections? It is impossible to treat the links between the discourse referent introduced by the pronoun and the DR-theoretic structure characterizing the projective propositional antecedent as identity between the objects of those attitudes, since that would produce at best the wrong semantics for at least one of the attitude verbs and at worst sheer nonsense.3 8 Rather, the anaphoric link involves a characterization of the object denoted by the pronoun from material supplied by the antecedent. This reconstruction is impossible at the level of possible worlds or model theoretic interpretation. Once we have determined a given projective proposition in possible worlds semantics terms, we have only a set of sets of worlds. We have in principle no way of getting back to a propositional generator of this set. But this is relatively easy to do at the DRS level. The objects of projective attitude verbs consis of a subDRS and an operator. To reconstruct the new attitude object from an antecedent attitude object of a different and incompatible type, the reader strips off the operator of the old attitude object to obtain the subDRS or predicative DRS that provides the "core content" of the object. The next verb may require that the structure of this core content be modified. For instance, it may require that a predicative DRS be transformed into a subDRS or vice-versa (the latter happens especially in the case of sloppy identity). This modification makes use of the control equations provided by many attitude verbs. The anaphoric reconstruction then adds whatever is the appropriate operator for the type of attitude verb. Given the amount of work involved in these anaphoric connections, it is not surprising that they are subject to constraints. The appropriate constraint is that such anaphoric connections are possible only in the presence of cohrence relations. One cannot reconstruct the appropriate object without certain additional information from the text. In view of the important role that discourse and coherence relations play in proposition-type anaphora, it is also not surprising that anaphoric links between the complements of projective propositional verbs are allowed only if the reader is able to construct a coherence relation (occasioning, causing, explaining) to hold between the two attitudes. The presence of such a discourse relation allows us to reconstruct the appropriate complement for the verb whose complement is the anaphor from its antecedent. The bad case in (28.c) is one where no coherence relation obtains between the two clauses. Speakers say that case is puzzling, precisely because they don't know "how to put the discourse together" in the words of one informant. Consider the following minimal pair: (29.a) John allowed Mary to go to the park. She asked him ¢. (29.b) John allowed Mary to go to the park. She had asked him ¢.

ANAPHORA AND DISCOURSE STRUCTURE

351

To speakers who still have the pluperfect in their dialect of English, (29.b) is much better than (29.a), because it naturally provides for an explanation link between the two events. (29.a) on the other hand, where the action in the second clause is interpreted as simultaneous or following that of the first clause is almost impossible to get. One naturally reads it as preceding. If the second event is read as preceding, it constitutes a natural explanation or cause for the first event. The felicity of the anaphoric link: then depends upon our ability to construct an appropriate scenario and to create an acceptable causal, or temporal path. This is very similar to the problem of constructing paths to facilitate event anaphora. The method for handling anaphoric connections between different types of projective verbs extends to anaphoric connections between pure propositional and projective verbs. Although in general such connections are not allowed, reconstruction is possible given the appropriate discourse relation. The contrast between the pair in (30) is analogous to the contrast in (29): (30.a) John believed that he could go to the park. His mother allowed it. (30.b) John believed that he could go to the park. His mother had allowed it. By putting the second attitude verb into the pluperfect, we allow for a natural explanation for John's belief. This explanation link: now allows us to reconstruct what it was that John's mother allowed and makes the anaphoric connection felicitous.

7. CONCLUSIONS ABOUT ABSTRACT ANAPHORA In chapter 6, I introduced abstract anaphora, and in chapter 7, a theory of discourse segmentation. In this chapter I have put the two together and discussed the effects of discourse structure on abstract anaphora. I have concentrated on the interaction between SDRS construction and the constraints of availability and weIlfoundedness. These dictate constraints on the acceptability of embedded constituents as anaphoric referents. I showed how a wide number of phenomena support the discourse theory and the discourse constraints on anaphora. Also I have indicated how SDRS construction and the constraints affect event and group anaphora as well. In the next chapter I look at one more application of the theory of discourse structure and anaphora--the theory of concept anaphora.

11 concentrate here solely on pronominal anaphora. Lascarides and Asher (1991) and Eberle (1991) investigate how discourse structure affects temporal anaphora. 2The importance of discourse segmentation to anaphora is already well-known in studies of individual anaphora (Grosz 1977). But since events or propositions are the natural terms of coherence relatIons, one would expect that these relations are even more important in determining the availability and salience of antecedents of some abstract type. 3 For a discussion and defense of this claim, see Fox (1987) and Grosz & Sidner (1985). 4This expands Fox's definition of active and controlling segment. It captures and refines the notion of a rigfit frontier <Webber 1988). Dahlgren and Lord (1990) show findings to support my constraInt and actually an even stronger one in their study of Street Joumal articles. ln those

wan

_-

------------"--"-----CHAPTER EIGHT

ANAPHORA AND DISCOURSE STRUCTURE

articles anaphoric reference involving individual discourse referents occurred in the same segment or to the gfobal topic (occurring in some dO!llinating n~e). Pox (1987) has examples from narrative literature that show that other connectiOns are possible. SSince the underlying set theory of DRT is standard set theory with foundation, we must make each one of the nested DRSs alphabetic variants of each other. k in each DRS will be replaced by a new discourse referent. But then we have a coherent DRS. The embedding conditions for such an infinitary DRS amount roughly to say!ng the followi~R: there i~ a.true propo~ition such tha~ it is identical with the proposition that there IS a true proposItion that IS IdentIcaf With the propoSItion that there is a ... 6In virtue, that is, of an axiom like [ & back in space(lX) & shuttle-departs@] > part-Of(lX, ~). as well as the general axioms for Elaboration. It. is also possible that Explanation rela~s k I and k 2 • ?ut it is not surprising that the first sentence of (5) IS a tOPIC sentence. !n newspaper articles (~m which (5) was denved), there are almost always sentences that state the tOPIC of the story. The headline of the story is often useful in this regard too. 7A similar, though simpler, unambiguous example of attachment occurs with the Financial Times example (2) of thiS chapter. 8 Segmentation built up by discourse relations thus differs from th~ segmentation of c9~tent brought on by semantic or logical opera.to~s. These really are essential to the .truth conditIOnal content of the discourse and cannot De elimInated. Too often (Fox 1987 PolanYI and Scha ~984), logical relations like the conditional have been assimilated to discourse relations, obscunng an important distinction. 9Thanks to Kathy Dahlgren for noticing this example. 101 have not given K* a topic statement. One could give a topic, but I see no need to do this. My theory does not say that such constituents fonned by rhetorical relations need to have topic statements. llAs Rainer Btuerle (1987 and Saebo (1990) show with evidence from Gennan, dis~ourse PaI1icles function may make the difference petween acceptable. and unacceptab!e anaphonc connections. Parallelism and contrast have to do With the sameness or difference of polanty. In the examples abo,:e, we have two clauses of contrasting polarity-- p<)sitive attitudes give us a p
22By the definition of availability, K21\ JK:! is also available to the di~cours~ r~ferent introduced b~ the prononn in K4. This interpretation would make the content of the entire plamtIffs story also a pOSSible antecedent to the discourse referent introduced by it, but the contrast then w9uld be defmed betwee~ truth and the jury's disbelief, y;hich is not as strong as the contrast given above, and so thiS identification is not a real possibility. 23It is perhaps possible that K5 does. not force a topic s.hift but only a mo.dificatio~ of the previ~us topic. K5 still describes a part of the trial, after all. ~ut thiS stretc~es our notion of topiC .Int;<> somethIng it is not designed to do; it too bec
352

[

353

DISCOURSE STRUCTURE AND CONCEPT ANAPHORA CHAPTER NINE

APPLICATIONS OF THE THEORY OF DISCOURSE STRUCTURE TO CONCEPT ANAPHORA AND VP ELLIPSIS

In this chapter I apply the theory of discourse structure elaborated in the previous two chapters to concept anaphora. The semantics and discourse effects of parallelism and contrast as well as other rhetorical relations will play an important role in the analysis of concept anaphora. Discourse parallelism and contrast are natural extensions of syntactic intra-sentential constraints that many researchers have claimed guide anaphoric processes like VP ellipsis. 1 The discourse constraints, however, are needed to handle examples of VP ellipsis that other theories cannot analyze.

include the predicative DRSs derived from C-abstraction. I shall call such predicative DRSs quasi-constituents. I shall then allow discourse relations to take quasiconstituents as well as constituents as arguments. Then we shall be able to apply the machinery of SDRS updating to help with cases of concept anaphora. An application of C-abstraction potentially yields many different sorts of predicative DRSs. Thus, C-abstraction is defined relative to a concept discourse referent in a particular context; which predicative DRS an application of C-abstraction yields depends on the condition in which the concept discourse referent occurs. If the concept discourse referent occurs in a condition which requires, for its satisfiability, that the concept discourse referent picks out a concept with n argument places, then Cabstraction must produce a predicative DRS with n argument places. For VP ellipsis or many examples of the so called "do it" or "do so" anaphora, the predicative DRS is typically derived from the verb phrase. 2 But as the examples from chapter 6 indicate, not all forms of concept anaphora pick up predicative DRSs formed from verb phrases, and so there are several quasi-constituents to consider. Consider for instance: (La)

1. EXTENDING SDRS THEORY

(1.b)

As discussed in chapter 6, concept anaphora is a relation between a concept discourse referent and a predicative DRS, which I call the "source." In VP ellipsis the source always involves a predicative DRS derived from a verb phrase, but in concept anaphora other predicative DRSs are available. This sort of anaphora is very similar to those instances of proposition anaphora in which a discourse referent is identified with a subDRS. One major difference is that an additional principle of construction is needed to isolate the appropriate predicative DRSs--the principle of C-abstraction, which was introduced in chapter 6. The task of this chapter is to see how discourse structure and the discourse constraints, availability and well-foundedness, affect concept anaphora. We have already seen in chapter 8 that concept anaphora behaves just as one would expect according to the well-foundedness constraint. A predicative DRS source for a concept discourse referent c cannot contain c in its universe. This rules out discourses like John [does itil, where it introduces a concept discourse referent and does it yields the predicative DRS source. The constraint of well-foundedness implies that the concept discourse referent c and its source must occur within two constituents, neither of which is d-subordinate to the other. A more involved question is: How does availability affect concept anaphora? As the definition of availability stands, it applies to concept anaphora, since C-abstraction introduces DR-theoretic structures within certain constituents. But to be really useful, we must extend the SDRS machinery. SDRS theory relies on the notions of constituents or d-subordinate subDRSs. Parallel and Contrast exploit these concepts, as do other discourse relations. We must extend the notion of d-subordination to

(1.c)

354

355

Every Swiss farmer who owns a donkey beats it. But if it's an Austrian farmer, that isn't true John always argues with Mary. That's not true of Sam and Susan. They have a peaceful marriage. John cheated Mary out of her inheritance. Then he did it to Susan.

Even with these forms of concept anaphora, there are constraints. Although the predicative DRS linked with the pronoun in such examples need not be the entire verb phrase, it must nevertheless contain the condition derived from the main verb or the matrix condition of the constituent of which it is apart. 3 From this review of C-abstraction, we may define what are the appropriate predicative DRSs to use in extending SDRS notions like d-subordination and modified embedding tree. The precise definition of the appropriate predicative DRS relative to a discourse referent or DR-theoretic structure ex and a constituenty in a tree 't (for y), :F(y, ex, 't), is given in the Appendix of this chapter. I define an appropriate predicative DRS using DR-theoretic structures, as well as discourse referents, in order to define quasi-constituents even when no concept discourse referent is present. As the concept discourse referent or DR-theoretic structure will have been introduced by a particular sort of construction and will occur in a particular type of condition, this, together with an ME tree 't, uniquely determines the appropriate predicative DRS in a constituent of't. The next step is to extend the notion of embedding trees and d-subordination by adding predicative DRSs of the appropriate type. An embedding tree may be extended to produce an extended embedding tree relative to a designated discourse referent or DR-theoretic structure by inserting between nodes ex and ~ the appropriate predicative DRS containing the matrix condition for the immediate, d-subordinate constituent~. Similarly, I extend ME trees to modified extended embedding trees or

356

CHAPTER NINE

DISCOURSE STRUCTURE AND CONCEPT ANAPHORA

MEE trees. I will use as notation for the extended d-subordination or d*subordination, relation, d*~ Graphically, this is what the definition of a MEE tree gives relative to the ME tree that it extends.

particles that introduce them, determine what are the desig~ated DR-theo:~tic structures for defining the appropriate predicative DRSs. According to the defimtI~n of MEE tree, then, each constituent has an MEE tree consisting of two nodes each, m which the lower predicative DRSs are derived from the respective VPs of the two sentences.

Modified Embedding Tree ME Tree

k

kl~k2

Modified Extended Embedding Tree MEETree k

357

ko

k[I/~k12

I Po

1

k3

PI

P2 [

k3 [

P3 It is straightforward to define Parallel and Contrast and Parallel* and Contrast* with respect to such MEE trees, mimicking the definitions of chapter 7 on ME trees. The relations will now accept quasi-constituents as well as constituents as arguments. We must thus constrain the tree isomorphisms so that they map nodes of the one type onto nodes of the same type. Like constituents at the discourse level, the predicative DRS quasi-constituents of MEE trees are individuated by discourse relations. They are not just formed as superstructures of the basic DRSs introduced by the construction procedure; they result from a use of C-abstraction in conjunction with a modified embedding tree, the choice of which is motivated by the presence of a Parallelism or Contrast or some other discourse relation. Thus, discourse relations not only impose constraints; they are essential to the analysis of concept anaphora on my view With the extensions of Parallel and Contrast to quasi-constituents and MEE trees, we can now analyze discourses that exhibit both parallelism and contrast but also have simple ME trees. Recall that Parallel* and Contrast* may hold of two constituents, only if two relations have different scopes. But with ME trees for simple constituents, there is no possibility for assigning different scopes. Thus, a discourse like (2) from the last chapter is not predicted to be good: (2)

John likes Mary. But I like her too.

The presence of the discourse particles but and too require that the constituents support both Parallel and Contrast. For (2), however, there is only one simple ME tree for each constituent ko and kb and so the two relations cannot have different scopes. The MEE trees for ko and kl allow for different scopes. The parallel discourse particle too has scope over the VP and so the DRS condition too(K) has scope over the predicative DRS that the VP introduces. It is this predicative DRS that defines the appropriate predicative DRS in k o; the scopes of discourse relations or the

The contrastive particle but has scope over the entire sentence, while the parallelism particle too has scope only over the VP. We can ea~ily imagine a contrast betwe~n .the two highest constituents of the MEE trees; there IS a contrast between John likmg Mary and me liking Mary. On the other hand, the fact that too has scope over the VP is accommodated by the tree isomorphism between the two verb phrases and the fact that the two properties introduced by the VP are identical. Parallel has scope over the predicative DRSs, while Contrast has scope over the root constituents. (2) makes perfect sense now.

2. EXAMPLES OF OVERT CONCEPT ANAPHORA Let us first look at a simple example of over concept anaphora. It yields some familiar morals. (3)

John forced Fred to eat the funny looking soup. Sam did it too.

The second sentence of (3) contains a parallelism discourse particle. In order for the SDRS resulting from (3) to be coherent, we must have a Parallel* relation and update the SDRS using the constituent revision procedures associated with parallelism. The second sentence introduces a concept discourse referent c occurring within the condition do(x, c). This licenses the use of C-abstraction; and by the definition of ,}(y, C, 't) the appropriate predicative DRS relative to y, c and 't, an appropriate predicative DRS identifiable with c must be a one place predicative DRS with a. 'A.abstracted Agent role. This suffices to define uniquely two extended embedding trees, which look like this:

CHAPTER NINE

DISCOURSE STRUCTURE AND CONCEPT ANAPHORA

k'o

I

c

Note here the relation between the concept discourse referent and the VP within which it is embedded; the do action verb only serves to define an appropriate predicative DRS--the relevant part of the VP do it is just the concept discourse referent introduced by the pronoun. 4 This is a consequence of clause (iv) in the definition of J{y, c, 't) in the Appendix. Assuming that the discourse particle too has scope over the entire second sentence, we must construct a tree isomorphism that takes the whole embedding tree 't2 into a subtree of'tl. Further, the definitions of chapter 7 require that the subtree of'tl have the same root as 'tl. We may defme two bijections, since we may derive two MEE trees for 't I--one is 't b the other a tree in which k o, PI and kl collapse together. This leaves two possibilities for the bijection pertaining to c: we can map c onto Po or c onto PI. The first bijection obviously satisfies parallelism. The second, however, does too, since force Fred to eat the funny looking soup entails that he did eat the funny looking soup, and it may simply be this property, the eating of the soup, which the author intends to assign to the two agents. The constituent revision procedure under Parallel then requires that c be identified with either Po or PI--namely the predicative DRS formed from the VP force Fred to eat the funny looking soup or the predicative DRS formed from the VP, eat the funny looking soup. These are just Jhe expected readings for (3)--the reading where c is identified with the predicative DRS derived from the higher VP being preferred. The theory extends to handle quite complex examples. (4.a)

(4.b)

Sam doubted that they had to [prepare for the Latin test]i. He did not study, and he flunked. Susan also doubted that they had to do it i. But she did iti anyway, and she got an A. John [ate the funny looking SOUP]i. John got sick. He went to the hospital. But George did iti too, and he didn't get sick at all.

Consider first (4.a). The SDRS for (4.a) contains two constituents in parallel, one for John and the other for Susan. These constituents also each contain two constituents-one about an attitude, the other about the results. The almost perfect parallelism in (4.a) between the two attitude predicates forces the marked anaphoric connection between the first occurrence of it and the indicated antecedent, even though the indicated antecedent is not the closest antecedent. There is also a Contrast relation,

359

which one may satisfy in two ways. One way is that given the same doubts, the behavior of John contrasts with that of Susan. The other is that Susan's behavior contrasts with her doubt. The latter is much more salient. Notice that it is the Contrast relation that is appropriate for determining the second concept discourse referent's antecedent. Below I give an extended constituent graph for (4.a), which depicts the appropriate bijections for the Parallel and Contrast relations. The arrows again represent the tree isomorphism.

KI

•

~4---------------K2

•

OClt

KI3

\

OC

K!2

/\

2

K21

\

P I3 / \ P21 \ -,P 121 P!22 \ KI31_------------l---K211

I

PI311_----------~---

I

I

PI3111~4------------_

C

Contrast(K b K 2) Result(K I3 , K 12 ) Result{K2 b K2 2) Contrast*(K 12 , K2 2), Parallel*(K I3 , K 21 ) Here is a table indicating from what text the constituents and appropriate predicative DRSs are derived. K 13: Sam doubted that they had to study for the Latin test. K2 3: Susan also doubted that they had to do it. KI2 : He did not study and he flunked. K22 : But she did it and she got an A. P 13 : doubt that they had to study for the Latin test. P 2 I: doubt that they had to do it. P I22 : flunk PhI: study P 22 : get an A c: it K 131 : that they had to study for the Latin test K 211 : that they had to do it. PI 311: had to study for the Latin test P 13111: study for the Latin test

DISCOURSE STRUCTURE AND CONCEPT ANAPHORA P 2111 : had to do it

I

Both the Parallel and Contrast relations are maximal bijections on the structures they are defined on. The update procedure dictates that the antecedent for c and c I is the predicative DRSs PI 3II I. Given the parallelism and contrast defined, this is predicted to be the only antecedent. Moreover, the theory predicts that since the contrast and parallel relations are maximal, this is the preferred binding of the anaphors. 5 To explain the anaphoric connections in (4.a), we need only our normal apparatus of discourse relations and C-abstraction. Besides the tree isomorphism that defines the parallelism for the attitude contexts, there is a tree isomorphism from K24 to K23 defining a Contrast relation. I used one MEE tree to define one tree isomorphism and a parallelism relation between two constituents and another to define another tree isomorphism and a contrast relation between one of those constituents and another constituent. The tree isomorphism from K2 3 to K24 is defined on a particular modified embedding tree: the conditions in K 23 that result from the processing of doubt that they had to do serve to define the opposite polarity from do in K24. The square indicates the one target node for the relevant MEE tree and shows the collapsing effect of the MEE tree on nodes of the other MEE tree used to define the parallelism. The discourse structure of (4.b) is less challenging but contains a new element we have so far not encountered.

Kll

I

KI2 and K 13 , which are derived from the clauses, John got sick and he went to the hospital., are linked by the relation of Result to KI b which derives from the clause John ate the funny looking soup. Thus, we take KI3 as a continuation of K 12 , and so we will infer by topic based updating a dominating constituent Kill' which now inherits the Result relation to KII from the constituents it dominates. The original constituents KI2 and KI3 now are elements of an SDRS llC 112 , directly dominated by

361

Kill' KII is the implicitly represented topic ofllC l . All the constituents in llC l are about John and the results of something he did. llC 2 contrasts with the constituent about John and informs us about the actions of George, so it forms a distinct constituent from llC l . This means that we must close offllC h and then by our construction rules, Kll will become the explicitly represented topic of llC l . Although llC 2 comes from one sentence, it has two constituents--one about a topic event and the other about a result. Thus, we have an exception to our default rule that basic constituents result from full sentences, not separate clauses; but in (4.b) the clear discourse function between the two clauses and the parallel structure of the preceding discourse serves to separate them. The concept discourse referent introduced by the pronoun it licenses the use of Cabstraction in building a MEE tree for (4.b). By the definitions, the appropriate predicative DRSs that will arise from C-abstraction will be those that result from the processing of VPs. We now want to explain the contrast and parallelism and their scopes on the clause that generates llC 2. Consider the extended embedding tree below for (4.b) relative to c. I assume that the scope ofthe contrast concerns all ofllC 2 and is the relation by means of which llC 2 is attached to llC l . The scope of the parallelism particle too is only over the first clause or the DRS K21 derived from it. We need to appeal to a MEE tree in which the structure under K2 I is collapsed. Here is the appropriate MEE tree for the whole structure with the natural isomorphism between the various nodes drawn in; the collapsing effect of the MEE tree is shown by the box; the structure consisting of the SDRS below Kill and its two DRS constituents KI2 and KI3 is ignored. The natural isomorphism suggests mapping lK2 to llC h K21 to K I h K22 to K2 and c to P II. This gives us the intended reading, but what do we do about P 22? The natural suggestion is to map P 22 to the join of P I2 and P 13 , P I2 1\ P 13 , where 1\ applied to predicative DRSs yields the standard sort of property conjunction defined in the Appendix. The strategy of exploiting joins just used gives the right results for examples like: (4.c)

John [ate the funny looking soup]j. John [got sick]j. He [was taken to the hospitalk George did itj too, but thatj didn't happen to him.

It seems to me (4.c) can only have the reading indicated by the indices on it--namely that George ate the soup but he didn't get sick and wasn't taken to the hospital. Let us assume that that is a pronoun that picks up an event type--presumably one in which the Patient or Theme role is lambda abstracted. Then the join of the predicative DRSs above gives us just the right concept with which to identify the discourse referent introduced by that.

3. VP ELLIPSIS I now tum to the effects of discourse structure on VP ellipsis. In most analyses

DISCOURSE SlRUC1URE AND CONCEPT ANAPHORA of VP ellipsis, the antecedents of VP ellipsis are assumed to be present in the previous clause. As many have noted (Bresnan 1971, Sag 1976), syntactic parallelism between two adjacent clauses often plays an important part in which V is recovered. If there were a constraint on VP ellipsis such that VP ellipsis was constrained to hold only between two adjacent clauses, then one could avoid the discourse machinery and have a much simpler account. As I think Klein and Stainton-Ellis (1989) convincingly demonstrate, however, this is not the case. VP ellipsis looks much like concept anaphora with explicit anaphors, and is sensitive to discourse effects. Here are some of their examples, with the null VPs and their intended antecedents indicated. (5.a) (5.b)

(5.c)

(5.d)

(5.e)

(5.t)

If you [work hard, make the right choices, and keep your nose clean] 1. you [get ahead] 2. If you don't ¢I you don't ¢2. It was of course preposterous; nothing so elementary could possibly [work] I; there must, one would think, have been [some other precautionsh. One would be wrong. There weren't ¢2 and it did ¢I. Xenophobia pestis, like the hardy native perennial it is, burgeons as lordly young Mediterranean male cyclists sail into oncoming traffic with such seigniorial arrogance that even as we swear and skid we look round wildly for street signs to see if he's [right] I and we're [wrongh and the one-way system's [undergone one of its periodic reversalsh He isn't ¢I. We aren't ¢2.lthasn't¢3. A: You never [go swimming.] I B: That's because I don't [look good in a bathing costumeh. I might ¢I if I did¢2 A: He's just [appointed Hawkeye chief surgeon over meli. B: He can't ¢d Doesn't he [know that's [against regulationshh? A: he did ¢b it is¢3 and he does¢2. I was [really thinh then, and I tried on some ski-pants that [looked really good on meh, and I should have [bought themh But I didn't ¢3, and now I'm not ¢1. and they wouldn't ¢2.

These examples, drawn from actual written text or oral conversation, show that the simple assumption about VP ellipsis as a phenomenon concerning only adjoining clauses is wrong. To discover the appropriate antecedents for these examples, we will have to exploit discourse structure and semantic content. As observed earlier in chapter 7, the well-foundedness constraint also applies to VP ellipsis. The predicative DRS may not contain the identifying condition introduced by the anaphor. The major point of interest, however, is how availability interacts with VP ellipsis. Let us begin by looking at some simple examples. (6)

John didn't say that Mary [hit him] I. But Bill thought she did ¢I.

The availability constraint predicts that the embedded, predicative DRS K produced

363

by hit him will be available to a concept discourse referent c introduced by the null VP node only when the context of K suggests some discourse relation like Parallel or Contrast with the context of c and that relation is maximized by the tree isomorphism on which c is paired with K. Because c is introduced by a VP, C-abstraction must pick out a I-place predicative DRS that is also derived from a VP or a Boolean combination thereof. So the extended embedding tree for (6) and its constituents is completely determined. In this case, the contrast is clearly maximized by picking the following two MEE trees and tree isomorphism 1'} for the constituents, KI and K2 derived from the two sentences. The collapsing effect of the MEE tree is shown by the rectangle on the extended embedding tree.

KII

....- - - - - -

I

The MEE tree on the left collapses the subDRS constructed using the negation and the predicative DRS derived from the higher VP; together these defme a predicative DRS node with the matrix condition for Kill in KJ. (say(x, Kill)), which gives a salient and maximally plausible contrast to the matrix condition of K211 in K 2, think(y, K 211 ). The MEE tree on the left is also the maximal MEE tree for which the contrast is defined. By the rules for revising contrasting constituents, we get the intended reading on which c is identified with Pili. Because 1'} is the tree isomorphism that gives us the maximal contrast and in fact the only plausible contrast, the theory predicts that this reading is the only one. A slightly more complex example of VP ellipsis is (7). (7)

Every Swiss farmer who owns a donkey beats it. But if an Austrian farmer does, he doesn't.

SDRS structure is needed for this example; it exploits a contrast to assign the concept discourse referents the right predicative DRSs. But the contrast cannot be defined on syntactic or clausal structure; it must be defined on the semantic structure of embedding trees. At the syntactic level, there is little to suggest a tree isomorphism-the first sentence is a simple clause while the second is a compound sentence. The embedding trees for the two clauses are not quite isomorphic. The "* shows the DRS operator that holds between the two subDRSs to help see what is going on. K 23 is the subDRS of K2 2 within the scope of the negation operator. Note that the

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - --

CHAPTER NINE

DISCOURSE STRUCTURE AND CONCEPT ANAPHORA

second extended embedding tree has two concept discourse referents instead of predicative DRSs, since K2 2 and K21 contain the conditions, do(x, CI) and do(x, C2) respectively. But both discourse referents are introduced by null VPs, and so again the extended embedding tree is determined to contain only VP translations in addition to the constituents of the original embedding tree. The rectangle again shows the collapsing effect of the choice of MEE tree on the original extended embedding tree. The arrows give us the tree isomorphism.

have the equation z = ? filled in. Thus, in identifying C2 with P l2 " the meaning of C2 is not completely determined. Anaphora resolution must be performed to complete this equation, and an appropriate antecedent for z', the correlate of z in P l2 " must be found. All the anaphorically relevant grammatical features of z carry over to z'- these comprise gender, number and also disjoint reference domains.? Notice, however, that as is the case here, the discourse referents accessible to z may not be accessible to z'! That is because the logical context of P 12 ' may differ from that from which P l2 was abstracted. In the case of (7) under discussion here, z' is identified with y', a discourse referent introduced in P 11 '. That is permissible and perfectly interpretable model-theoretically, since the following two DRSs are equivalent:

304

II II II F

r

I

MEE tree for sentence 1

MEE tree for sentence 2

K I · · - - - - - - - - - - - - - - K2

----------

~ --"""K 22

I

u, y', e2 ~---~

CI

= I.e

Av

Swiss farmer(x) donkey(y) e-own(x, y)

Austrian farmer(u)

,------

CI = I.e AV I--_..L-V'_ __ donkey(y') e -own( v, y')

....

....

z=? el-beat(x, z)

Zl

=?

--, C2= I.e' AW

I

y'

donkey(y')

~2

x,y,e

Austrian farmer(u)

Austrian farmer(u)

I

The negation and K22 serve as part of the matrix condition for K2 3. 6 This tree isomorphism gives us a maximal contrast and indeed this is the only tree isomorphism on which a contrast is plausible. So the theory requires the identification of CI with an alphabetic variant of PI!> P II ', and the identification of C2 with an alphabetic variant ofP I2 , P I2 '. After constituent revision, the constituents of (7) look like this:

365

I

I

donkey(y') e2-own(x', y')

I e -own(v, y')1 e2- C2 (u)

The equivalence above is an example of an application of DRS conversion of C2 and u and the following rule involving the characterization relation =, which is also valid: a = /3,
z'

1---------'

z'= ? e' -beat( w, z'

(7) also introduces some intriguing notions about anaphora. P I2 contains a discourse referent z introduced by a pronoun; but as it is a VP translation, it does not

(S.a) (S.b) (S.c) (S.d)

John said that Mary hit Fred. Bill did ¢ too. John said that Mary hit Fred. But Bill certainly did ¢. John said that Mary hit Fred, and Bill did ¢. John said that Mary hit Fred. Bill said she did ¢ too.

It appears that in (S.b) and (S.d), the null VP must take the lower VP of the first clause as its antecedent, while (S.c) is ambiguous. Let us look at these examples in some detail. All of them except (S.d) have exactly the same extended embedding trees

DISCOURSE STRUCTURE AND CONCEPT ANAPHORA for their two constituents. Below '1:1 is the extended embedding tree for the first constituent while '1:2 is the extended embedding tree for the second. '1:1

'1:2

KII

K21

I

I P ll

C

I KI2

I P 12 The extended embedding trees for the two constituents of (8.d) are isomorphic to each other and to '1:1. Consider (8.a) fIrst. There are at fIrst two sets of possible MEE trees for (8.a). In one set, the MEE trees are isomorphic to '1:1 and '1:2 above. This leads to the following tree isomorphism between '1:2 and a subtree of 'I: I: Figure 1: '1:1 K ll· · - - - - - - K21

I

I

PI 1""-------- C

I K12

I In another pair of MEE trees, the top nodes collapse as indicated in the diagram below with the box. This means that the matrix condition of P I2 in KII is complex.

Figure (2) presents an MEE tree that will not support parallelism, for the matrix conditions for P I2 and c are not only far from identical, they are not even plausibly equivalent; they suggest very strongly a contrast between just saying that

Figure 2: '1: 1 Kll

I

.

'1:2

'1: 1

'1:2

K21

Kll

I

I

K21 I P 21

[V' P I2

367

P ll

I K12

I P I2

I K22

I

C

368

DISCOURSE STRUCTURE AND CONCEPT ANAPHORA

The presence of the particle too which may have scope at least over the main VP of the second sentence requires that we find a parallelism relation between the subtree defined from that VP and a corresponding subtree of 'to Moreover, the maximality constraint for parallelism contexts dictates that we must maximize the size of the subtrees of the MEE trees defining the parallelism relation with respect to the original extended embedding trees. But we can define parallelism on the extended embedding trees 'tl and't2 themselves. So the constraint dictates that we must use 'tl and't2 to define the tree isomorphism and the parallelism relation. By the constituent revision procedure, this means that c must be identified with the predicative DRS formed from the lower verb phrase of the first sentence, or PI 2. Much more complex applications of availability are to be found in Klein's and Stainton-Ellis's examples. The example in (5.a) for instance contains a discourse relation that we might call Converse. Converse is a relation that exploits the DRtheoretic form of constituents. The two constituents must each have a condition of the form of a conditional (preferably the only condition), and if the first constituent is of the form a => ~, then the second should be of the form ,a' => ,W or W=> a', where a' and Ware logically equivalent with a and~. The formal definition is found in the Appendix. Like Parallel and Contrast, Converse exploits the discourse structure and also forces a particular kind of updating of the SDRS structure. We should expect this for many rhetorical relations. See the Appendix for details. With converse so defined, the theory predicts that there is only one possible anaphoric linking for the concept discourse referents introduced by the processing of the null VPs in the second sentence of (5.a). Here is the MEE tree of (5.a) with the tree isomorphism indicated by the arrows and the converse relation given by the ellipse. One can also see where the contrasts are in each bijection--they are given with the matrix conditions for the concept discourse referents in K21 and K2 2 respectively, which contain the negations outside the subDRSs K2 II and K2 2 I.

(5.b)

369

It was of course preposterous; nothing so elementary could possibly [work] I; there must, one would think, have been [some other precautions]. One would be wrong. There weren't ¢2 and it did ¢I.

There are several modalities to be handled in this sentence and pose a challenge for DRS construction. The first clause introduces a constituent KI that is a commentary on some event, object or state of affairs. The next two clauses, introducing constituents K2 and K 3, appear to continue this general commentary or perhaps more accurately to elaborate on it. Given the treatment of no in chapter 2, K2 will contain two subDRSs K 20 and K2 b and the complex condition K 20 => K2 b where K2 I has only one complex condition, ,K 22. K3 is equivalent, I think, to one would think that

there must have been some other precautions. The next sentence, which introduces a constituent K4, breaks with the previous commentary and introduces a commentary on it. I will suppose that K4 contains a proposition discourse referent p within the scope of the evaluating context--wrong in thinking that. We must attach K4 to the SDRS containing K I- K 3. K4 could either be attached to K3 or to K I. Given the high attachment, we have the following picture of the SDRS with the discourse processed this far. One can see the structure of K2 with its constituents K 20 and K2 I. K22 is a constituent of K2 I containing itself a complex condition OK 2 3, where K2 3just has the atomic condition work(x) in it. The high attachment also allows z to be identified with K. Clearly, K is available and SDRS accessible to p.

CI

The extended constituent graph makes clear that c and c I have only P II and P 12 as antecedents. There is no MEE tree other than the one that is isomorphic to the extended constituent graph that will enable Converse to be satisfied. A similar analysis is available for (5.b).

The next sentence, introducing a constituent K5, makes clear that the high attachment is preferred. For K5 gives the grounds for why one would be wrong in thinking both K2 and K3--i.e., K. K5 must be attached to K4 or Kb and only K4 is a plausible attachment point that would give us this meaning. Let us assume that p has

~

_____

~~=~~~-~-~~~~~-------~~IiIiF""---'~-----------------------.--.-

CHAP1ER NINE

DISCOURSE STRUCTURE AND CONCEPT ANAPHORA

been identified with l{, and so l{ is a constituent of l<4. The rhetorical relation that obtains between the l<4 and KS is Support or Evidence. This relation exploits SDRS structure, as well as content. In order to maximize the support relation that KS has for l<4 then, we must find the appropriate predicative DRSs for the concept discourse referents Cl and C2 introduced respectively by the first and second null VPs of the fifth sentence. Such a relation is difficult to define in general, for the satisfaction conditions will depend on what one is trying to support. But here Support uses the parallel structure between l{ and the two clauses of KS. l<4 asserts that -,(K2 and K3)' and with the appropriate identifications for the concept discourse referents, Ks says that the machine actually did work and that there were no precautions--thus refuting K2 and removing any support also for K 3. This would be a way to maximize the Support relation. If we always try to maximize those discourse relations with scalar qualities, then the theory predicts that this is the only assignment to Cl and C2' I won't try to draw the MEE tree for (5.c). The reader in possession of a drafting board and lots of paper is invited to do so.

relevant tree isomorphism 1'} for defining the contrast to be between these two MEE trees. Now the discourse referent introduced by the null VP is mapped by 1'} onto the appropriate predicative DRS, as shown in the picture on p.391. Maximizing contrast in this case (because of the negation) forces us to match as closely as possible the contents of the first and second clauses; if we can make them identical, we will get a maximal contrasting pair of themes from the VPs. To do this, we should assign to each subject the same, strongest compatible property. I mean 'strongest' here in the sense of entailment. We have only one option for doing this in (7). The property is that of beating a donkey that one owns. Thus, we must, by the maximizing contrast constraint identify z with y' in the SDRS above, and so the constituent revision procedure in effect predicts just the desired reading. (9) is a very simple example in which both strict and sloppy readings arise. Below it is its SDRS prior to anaphora resolution.

370

(9)

Bill loves his wife and Fred does too.

4. SLOPPY IDENTITY A striking feature of VP ellipsis, as well as other forms of abstract entity anaphora, is the ambiguity that certain VP ellipses exhibit between sloppy and strict re~~ngs. These rea~ngs occur when a discourse referent is introduced by a pronoun wIthm a VP that furnIshes a source predicative DRS for a concept discourse referent introduced by a null VP. So to understand these readings, we should perhaps review how such anaphoric equations within a predicative DRS might be resolved. Let us thus return to the discussion of example (7), which yields, recall, the following constituent after the identification of Cl and C2 with the appropriate predicative DRSs:

u, Cl> e2 Austrian farmer(u) Cl "" Ae AV

y'

donkey(y') e -own( v, y') e2- Cl(U)

-

-,

Zl> C2 e2 Zl =? C2"" Ae' AW

z' z'= ? e' -beat( w, z')

e2-c2(zl)

The relevant MEE trees that are maximal relative to the embedding trees of the constituents of (7) and that maximize contrast are pictured on page 364. Following the constraint of maximizing contrast required by the presence of but, we take the

371

kl

Sl> x, y, z Bill(x) sl-love(x, y) z's wife(y) z=?

s -love(u , Yl) ZI'S wife(Yl) Zl ""?

The particle too indicates that the SDRS must support a Parallel* relation between the two constituents in order to be coherent. The extended embedding trees between the two clauses of (9) are isomorphic. So following the constraint of maximizing parallelism required by too, we define Parallel* using the tree isomorphism 1'} defmed between the extended two embedding trees. Now the discourse referent introduced by the null VP is mapped by 1'} onto the predicative DRS introduced by the VP of the previous constituent, as shown above. Maximizing parallelism here forces us to match as closely as possible the content of the first and second clauses, and this requires picking a maximal common theme between the discourse referent. This means that ideally, we should assign to the subject of each respective clause the same, strongest compatible property. We have two options for accomplishing this with (9): we may with identify z with either the discourse referent introduced by the subject of the first clause, x, or the discourse referent introduced by the subject of the second clause, Xl' The first will end up assigning the property, lover of John's wife, to both John and Fred, while the second will assign the property, lover of his own wife, to both John and Fred. In either case, a common theme and hence parallelism is maximized. That is, the two possible ways of maximizing parallelism in the discourse

..-----

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DISCOURSE STRUCTURE AND CONCEPT ANAPHORA

relation are precisely those that the bound and free readings of the pronoun would yield (where the free discourse referent is identified with the discourse referent introduced by Freel). Here is a considerably more complex example of sloppy identity due originally, I believe, to Osten Dahl. Below are the MEE trees and relevant tree isomorphisms for its two constituents and for the two Contrast relations (one between the clauses of the second sentence, which is required by the presence of the particle although). The appropriate predicative DRSs are defined by the concept discourse referents introduced by the null VPs.

We have seen how particular examples exploit the embedded structure of various parallel and contrasting constructions. We have also seen how the notion of maximization of common or contrasting theme accounts for many sloppy strict readings without of course assuming that the original source VP is ambiguous in any way. There is one other sort of example that should be mentioned and that shows the power of the SDRS based approach. Sometimes the right readings are constrained not simply by the structure of the source VP but by its surrounding environment. Here is an example: 12

372

(11)

(10)

John realizes that he is a fool. Bill doesn't 16, although his wife does 16.

373

The leader of the Bolsheviks decided that they should attack at dawn. The leader of the Mensheviks did too.

The appropriate extended embedding trees indicate that the concept discourse referent must be identified with the predicative DRS derived from decided that they should attack at dawn. Because we must maximize parallelism, we must create a maximal common theme of both constItuents by means of our resolution of the anaphoric equations. Here we have two possible maximal common themes for the two constituents neither of which entails the other. Theme 1 x, U Contrast In the ME tree above, K21 = <16, {-,K211}> and K211 = . The SDRS updating and constituent revision procedures constrain the available readings for such cascaded VP ellipsis examples. The diagram above displays a tree isomorphism that maximizes the contrast between K21 and K I . So we must identify c with P II, and this means that c is identified with a predicative DRS in which there is an equation of the form z "'? To maximize the contrast, we resolve this anaphoric equation so as to get a pair of maximally contrasting themes. As in example (9), we may do this in two ways; we may fill in the equation either with Bill or with Fred to get a pair of maximally contrasting themes. A similar story goes for the contrast between K21 and K2 2. We may give the recovered VPs either a strict or a sloppy reading to maximize the contrasting themes. This means that we can, given the maximization constraint, predict only three readings for this discourse: (a) (b)

(c)

Fred realizes that Fred is a fool. Bill doesn't realize that Bill is a fool though his wife realizes that Bill is a fool. ' Fred realizes that Fred is a fool. Bill doesn't realize that Bill is a fool though his wife realizes that she is a fool. ' Fred realizes that Fred is a fool. Bill doesn't realize that Fred is a fool though his wife realizes that Fred is a fool. '

But these seem precisely to be the admissible readings for this example.

Bolsheviks(U) decides(x, I--_-=Z=--_-I

Theme 2 y,Y leader of(Y, y) decides(y,

,---------,

Z

1----'=------1

should attack atdawn(Z) Z=Y

should attack atdawn(Z) Z=U

We may construct either one of these common themes first by identifying the concept discourse referent c introduced in the second constituent with the predicative DRS, I.e AX

e - decides(x, 1-----'=----1 Z should attack atdawn(Z) Z=? and then identifying Z with either the discourse referent introduced by the Bolsheviks (to get the first theme) or the discourse referent introduced by the Mensheviks (to get the second theme). Once again the constraint of maximizing parallelism plays a crucial role in getting the right readings for VP ellipsis. The same approach also explains examples of sloppy identity with proposition anaphora. Consider for instance the pair in (12):

~~-----TI-4~~=~=~~-~C-H-A-p-m=R-M-~-------------··--;~-r~~···-·-·--~~~~~~~~~-

(12.a) Mb ary has been going around saying that Al proposed to her. Susan has een saying this too. (12.b) Mary has been going around saying that Al proposed to her, but Susan has been saying this too.

__________ 2

/~I

KI

"K 1 1 "* K I 12 _________ c ______ P 12

(12.a) is another instance of where parallelism yields either the strict or sloppy reading. Speakers find it genuinely ambiguous. The presence of too in the second clause entails that a relation of parallelism must hold between the DRSs constructed from the two sentences in (12.a); presumably the designated scope elements are the quasi-constituents formed from two main clause VPs. But here too parallelism may be maximized in two ways. The first way is to make the proposition Susan states (call this K) the same proposition as that stated by Mary (call this proposition K'). The second is to attribute to Susan the same property as to Mary by making each one of them claim of themselves that Al proposed to them. In both cases the predicative DRSs derived from the main VPs in (12.a) yield identical properties, and so we have a maximal common theme and a maximization of the parallelism. (12.b) has both parallelism and contrast. It seems to me that (12.b) in a neutral context only provides for the sloppy reading. The discourse constraints predict this. The presence of the contrastive but signals a contrast, with the contrast necessarily taking wider scope over the parallelism relation required by the occurrence of too. There is no way to get contrast if K = K' (where K and K' are as defined in the previous paragraph), however, unless the context makes clear that there is a contrast say in reliability between Susan and Mary. It is much easier to get contrast if we ascribe to Susan and Mary the same property, because our world knowledge about proposing makes us expect that Al proposed to only one girl, and that expectation contrasts with the claim of the second clause. Proposition anaphora using anaphors like this, that or the same thing also licenses sloppy readings that exploit other rhetorical relations besides Parallel and Contrast. 13 Consider for instance, (13)

Every German thinks that he is the best driver on the Autobahn. Claus certainly believes this. 14

Many speakers find the sloppy reading for (13) not only available but perhaps even preferred. Why is this? Mann and Thompson (1987) or Hobbs (1985) might call Instantiation the relation that holds between the two sentences in (13); the second sentence yields an instantiation of the DRS derived from the fIrst and appears to serve as (rhetorical at any rate) evidence for the general claim. The SDRS for (13) contains an Instance and perhaps also a Support relation holding between the constituents derived for the fIrst and second sentences. The Instance relation is again a rhetorical relation that is satisfIed just in case one constituent has a certain formal relation to the other; this formal relation requires a tree isomorphism and a use of Parallel*. The precise defInition of instance is in the Appendix. The extended constituent graph for (13) with the appropriate tree isomorphism looks like this.

Given Parallel* between K2 and K" we identify c with an alphabetic variant of P 12 , which looks like this:

'As 'Ax s - thinks(x , I

z I) best driver(z) I I I z = []

P I2 is an incomplete predicative DRS, since it is derived from the VP. So we must now pick the discourse referent antecedent for z. To satisfy Instance, we must ensure that K2 assigns to Claus the same property that is generally assigned to Germans in K I. This means once again that we must fInd the strongest common property attributed to the agents in KI2 and K 2; this is the property of x thinking that x is the best driver. So z is identified with x in the predicative DRS identified with c. The discourse relations apparatus again suggests the sloppy reading, although (13) exemplifIes a discourse relation different from Parallelism or Contrast. How does this approach to VP ellipsis and strict sloppy readings in particular contrast with other approaches? A traditional way of accounting for the ambiguity is to postulate two different bindings for the pronoun to lead to the following two different translations of the VP in the standard lambda calculus: 'Ax (x loves Bill's wife) and 'Ax (x loves x's wife). Sag, for instance, uses such an approach. From the present perspective, however, this solution relies on a certain processing priority-namely, that the anaphoric equations inside structures that are potential candidate antecedents are always to be resolved first. This appears to presuppose an ambiguity in the original VP that is not there when the second clause containing the null VP is not there. 1S My approach does not assume any ambiguity in VP meanings, though it does claim that the component of meaning determined by anaphora resolution is guided by discourse context. Sag's approach also is too restrictive a proposal to handle many cases of sloppy VP ellipsis--in particular to account for (14), (15) or those in (16) below. Another difficulty with Sag's approach is that it yields the wrong results, if it is generalized to handle deep proposition and concept anaphora. Consider (12.a) again: (12.a) Mary has been going around saying that Al proposed to her, but Susan has been saying this too. (12.a) has two readings: the first is that Susan says that Al proposed to Mary (the strict reading); the second is that Susan says that Al proposed to Susan (the sloppy

------------------------------------------

---------=~~~~==~~----~----~~---===~~------------~--------~~~--------~~------.

376

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DISCOURSE STRUCfURE AND CONCEPT ANAPHORA

reading). If one resolves the anaphoric pronoun within the sentence first prior to finding the referent for this, it appears that only the strict reading is available, unless one reads the report in (12.a) as some sort of saying de se. I don't know if this is plausible, but in any case even if it is, problems remain. For if we interpret the first clause of (12.a) as a report de se --i.e., as consisting of an individual and a property ascription to that individual, then one natural candidate for the logical form of the VP of the saying report is as follows: AX(X says(x , Au(AI proposed to u)). This,logical form gives us the "essential indexical" interpretation of the sentence that implies that Susan knows that it is she who is being courted. But this will yield only the sloppy reading. There is also an alternative logical form for the VP: AX(X says(x, AU(U lives in a world w in which Al proposed to Mary)). This yields the strict reading. But on this account we cannot have a strict reading of the anaphor with the "essential indexical," de se interpretation of the fIrst report. Since that seems perfectly possible, I conclude that something is amiss with this approach. A recent proposal using DRT is that of Roberts (1987). She proposes to give two different translations of the VP also, depending on whether the pronoun is interpreted as syntactically "bound" or free: AX (x loves y's wife) (free reading), where y may be identified with Bill or some other individual in the discourse, and AX (x loves x's wife) (bound reading). This proposal suggests that deep anaphora must be done after surface anaphora. This approach also predicts an ambiguity in the VP for (9). This proposal is also too restrictive, although it is an improvement over the previous proposal. 16 Another very recent proposal for treating VP ellipsis by Gawron and Peters (1988) deserves comment. It proposes in essence three readings for a pronoun inside a VP using a complex principle for noun phrases called absorption. The principle in effect suggests that in VP ellipsis a discourse referent may be identifIed with a role of a particular kind. More specifically, suppose that a VP gives rise to a property of the form AZ cp(x, u, z) and there is a functional dependence f ofu on x --i.e., f(x) = u. The absorption principle states that if in a sloppy identity case of VP ellipsis the recovered VP is AZ' cp(x', u', z'), then f(x') = u'. This view is closest to the one I have proposed. Where Gawron and Peters and I differ concerns what constitute the functional dependencies. If I understand them correctly, the functional dependencies they consider are quite restricted and grammatically related. I take the functional dependencies to depend on discourse relations. This difference yields different predictions; Gawron and Peters cannot handle (14) or (15) below. None of the approaches I have mentioned handle the cases of VP ellipsis that are based on discourse relations--for example those found in (7) - (5). They are not equipped nor designed to do so.17 In fact even when augmented with a theory of discourse structure, such approaches would have difficulty with examples like (7), in which the discourse structure relies on using DRSs as the basic units of discourse structure. But more importantly, my approach to strict/sloppy readings, unlike theirs, grows out of my general, discourse based approach. In fact, the predictions about strict and sloppy readings are a consequence of the discourse based theory; no extra mechanism is needed on top of the general mechanics of abstract entity and individual

anaphora and the constraints specific to VP ellipsis is needed to generate the predictions about strict and sloppy readings. My approach does not generate an ambiguity in the VP meaning to account for the difference between strict and sloppy readings the way Robert's, Sag's or Gawron and Peters's proposals do. What explains the difference is the way anaphoric relations in general are sensitive to the discourse context. Discourse relations determine which properties and propositions are available; and that means that if those properties or propositions have incomplete conditions like those introduced by anaphoric pronouns, then these relations must, to determine the properties, specify how those conditions are to be completed. I conclude my application of the theory of SDRSs to VP ellipsis with a few more examples for which my discourse based theory of VP analysis seems to offer some advantages. Here is one sort: 18 (14)

377

Every boy danced with at least one girl who kissed him. In fact only John danced with a girl who didn't.

This yields the following SDRS with two constituents, one continuing and contrasting with the other:

~ boy(y)

y,x, e, Z girl(x) e-dance-with(y, x) kiss(x, z) z=y

=*

u, v , e' John(u) e'-dance-with(u, v) girl(v)

I

I

e\, c el-c(v)

-,

C"'Ae Ax

I

ZI

I

I e -kiss(x, ZI)I ZI =? Continuation(kJ, k 2 )

Contrast(kJ, k 2 )

I have filled in the antecedent for Z above, since there is only one available, y. But what about ZI? The use of only suggests that a Contrast relation should be sought between the structures given by the first and second sentences of (14).1 9 The discourse referent introduced by every boy, y, and, the discourse referent introduced by John, u, can be assigned maximally contrasting properties: y has the property AV

-------------------------

378

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DISCOURSE STRUCTURE AND CONCEPT ANAPHORA

[{x}, {girl(x), dance withey, x), kiss(x, v)}], while u has the property AV [{x}, {girl(x), dance withey, x), -,[ { }, {kiss(x, v)}]}]. Thus, this example fits a familiar pattern in my analysis. But this example is hard to handle for those who categorize pronouns as either instances of bound or discourse anaphora at the syntactic level. z has to be free to be identified with the discourse referent introduced by each boy, but on the other hand, the free reading is not even possible. On the other hand, if z is bound to the A-abstracted variable in the VP, it will be identified upon the application of that VP to the translation of the subject of that clause with a discourse referent with the wrong gender features! This example is also difficult for approaches that would attempt to create complex "copying routines" to handle sloppy identity in VP ellipsis. One way of handling VP ellipsis might be simply to copy the predicative DRS C generated by the full VP in Sl and use that as the translation of the null VP in S2; sloppy identities are to be handled by potentially replacing the discourse referent introduced by the subject of Sl with the subject of S2 in anaphoric equations contained within the copy of C.20 But we can easily extend the sort of examples in (14) to ones where the copying routine just outlined won't work:

ungrarnmaticality of the sloppy reading on (16.b) is not because of Sag's requirement An example like the following shows that Sag's explanation cannot be quite the right story.

(15)

Mary hated every boy who danced with at least one girl who kissed him. Since John was the only one who didn't dance with a girl who did, Mary ended up hating everyone except him.

My discourse approach can handle such examples, on the other hand, because it has many more resources at its disposal. The discourse approach exploits the parallel structure in the first two clauses and the fact that the discourse has the form of an inference, where the since clause is an instance of the generalization in the first sentence. By the updating procedure for constituents that bear discourse relations to other elements, we would predict not only the felicity of identifying the discourse referent introduced by the null VP with the event type AeAx [ e kiss(x, z), z = ?] but also its necessity. The discourse approach also appears to explain a curious observation of Sag's. Sag (1976) notes that recovery of the deleted VP is not possible in (16.b) under the sloppy reading, although it is fine in (16.a): (16.a) Johnj said that Mary kicked hirnj, and Billj did ¢ too. ¢ = said Mary kicked himjj . (16.b) Johnj said that Mary kicked himj, and Billj said she did ¢ too. ¢ = kicked himj, *} The ambiguity of (16.a) is familiar; it has the same explanation as the one I have given for (9). (16.b), on the other hand does appear to be surprising. Sag explains the discrepancy by appealing to alphabetic variance. He claims that the elided VP must be an alphabetic variant of the full VP. This would explain why the * reading of (16.b) is unacceptable. Nevertheless, there are examples that show that the infelicity or

(17)

379

Every boy in the group said that Mary kissed him. Sam said that she did. Bill said that she did, and Fred said that she did.

Most speakers find (17) felicitous, but the VP ellipses there must have sloppy readings, because the scope of every does not extend over the entire discourse. But it is also clear that on Sag's account the properties that are the translations of the recovered VPs will not be alphabetic variants of each other.21 Consequently, Sag's explanation of the discrepancy between (16.a) and (16.b) cannot be correct. 22 It should be clear how my account would handle (17). We rely on discourse segmentation to supply us with the rhetorical relation--again, we have a relation of Support or, better yet, Instantiation between the DRS Kl expressed by the first sentence and the DRSs, K 2, K 3 , K4, expressed by the next three clauses. In order, however, for K 2-K4 to be instances of Klo the discourse referent introduced by the pronoun must be identified with the discourse referent introduced by the subject of the matrix clause. This predicts the sloppy reading of the VP in each case. The semantics of the discourse particles once again accounts for the impossibility of the sloppy reading of (16.b) on my DRT-discourse relations account. Since too combines here with an anaphor referring to a concept, the parallelism between the two clauses must be maximized. Such a maximization should entail that the same property is attributed to Mary, if that is at all possible. There is such a maximization possible, but then that property can only be the property of kicking John. So only the strict reading is predicted to be available (or at least strongly preferred). Proposition-type anaphora, VP ellipsis and concept-type anaphora all exhibit more complex forms of anaphora than the ones I have considered so far. Consider for instance the example of so called "pseudo-gapping" (due to Sag & Hankamer 1984): (18)

Mary didn't hit Bill, but Sue did ¢ Sam.

Similar examples to this one can be found in concept-type anaphora as well as proposition-type anaphora (19.b) is due to Rainer Bauerle): (19.a) Mary didn't hit Bill with a pogo stick, but Sue did it with a baseball bat. (19.b) I had a flat tire on the interstate. That never happens in town. (19.c) I always have flat tires on the interstate. That isn't true in town. The operations involved in (19) are more complicated semantically than those we have seen before. Intuitively, the sentence containing the deleted VP in (18) or the anaphoric pronoun in (19.a-b) also contains an NP whose content should be substituted for the content of the NP contributing the parallel argument of the verb that is part of the antecedent for the anaphor. That is, the reconstructed property attributed

CHAPTER NINE

DISCOURSE STRUCTURE AND CONCEPT ANAPHORA

to Sue in the second clause of (18) is the property of hitting Sam. In (19.a) the property attributed to Mary is the property of hitting Bill with a baseball bat. In (19.b) the property attributed to the event introduced by happen is the event type of my having a flat tire in town. Finally in (19.c) the anaphoric pronoun picks out the proposition that I always have flat tires in town. Luckily, we already have most of the machinery required to make sense of these examples. The linguistic antecedent yields under the construction algorithm a structure that must be "thinned" to produce an appropriate predicative DRS to which one can then apply property assimilation; syntactic and semantic parallelism or contrast guide the interpreter as to which discourse referents and conditions should be thinned from the original structure and which conditions and discourse referents should be added through property assimilation. Gapping is also a construction in which the machinery proposed here might have some application. Gapping and pseudo-gapping are even more constrained than VP ellipsis. Gapping contexts don't permit existential generalization or syllogistic forms of reasoning and fail to exhibit implicit-explicit information patterns. The contexts in which gapping is permitted are highly restricted and very strongly syntactically governed. Here is an example of Hans Kamp's that nevertheless shows that even these highly syntactically constrained constructions are susceptible to discourse effects.

now need to find a maximal common theme to maximize the parallelism. The maximal common theme for the sloppy reading of (20) is something like this (where + is a function from a pair of discourse referents to a group of containing those two discourse referents):23

380

(20)

Carmen is easily the most interesting person to have moved into the community during the last few years. Bill has suggested to Frank's wife that they should go to the show and Carl to Alan's wife.

x

Carmen(v) suggest(x, y,

y

Z should go to the show(Z) Z""y+v

This theme can be realized by identifying the concept discourse referent introduced in the second clause by the gapping construction with a predicative DRS of the appropriate sort and resolving the anaphoric equations within the predicative DRS so as to maximize parallelism and realize the maximal common theme given above. Thus, my account extends naturally to examples like this. It is difficult to see how one could account for an example like (20) on a pure, syntactic theory, since the notion of a common theme seems essential to getting the right prediction in that case. Another possible application for abstract entity anaphora concerns the "role" values for anaphors, a topic explored in situation theory (Barwise and Perry 1983, Gawron and Peters (1988» and in Fauconnier (1985). Consider the following:24 (21)

Kamp's intuition about (20) is that the only sloppy reading of (20) in which Bill suggests that Carmen and Frank's wife go to the show is the one in which Carl suggests that Alan's wife and Carmen go to the show. The readings that underlie (20) depend on the DR-theoretic operation of summation over discourse referents, and so on my discourse hypothesis about sums, the summation should be affected by discourse structure. Here topic revision is not directly responsible for the formation of a group, but it is at least indirectly responsible. The first sentence introduces Carmen as a topic of discussion. One might take the second sentence to introduce a constituent that is a Result of the flrst; Carmen's being the most interesting person has led to Bill's and Carl's suggestions. One could also interpret the discourse as giving rise to a Support relation between the two constituents. In either case, Carmen is the implicitly exhibited topic and to clarify the topic structure to render maximally plausible the Result relation, Carmen should be doing something in the second sentence. Now for gapping contexts, we use the same constituent revision procedure as in overt concept anaphora or VP ellipsis, except that tree isomorphisms within gapping must take account of syntactic structure. Let us adjust the account so that tree isomorphisms are defined on interpreted syntactic trees; this forces a mapping from the missing interpretation of the verb to the property given by has suggested that they should go to the show. In view of the requirements of maximizing parallelism, we

381

The Democratic National Committee suggested that the next Democratic nominee for President sell whatever stock he might have in companies doing business with South Africa. Gephart agreed to that, and Dukakis agreed to that too.

The idea in (21) is that Gephart and Dukakis each agreed to the proposition that he as President would sell his stock in companies doing business with South Africa. It appears that the mechanisms for talking about roles in situation theory could easily be grafted onto to DRT, if they are not already present in my use of themes.

5. CONCLUDING THOUGHTS ON ABSTRACT ENTITY ANAPHORA There are some appreciable differences between abstract entity anaphora and individual anaphora and between various forms of abstract entity anaphora, although they all have a common semantic theme. VP ellipsis uses a special kind of anaphor, and so it should not be surprising if the anaphoric constraints for this form differ from other forms. We have already seen such differences with other anaphors. VP ellipsis and gapping are much more syntactically constrained than some forms of deep anaphora and appear to require an explicitly given linguistic antecedents. But VP ellipsis, gapping, pseudo-gapping, and deep concept anaphora employ discourse

CHAPTER NINE

DISCOURSE STRUCTURE AND CONCEPT ANAPHORA

features in much the same way; both often rely heavily on relations like parallelism and contrast to detennine their antecedents as well as features such as sloppy vs. strict readings. This completes my study of abstract entity anaphora. It is now time to take stock. Often the antecedents of an abstract entity anaphor are the result of discourse segmentation. Further, even when the antecedents are postulated by the semantic processing algorithm, discourse structure heavily influences which of these are acceptable antecedents. Thus, discourse structure has a dramatic effect on the individuation of propositions and properties in natural language metaphysics. This reinforces on the one hand the approach to abstract entities exploited by DRT: what propositions a text expresses and what properties interpreters recognize as objects mentioned by the discourse (and capable of being referred to) will be determined not simply by the meanings of the text's constituent sentences but also by the way that meaning interacts with a previously set up discourse structure. From our examination of DRT, we have seen that the proposition a sentence expresses cannot be determined in general without exploiting the discourse of which it is part. Abstract entity anaphora has shown us that we have to exploit not only the content of the previous discourse but also its structure and that this structure has a very definite effect on the meaning of the text. Further, insofar as this discourse structure is built by drawing upon a wide range of knowledge--especially beliefs about what the speaker or author may have intended--a much richer, but also less compositional, notion of discourse meaning has been developed. Finally, we have learned some morals for natural language metaphysics and the nature of propositional summation properties within a text, which, recall, we did not develop in chapter 1. The principles that guide the propositional structure of a text are very complex. An interpreted text does not give rise simply to a list of atomic sentence-like propositions or property ascriptions to tuples of individuals put together by means of logical operations; rather, an interpreted text is a system of propositions hierarchically organized and individuated by the interpreter's beliefs about the subject matter and about the communicative intentions of the author. The individuation of bits of content into structured propositions and properties is pragmatic and relative to purposes of communication. The moral that a study of discourse structure and anaphora points to is thus rather surprising. It is this: the structured propositions and properties mentioned in a text don't have "any life of their own"; they are constructs-artifacts of the interpretive process, essential for forming attitudes about contents but not in any way mind independent objects. I will investigate the philosophical implications of these last chapters on abstract entity anaphora in the next.

which also occurs in the definition below. Hopefully, the context makes clear which is which!

382

DEFINITION: Suppose 8 is a concept discourse referent in UK or a predicative DRS AXb ... , AXnK' such that for discourse referents Ub ... ,U n, K' (UdXb ... ' un/xn) is a

part of K, K d~ p, Yd~ a and either or a = p. Suppose further that 't is a modified embedding tree for a. Then, :F(y, 8, 't) is a predicative DRS that (i) meets the constraints of C-abstraction with respect to the conditions in which a occurs in K, and (ii) if there is a 1 such that <1, y> E 't , then :F(y, 8, 't) contains the matrix condition of 1 in yand :F(y, 8, 't) is a part of y, (iii) if there is no 1 <1, y> E 't, then :F(y, 8, 't) contains the condition derived from a verb of the text giving rise to yand :F(y, 8, 't) is a part of y, (iv) there is no condition
Remark: Clauses (i) through (iii) encode the constraints on C-abstraction discussed in chapter 6; clause (iv) is merely a technical convenience that ensures an appropriate match between concept discourse referent and predicative DRSs. It is not hard to see that given y, 8, and't and the assumption that roles for each verb are unique, :F(y, 8, 't) is unique. Note that in virtue of the requirement that , which means that P is attached to a, or a = p, my definition yields appropriate predicative DRSs not only for a constituent to which the constituent containing 8 is related but also for the constituent containing c.

e

DEFINITION: (D*-subordination) a d*-< P iff

(i) (a d-< P or a is a part of P or a is a concept discourse referent declared in U~) or (ii) 3y (a d*-< y & yd-< P or yis a part of P). DEFINITION: a d*~ P iff a d*-< P or a

= p.

DEFINITION (MEE Tree): Suppose cr is a concept discourse referent in UK or a predicative DRS AXIo ... , AXnK' such that for discourse referents Ulo ... ,U n, K' (UdXIo ... , un/xn) is a part of K, K d~ P & (<<x, P> or a = P) and suppose that't

= is a modified embedding tree of y in 8, where 8 d~

a and y d~ 8. A

modified extended embedding (MEE) tree oiy in 8 with respect to 't and cr is a tree , where A' = A U {:F(s, cr, 't): SEA} U {c': 3YE A C' E Uy }. NOTATION: For predicative DRSs I wiIl use capital letters P, Q with or without

6. APPENDIX OF DEFINITIONS AND CONSTRAINTS FOR CONCEPT ANAPHORA

subscripts.

Extensions of SDRS Theory: Recall that our notation for saying that two constituents are attached to each other is . Do not confuse this with the pairset notation,

7

383

2

2.

384

CHAPTER NINE

DISCOURSE STRUCTURE AND CONCEPT ANAPHORA

385

Discourse Relations on MEE Trees CONSTRAINT: Every bijection between MEE trees that defines a parallelism or

contrast relation must map predicative DRSs onto predicative DRSs and SDRS constituents onto constituents.

= AXI' .. AXn K and ~ = AYI ... AYn K' are predicative DRSs and Xi and Yi fill in the same thematic role for each i, then a 1\ ~ = AXI ... AX n K U

DEFINITION: If a

K'(xdyj, ... , xn/Yn). DEFINITION: Converse(a,~) in

Ko iff (i) there is a complex condition in ~ of the form 0 - 0' and a condition in a of the form Y-1. (ii) for all w, (M, w) ~ 0 - 0' iff (M, w) ~ 1 - Y. (iii) 31'}: a ---> ~ (1') is a tree isomorphism & Contrast*(o, y) in virtue of 1'} and Contrast*(o',1) in virtue 1'})

FACT: Suppose Converse(a,~) in

Ko and 1'} is the tree isomorphism on y and 1 into

o and 0' as defined above, and suppose that some leaf ~I of'ty or 't y is a discourse referent k. Then in updating Ko with a, ~I is replaced with ~I 1\ 1'}(~I)' DEFINITION: Instance(a,~) in

Ko iff (i) there is a complex condition in a of the form 0 - 0' or 01>0'

(ii) ~ ~ 0 U 0'. (iii) There is a condition y in ~ such that Parallel*(o', y) in virtue of a tree isomorphism 1'}: 't* ---> 'to', where 't* is a subtree of 'to' .

1e.g., the Aux over Aux hypothesis discussed by Bresnan (1971) and Sag (1976). 2For examples like, The garbage had to be taken out. So Fred did it, it depends how passives are represented in the syntax and what the exact translation procedure from syntactic structures to semantic representations is. If passive is taken to be a lexical operation, then the predicative DRS picked up by the concept discourse referent introduced by the pronoun is not just a translation of the VP. 3ExceI?,tions to this constraint involve the use of the the):,pronoun to refer to concepts as well as so called 'one anaphora" discussed by Luper-Foy (1989). Here are examples of one anaphora: The women of the village always came to Sunday fair. They like that sort of thing. Three golden retrievers came to visit yesterday. One was especially pretty. 4The verb do that goes with explicit concept anaphora also introduces an event discourse referent. The presence of an event discourse referent explains why these intended anaphoric links are not OK: Sam [had to study Latin];. Fred did that, too. Sam [had to study Latin],. Fred had to do that, too. The second sentence of course has a perfectly acceptable reading-- namely where Fred had to study Latin. It is interesting to note the apparent impossibility of IJicking up modals with deep anaphors; that arises from a lexical conflict-- mooal properties are stative; ihat is, they denote types orstates. Stative properties don't combine well with action verbs like do and happeI}, which are subcategorized for eventtypes. They can, however combine perfectly well with auxiliary do, which is the verbal form used in

VP ellipsis. lowe this suggestion about the two forms of do to Ewan Klein. 5Many of the nodes in the embedding tree are not available because of lexical mismatches. One could not identify the discourse referent introduced by the pronoun in K2 31 with the DRS that is the object of doubt, because there is a lexical mismatch between the stative verb doubt and the action verb do. Do categorizes its argument as an action or event type and so the discourse referent C cannot be identified with a state type. 6Negation may take a property AY
a

'tl

't2'

KII

I P II

I

KI2 •

I

P I2 ..

C

But in this case too, there will be a contrast between the matrix condition of K21 in Ko and KI 2 in K II . 10 The figure in footnote 9 of this chapter also supports contrast. The attitude of the speaker -- his certainty-- contrasts with John's saying, though presumably this contrast is less strong than the one mentioned in the text. 11 Again the figure of footnote 9 is a possibility. 121 heard about this example from H. Kamp. BOn the other hand, the pronoun it does not. Polly Jacobson has informed me that other people share my intuitions on this score at least. This points to slightly different processing rules for the different pronouns, but I won't go into that here. 141 am indebted to Rainer Bauerle for this sort of example. But consider how it and other pronouns make a difference: (58') Every German thinks that he is the best driver on the Autobalm. Claus certainly believes it. Many speakers in contrast to their feelings about (58) find the sloppy reading of (58') extremely hard to yet. 5For instance Klein's, Roberts's and Gawron and Peters's. As far as I know, this sort of criticism is originally due to Hans Kamp. 16Gawron and Peters (1988) also criticize this proposal as too restrictive. 17Priibst (1990) develops an interesting discourse based account of VP ellipsis using the discourse syntax of Polanyi and Scha, but it does not exploit semantic content in a thoroughgoing way and so is much more limited than what I have been developing. The work is to be completed in Priibst's dissertation which I have not yet seen. 181 am grateful to Mats Rooth for this example. 190nly does not just indicate a relation of contrast. See Rooth (1984) for a semantics for only. 20rhis was suggested by Hans Kamp and is reported by Gawron and Peters (1988). 21 Nevertheless, DRT and Sag's account share a commitment to an analysis of VP ellipsis at the level of logical form. Sag's observations about relatives and wh questions and VP ellipsis all appear to be right and carry over into a DR-theoretic account. None of the predictions he makes for those sentences or those invol ving quantifiers hinge on the requirement of alphabetic variance where pronouns are concerned. Indeed without pronouns, the identification condition and alphabetic variance amount to the same thing. 22The discrepancy between (16.a) and (16.b) is not confined to surface anaphoric phenomena: (16.c) Johni insisted that Mary kicked himi, and Billj did that too. that = said Mary kicked himi,

-------------------------------

386

CHAPTER NINE CHAPTER TEN

(16.d) Johni insisted that Mary kicked himi, and Billj insisted she did it too. it = kicked himi, *j The explanation for the felicity of both readings in (16.c) is quite analogous to that for (16.a). There are at least two potential antecedents for the discourse referent introduced by him in (16.a) that will maximize the parallelism between the two properties being predicated of the subjects of the matrix clauses; one of them is the lambda abstracted discourse referent in the VP. Application of the resulting property in this case yields a perfectly satisfactory sloppy reading for (16.c). 23 Again for a discussion see Kamp and Reyle (199+). 24This example is due to an anonymous NSF reviewer.

MODEL THEORY FOR ABSTRACT ENTITIES AND ITS PHILOSOPHICAL IMPLICATIONS

Throughout this book, I have principally concerned myself with natural language semantics and the natural language metaphysics underlying it. So for the most part, I have concentrated on discussions of DRSs, the partial models whose task it is to reflect to some extent natural language metaphysics in their discourse referent types. This chapter concentrates on themes of real metaphysics, the model theoretic interpretation of the DRS construction procedure and its possible philosophical implications. The chapter has two parts--a technical one and a speculative one. The first part (sections 1-3) develops the model theoretic interpretation for the semantic construction procedure for sentential nominals, quantification over abstract objects and abstract object anaphora, extending the basic ideas of Asher (1986) which were sketched in chapter 3. The key idea is that DR-theoretic structures not only characterize a level of semantic representation but also inhabit the domain of the models--ultimately as possible types of mental states of agents in those models. Following Aczel (1980, 1989) and Turner (1989), I will characterize the DR-theoretic structures in an algebraic way and show that they form a model for the lambda calculus. Because DR-theoretic structures inhabit the domains of the models, they may contain discourse referents that are mapped onto alphabetic variants of themselves. This, in conjunction with particular interpretations of DRS predicates, gives rise to familiar paradoxes involving self-reference, like the Liar or Russell's Paradox. I will briefly mention some techniques for dealing with these difficulties; a full examination would double the size of this book. In particular, I will point out how a representationalist semantics offers quite different resources for attacking these issues in comparison to a theory which explicitly eschews representations. In particular I will look at Cresswell's (1985) theory of structured meanings. The second part of the chapter (sections 4-5) addresses the metaphysical theme of conceptualism. The model theory suggests that abstract objects are conceptual constructs, and a semantics that makes use of representations offers a way to develop the metaphysical thesis. I examine the consequences of representational semantics and defend the philosophical thesis of conceptualism. Over the course of the previous chapters, I have advanced reasons for thinking that the realm of abstract entities in natural language metaphysics is not a Platonic realm of mind-independent entities. The typology of natural language metaphysics is fluid and often ill-defined; the typing constraints of natural language metaphysics can, for instance, often be overridden in anaphoric connections. It is also difficult to determine any context-independent 387

.

........------~=~~~~~~~~~~---~--,~--~ --~--------------

388

CHAPTER TEN

MODEL THEORY

individuation principles for abstract objects like propositions. We have found that the propositions expressed by a given text do not have a determinate fonn--at least not just with respect to the semantics of the text itself. Their individuation depends on discourse structure, and on the purposes, knowledge, and interests of the participants in the discourse. Such behavior supports the contention that abstract entities are simply constructs useful for classifying infonnation; their individuation principles and the typing restrictions they engender are no more strictly drawn than is necessary for the purposes for which they were invented. If such abstract objects are constructs, it should in principle be possible to eliminate them. In virtue of my analysis of sentential nominals and abstract object anaphora, natural language metaphysics allows a reduction of abstract entities to conceptual structures, or more precisely to equivalence classes of DRSs or predicative DRSs together with their intensions. We can represent propositions and propositional structures by sets of DRSs and equivalence classes of structures consisting of DRSs and relations defined on them. Our look at property anaphora also encouraged us to make predicative DRSs the values of concept discourse referents under embedding functions. Concepts are simply treated as another sort of abstract object and DRtheoretic construct. By using DR-theoretic structures we can eliminate these abstract objects.! What does this reduction portend? Insofar as DRSs and predicative DRSs are mental constructions, these findings support the conceptualist's thesis: propositions and perhaps also other abstract entities are the result, or perhaps rather the byproduct, of a creative mental activity--the interpretation and integration of infonnation from verbal and perhaps also nonverbal sources. The reduction gets rid of propositions and perhaps other abstract entities in favor of ways of classifying the contents and structures of mental states.

The way that I have represented VP ellipsis borrows from the syntax of higher order logic. For a variety of reasons, a higher order language seems to be easier to fIt directly to the patterns of natural language use of propositions and properties. But the demands on a theory of propositions and properties make it impossible to capture the constraints on interpretation that can arise in such contexts by using just extensional higher order logic. Domains for extensional higher order logic, after all, countenance just two propositions, the true and the false! Even an intensional higher order logic, in which propositions are identifIed with sets of possible worlds, will not suit our needs. We need to resort to an intentional higher order logic along the lines proposed by Thomason (1980a), in which an algebraic structure of intentional objects is posited along with a way of mapping these intentional objects into appropriate extensions or, better, intensional contents. This is a very natural framework for DRT: the intentional objects are the DRSs and predicative DRSs, while the intensional models, the beginnings of which were sketched in the appendix to chapter 2, yield the appropriate contents. The correctness defInition furnishes the required mapping between these two structures. If we follow Thomason's idea, then, we must distinguish DRSs when they refer to their intentional meanings--i.e. DRSs themselves--and DRSs insofar as their conditions simply constrain the assignment of a proper embedding. More generally, we must distinguish between the constraint on interpretation imposed by the partial model and the intentional object itself. This is just the distinction between DRS predicates and DRS operators, familiar from chapter 3. In chapter three, we introduced a different type of variable to range over DRSs or predicative DRSs themselves rather than their contents. But there is a systematic connection between these two that we would like to exploit. Hence, I introduce a function constant v into the DRS language, denoting a function from elements of the intentional algebra into intensions. 3 Thus, K will denote a DRS, while vK denotes a DRS's intension. We should henceforth write vK ~ vK' to indicate the DRS condition introduced by the conditional, but since I take the operator/ predicate distinction to be clear enough I shall leave out the v where no confusion results. To talk about DRSs in this section, I will often adopt the simpler notation of an intentional higher order logic following Thomason. I will assume that v is a function constant in an otherwise ordinary higher order syntax, in which simple formulas are tenns for propositions (DRSs). Typically, one requires v to be a homomorphism. If v is a homomorphism, we can push v across the operators in any fonnula, until it is appended in front of basic predicates; thus in what follows the signs for quantifiers and connectives have their usual truth functional meaning. While the syntax of the language in which we write DRSs appears to be higher order, the logical syntax of the language in which constraints imposed on interpretation by DRSs can be expressed is really not what distinguishes a first order theory from a higher order theory. This is a familiar point from the study of generalized models for higher order logic. A more interesting distinction between higher order and first order logic comes from examining the model theoretic properties of a given fonnalism; if the fonnalism's semantics gives rise to a complete

1. FIRST ORDER OR HIGHER ORDER DRT? Although DRSs as partial models are not to be confused with the box language in which they are expressed, we can ask questions about their logical structure in the following way. Are the constraints on interpretation now encoded in the partial models first order definable or not? That is, is there a first order fonnula that is satisfied iff the constraints on interpretation given by a partial model are? The question had an obvious, affInnative answer in the fragment of chapter 2. If we add to that fragment generalized quantifiers corresponding to determiners like most, many, and so on the answer to our question is again pretty clearly, no. I will leave group quantifIcation aside in this discussion, as the complexities introduced by groups are not relevant to the discussion of abstract entity semantics. 2 But even the fragment with the usual first order definable quantifiers, the quantifier introduced by the, and the reification of DRSs and predicative DRSs makes the question challenging to answer. Providing an answer will give us some clues about the underlying logical commitments of this theory.

389

-----~~~~~-~~~~~~------~--~~-"--~---------------391

CHAPTER TEN

MODEL THEORY

axiomatization and theories within the fonnalism exhibit the Lowenheim-Skolem and Compactness properties, then such a system deserves to be called first order.4 Thus, to determine the logical status of our DRS fragment, we must look to the semantics and the model theoretic properties of the underlying DRS logic. Semantically, second order logic is characterized by the class of standard models for second order logic, in which the second order variables range over all subsets of the (fixed) domain of individuals. The use of all subsets determines the semantic properties of second order logic--viz., incompleteness, and failure of compactness, and the Lowenheim-Skolem-Tarski theorems. 5 The class of general models for second order languages are those models in which the second order property variables range over some subset of the powerset of the domain of individuals. General model theory for second order logic, semantically speaking, gives us first order logic in second order clothing. Henkin (1950) proved that higher order logic with general models has the essential semantic properties of first order logic: completeness with respect to the class of general models, compactness, and the appropriate generalizations of the Lowenheim-Skolem-Tarski theorems. 6 For the purposes of this discussion, I will take these semantic properties as defining first order logic. One can destroy the semantic properties that define first order logic by adding to one's logic a certain amount of expressive power. Full second order logic can do this, but so can the addition of various predicates like true or attitudinal predicates like know and believe with particular intended interpretations, together with mechanisms that permit self-reference'? In particular, the DRT view of propositions gives us two ways to get self-reference. One, introduced in chapter 6, makes use of the external anchoring relation, anchoring a proposition discourse referent to an alphabetic variant DRS in which it occurs; the second way is to use quantification. It appears as though natural language semantics does not need the standard models for higher order logic.8 How should we compare intentional semantics to the standard extensional model theory for second order logic? Let us see how large is the domain of properties in an intentional model vis a vis the domain of individuals. To recapitulate again, the intentional, abstract structures, the DRSs and other DRtheoretic structures, are themselves elements of the models. Leaving aside the question of plural quantification, I will restrict quantification to abstract objects and individuals and just use the first order definable quantifiers. The intentional model theory, together with the assignment of intensions, yields the semantics we need to account for attitude ascriptions and other non-extensional phenomena. Let us suppose that all DRSs and predicative DRSs are finite and fonned from a countable list of primitive predicates and operation symbols. There is a many-one correspondence between representational structures (in this case DRSs and predicative DRSs) and the intentional entities (propositions, properties) they identify (alphabetic variants identify the same proposition). So there appear, given these assumptions and my modeltheory for abstract objects, to be no more (and no less!) than countably many propositions and properties. This conclusion depends upon our assumptions about the size of DRSs and the sets of their constituents. But my assumptions are surely reasonable and even generous, if the stock of primitive predicates and operations are

taken to describe the concepts that an individual or even a community over a finite time could plausibly have and use. Now we consider the link between intentional structures and extensions or sets. In the standard semantics of extensional second order logic, the domain of the second order quantifiers ranges over the powerset of the domain of individuals. Relative to a world and time of evaluation, every predicative DRS determines an extension that is a set of objects. But from properties to set extensions there must be a many-one correspondence, in virtue of the fact that there are coextensive properties. Thus, the second order variables of my theory determine a countable domain for extensional, second order quantification. If we assume a countable domain of individuals (recall that the intentional objects belong to the domain of individuals but these fonn also a countable set), the semantics that I have sketched is compatible with the assumption that the domain of any extensional second order quantifiers is a strict subset of the power domain of individuals. Thus, intentional model theory corresponds not to standard model theory for second order logic but rather to general model theory for second order logic. Because of this correspondence, one might expect a completeness theorem for a DRT logic which includes quantification over abstract objects. With certain restrictions on the anchoring relation and on the interpretation of DRS predicates that eliminate vicious self-reference in a manner similar to the way Gupta (1982) suggests with his use of Thomasonian models, this theorem follows as a generalization of Asher and Kamp's (1989) theorems (1)-(3) and (14). But these restrictions do not plausibly apply to natural language metaphysics, and once the restrictions are lifted, the semantic paradoxes arrive and completeness is lost in an obvious way.9

390

2. INTENTIONAL FRAMES AND INTENSIONAL CONTENTS I tum now to develop the two stages of the intentional semantics for the DRS language: an intentional frame, and a theory of intensional contents for the objects in the intentional frame. Following the work of Aczel (1980), the intentional frame is an algebraic structure in which DRSs and other DR-theoretic structures are characterized as language-independent abstract objects rather than sentences of the language of thought. Elements of the intentional frame will be assigned intensions by an intensional model. The interpretation of DRS predicates requires that the elements of the intentional frame--the partial models (DRSs) and functions from discourse referents to partial models (predicative DRSs)--are also in the domain of the intensional model. Clearly, this complicates the logic underlying DRT. This two stage semantics for DRT invites comparisons with a Fregean semantics. The rela.tion_llif1..'Y~n tfie 'DRS language, D~ffie sets of em6edcIiilgTiliiCtlons

th~(Y~fXJ~'E. is.!err!i.~~.~g:~l~fu~lCh mstmguiSfiesaTeVerorSense an.Q_ltl~xeLoLrefer.ence.--:r.he. semantical.xole.of.DB~~:m:~£:~e'~~~9tfes t111!t1!:!~l>S;<§J:nJclll.t.es...pla~_.aAouble,.Iole"""Q.nJ~ one hand,~~..§..truc1.q.~~ne

tru~_S£.!,1stig!1~~~
On

CHAPTER TEN

MODEL 1HEORY

the other hand, they contribute conceptual structures to the interpretation of the overall structure of which they are part. As such they naturally serve to characterize the objects of attitudes. These structures play the role of senses in a Fregean semantic theory. Nevertheless, there are some important differences between this theory and orthodox Fregean theories. First, Fregean theories do not incorporate the dynamic element of meaning that is an important part of DRT's approach to sentence meaning. Second, there is nothing corresponding to a hierarchy of senses in my DRT semantics. 10 A third difference arises when one thinks of the Fregean dictum that every expression has both a sense and a reference and that sense determines reference. This dictum gives rise to the following picture:

intentional interpretation. One constraint on our domain of objects comes from the principle of comprehension. If S is a grammatical natural language discourse none of whose presuppositions or selectional restrictions is violated, then the construction procedure yields for S a well formed DRS. Further, if K is a DRS and Xj, ... , Xn E UK, then AX! ... AXnK(xdxj, ... , xn/xn) is a predicative DRS. Predicative DRSs, as functions from discourse referents and other DR-theoretic objects to DRSs, require the domain of abstract objects to have a functional structure. If predicative DRSs are functions, then when they are applied to the appropriate objects, they must yield appropriate objects. TheJ::)<~§,<::9P:y"~!~i?I] ,qYfmitiQReasil}(,yiy,1.4,~",i!:J;t?,.§!tiS!~~ form of ~ conversion in which !"predi£ative DRS applies to individual discourse reterents;.. This form of applicationp;~d~~~-;=~~' logrcar'dimcultres:~"I~'th~~'~~~~tr~ctio~t procedure of [email protected],,!t
392

Expression

~

sense .4-------. reference g Any attempt to work out formally the Fregean picture demands a commutativity of the sense and reference functions S and R; one ought to have for every expression a: R(a) = g(S(a)).l1 My use of DR-theory sees the corresponding relations between DR-theoretic structures, the counterparts of senses, and reference rather differently. Embedding functions, which define extensions, are defined on DRSs, not DRS expressions. DRS expressions have no independently determined extension in the model. They only have a denotation at the DRS level. Their extension is simply the extension that the definitions of embedding function and correctness determine for the DRS level object they denote. In some cases, the embedding functions take elements of DRSs onto DRSs; subDRSs and predicative DRSs function like constants at the DRS level denoting themselves in the model. Here is the set-up in the DRT semantics. DRS Expression

embedding functions ,-------/-- DRS

Model

393

JJ,S~.P~Qicl!te.d.Qf P14er coru;;.eptii1ili'pJit"~r?aiiilLnfa'ssiv(r'an(rspunouitsemantic a5l}ity. - It is also compatible with,o;;;yrndiscu;r~filie"'DR'S""COifStruetien procedure, if we take the Aterms to denote functions. This is the view developed in the appendix. There I extend the notion of Frege structures; I define the space of DRtheoretic structures in an algebraic way to form an intentional frame. Intentional frames contain a closed family of functions :T = <:Tn>, where the base set of functions :To includes DRSs, while :Tn includes n-place predicative DRSs. Every intentional frame is an extended Frege structure.

As counterparts to Fregean senses, the DR-theoretic structures constitute an

intentional interpretation for a natural language discourse. The interrelations of predicative DRSs, DRSs, and discourse referents force certain constraints on the

I

--------'-------

_~~~~4~~r'--M&'~-~"~--.

394

CHAPTER TEN

The fact that DR-theoretic structures fonn a type of Frege structure is important. This shows that they can be used to furnish a model of the A-calculus and that a subset, PROP, of the base level DR-theoretic structures--DRSs and other constructs representing saturated entities--is closed under a set of logical functions whose interpretation is the familiar one of the quantifiers and connectives of first order 10gic.13 It is the truth definition of first order logic that specifies the interpretation of first order connectives and quantifiers. For Aczel a Frege structure comprises such a truth definition for the whole base domain; he calls this truth definition a truth set. Indeed Aczel makes the requirement that the set of true propositions be a subset of PROP.

Frege Structure Truth Axiom: TRUE

~

PROP.

Thus, a Frege structure incorporates an interpretation of its elements. For DRT intentional frames, the truth definition is given by the definition of a proper embedding relative to worlds and times of an intensional model, and it is this proper embedding that shows us how to define the familiar first order quantifiers and connectives within the DRT intentional frame. 14 It is important that we have an intensional notion of proper embedding; not only does it give an intuitive notion of content, but it also allows us to speak naturally of contingently self-referential propositions, which are an interesting feature of natural language metaphysics (more about this in the next section). To get a complete correlate of a Frege structure, we must consequently consider together a DRT intentional frame, the definition of proper embedding, and an intensional model. Since the interpretation of objects in the intentional frame is intensional, we must relativize the Frege Structure Truth Axiom to worlds and times, and we must define PROP relative to a world and a time. Intentional Frame Truth Axiom: For any intensional DRS model M and for all w, tin M, TRUE 9,{, w, t ~ PROP9,{,w, t. Notice that only a certain subset of the base domain, PROP, at a given world and time is designated as supporting the familiar first order definitions. The subset PROP of the base domain of an intentional frame does not even contain all DRSs. It cannot do so because of the presence of paradoxical DRSs. These DRSs cannot have a proper embedding, according to the usual definition of proper embedding, that is consonant with the desired interpretation of the DRS predicates. The standard correctness definition holds only for nonparadoxical objects. We could interpret it as a partial function on DR-theoretic structures. To interpret model theoretically all DRSs, we must change our conception of semantics. Seeing why this is the case and what the options are is the topic of the next section.

MODEL TIIEORY

395

3. PROBLEMS OF SELF-REFERENCE

I

Intentional frames have certain limitations that arise because of the expressive power of natural language and the strong fonn of comprehension that operates in the construction of DRSs. Natural language, as Tarski pointed out, is rich in ways to express paradoxical propositions and sentences about various abstract objects. There is an inherent danger of inconsistency when one allows quantification over abstract entities. A rash of paradoxes--Russell's, Curry's, the Liar paradox, and various forms of intentional paradoxes for various attitudes--all threaten to destroy the efforts of the unwary theorist about properties and propositions. Our present construction rules with the quantification over abstract objects countenanced in chapter 3, for example, provide the resources to construct paradoxical propositions, the presence of which might cause doubt as to the coherence of the whole enterprise. For instance, one can easily imagine the following situation: A: Something B says is false. B: Something A says is true. It is perfectly conceivable that A and B say nothing else in their lives (they are very taciturn). This is an example of a pair of contingently self-referential propositions; they are self-referential in virtue of facts about the world in which A and B say things. IS By the rules for interpretation of the truth predicate (and our assumption that the underpinnings of our model theory are consistent), such a situation cannot exist. But surely this is implausible. We can talk about what A and B said and refer anaphorically to the propositions expressed; for instance, we might say that the propositions expressed by A and B are problematic or paradoxical. Contingently selfreferential propositions are an undeniable aspect of natural language metaphysics. It is easy enough to express within the DRS language described in chapters 3-5 a DRS which says that there is a proposition that says that it is not true of itself; i.e., the proposition expressed by the that clause is self-referential in every possible world. By our principle of comprehension such a proposition must exist. Here is its DRS: (Kl) ~_~~_ _ __ I p says(p,

I~I ""W) II)

On the assumption that (Kl) has a proper embedding, the natural interpretations of the predicates and conditions in this DRS lead to contradiction. For instance, if we assume, using the v operator, a reasonable higher order axiom about saying, 'v'p'v'q(say(p, q)

-->

(Vp <-> Vq)),

......

..---------rrrz:---'==~~~~-__'""'";=;~=~==~~---~---~~----~'~,~-----------------'-----"'---'-'-'--'-

CHAPTER TEN we will quickly obtain a contradiction, Of course, (KI) is not by itself paradoxical. W,e co~ld.consistently maintain that (KI) has no proper embeddings. The difficulty WIth thIS IS that there seem to be propositions that fit just what (KI) asserts--again these are examples of contingently self-referential propositions. Consider, for instance, the examples in (I): (l.a) The proposition expressed by this sentence is not true. (l.b) This claim is not true. Accor~~g to our generous principle of comprehension, (l.a) and (l.b) must express proposIllons. It seems as though they should be interpreted as expressing the Liar. One cannot, it is true, write down a DRS inscription identifying a discourse referent with the DRS in which it is declared. This would violate the well-foundedness constraint. But tlte method for translating complex demonstratives into the DRS language, discussed in chapters 2 and 6, shows us how we can have self-reference and standard DRSs. Consider (l.b). Suppose we interpret the complex demonstrative this claim referentially.1 6 Then it will simply introduce a discourse referent of propositional type and an external anchor. Now external anchors, recall, are constraints on embedding functions; they pair a discourse referent with an object of the appropriate type in tlte domain. The appropriate type in tltis case is a DRS. All DRSs are in tlte domain of every standard DRS model--in panicular the DRS for (l.b). This is just the DRS that the external anchor assigns to the discourse referent under the most salient interpretation of (l.b). The result is a curious anchored DRS (Kl.b), which under tlte model theoretic interpretation, is self-referential)? ,

(Kl.b)

~~ 'I I ~

397

MODEL THEORY

{
(2) It is a fact tltat (2) does not denote a fact. exhibits the same pathological behavior as the Liar sentence (l.b) when we take tlte intuitive semantics of contexts like it is a fact that.. The intuitive semantics should entail tltat it is a fact tltat p iff p. There are also paradoxes governing attitude predicates. Epistemic and doxastic predicates threaten to engender paradox when we add natural constraints to their interpretation. For instance, the anchored DRS for (3) below, (3) This claim is not known.

I

p x

I

'I know(x, p)1

P

{
x

>} I

'\ know(x, p)\ leads to contradiction when minimal rules governing the logic of knowledge are assumed. 2o These rules may be thought of as codifying principles that we feel justified in using in reasoning about our knowledge; to get paradoxes concerning the attitudes, we need not suppose that the attitude is question is closed under those logical principles as a matter of fact. To formulate the paradoxical sentences, I have once again exploited deictic reference with either a complex demonstrative or a namelike device. As the reader will have guessed, it is also easy to assert tlte existence of the Russell property in my extension of DRT: Co

>}

true(p)

The anchored DRS (Kl.b) is perfectly consistent with our set theoretic description of DRSs; in particular it is a well-founded structure. We can construct such anchored DRSs, because the set of DRSs is included in the domain (at each tuple of indices) of the intensional model. This use of external anchors gives us self-referential objects tltat are paradoxical when we attempt to give an inwitive interpretation of the predicate true.1 8 Such examples are contingently self-referential, however, because the context might have been such tltat tltey were not anchored in a self-referential way. Difficulties with paradoxical abstract objects involve other DRS predicates besides truth. Given the range of abstract entities and predicates tltereof included in this study, we must be prepared to countenance a very wide area of semantic difficulty.19 The statement

Co"'Ac~

~

Comprehension principles for properties in natural language metaphysics are analogous to those for propositions--in the sense that any descriptive phrase for which a concept DRS expression may be constructed (passing selectional restrictions, etc.) denotes a concept. On this generous view, it follows from a sentence like (4) The concept of not being self applicative does not apply to itself that the Russell property exists in every DRT intentional frame. The DRS above is paradoxical solely in virrue of the basic interpretation of negation and the fact that this extension of DRT verifies a form of Pconversion. A typical tactic for maintaining consistency, is to admit as abstract entities only

MODEL THEORY those that pass stratified principles of concept or propositional comprehension. 21 But this is not the strategy taken with extended Frege structures. The logical operators are required to have their first order interpretation only over a restricted set of what we might intuitively take to be propositions. In an intentional frame, (i) but not (ii) is the case: (i) 'rIM'rIw'rlt in M 'rip E PROP w, t (M, w, t) ~ vp v -,vp, (ii) 'riM 'rIw'rlt in M 'rip E {DRS} (M, w, tH vp v -,vp, where' (M, w, t) ~ cp' means that for every w, tin M and every embedding function f, M satisfies cp at w, t relative to f.22 In extended Frege structures it remains open as to what we should take as the class of propositions of natural language metaphysics and what their interpretation should be. In chapter 1, it seemed that a generous principle of comprehension for propositions was called for. Even paradoxical DRSs are nevertheless part and parcel of natural language metaphysics. The semantic paradoxes are paradoxes and interesting ones at that, precisely because in some sense these paradoxical propositions and concepts undoubtedly exist as part of our natural language metaphysics. Such concepts as the Russell property exist in as robust a sense as other concepts, if we look to our linguistic tests of quantification and anaphora. We think the sentences that express paradoxical propositions and concepts problematic, but not nonsensical or ungrammatical. So we must accept such objects in some way in intentional frames. On such a view, the set of propositions in natural language metaphysics would have some correspondence with the set of DRSs, not with the set PROPw t for chosen w and t. I will continue to assume an unrestricted principle of comprehension for DRSs and naive propositions: every grammatical discourse yields a well-formed DRS. PROPw, t corresponds to the set of propositions grounded at wand t or propositions whose truth conditions are not paradoxical or logically problematic at w and t.; because of contingent self-reference, a proposition may be grounded at one world w and time t and hence an element of PROPw, t but not at another w' and 1'. I shall distinguish then between naive propositions, which correspond in some way yet to be made precise to DRSs, and the grounded propositions, which correspond to elements of PROPw,t. From unlimited comprehension, one gets immediately:23 PROPOSITION 1: 3p3p'

E

{DRS}

(~p

'" p' & not

~

vp ..... Vp').

The proof of this proposition relies on producing a particular DRS in an intentional frame--viz., a DRS whose only condition is of the form A,c-,(c(c))[A,c-,(c(c))], i.e. the Russell property applied to itself. Given an unlimited comprehension principle, there is such a DRS, as we have already seen. If the structure is a model of the lambda calculus, then A,c-,(c(c))[A,c-,(c(c))] = -,(A,c-,(c(c))[A,c-,(c(c))]). But the left and right hand sides cannot have equivalent truth values, on pain of contradiction; that is,

399

-,(V {A,c-,(c(c))[A,c-,(c(c))]} ..... -, v (A,c-,(c(c))[A,c-,(c(c))])).

The simple and familiar proposition above has far reaching consequences. We must now suppose that the familiar definition of proper embedding extended to cover the developments after chapter 2 can properly apply only to PROP and not to all DRSs. The situation is particularly embarrassing, since PROP is relativized to worlds and times for a given intensional model. But just to make the point completely clear, suppose that we defined a structure to be just like an intentional structure except that PROPw,t = {DRS}. The DRS alluded to in the previous paragraph, together with the definition of a proper embedding, yields a result which is inconsistent with the classical, first order definitions of the connectives. Consequently, PROPOSITION2: For all models M and every w, t in M, PROPw,t # {DRS}. COROLLARY: Not every closed family of functions with a set of functionals has a

truth set. These propositions leave us with a problem. We need to have a method of defining PROP. The only plausible way to do this is first to devise a more general interpretive procedure than the standard embedding embedding definition for all DRSs, and then to isolate which DRSs, under the interpretation, give us a suitable set of objects at a given world and time to serve as the defmition of PROP. Let us explore some options within intentional frames. Take a very simple case: For each model M and each world and time w, tin M, we have a function 0 such that given an element cp E PROPw,1> 0(cp) yields the familiar embedding definition's results at w, t, and for elements 'Jf E {DRS} - PROPw, t, 0('Jf) is undefmed at w, t. I will also introduce a two place connective, ""', such that for a, 13 E {DRS} M, w, t ~ a"'" 13 iff M, w, t ~ a ..... 13 or 0(a) and 0(13) are both undefined at w, t. One can sum up the paradoxical effects of the DRS construction procedure by proving in effect a version of G6del's fixed point lemma using the natural language metaphysics principles of comprehension. Suppose cp is an English adjective, which when combined with the copula takes abstract entity denoting constructions as a syntactic argument, and let ~ be anyone place function of expressions. Suppose that ~ and cp have translations into the language of logical analysis ~', cp'. PROPOSITION 3: 3p E {DRS}(~ vp

!!!!!

v~'cp'(p)).

Consider the English sentence this proposition is ((
MODEL THEORY

CHAPTER TEN

400

show that no axiomatization of the logic of propositions is possible. PROPOSITION 4: The logic of naive propositions is not axiomatizable, assuming

that it is consistent. By proposition 3 we have (5) 3p

E

{DRS} (1= vp "" -,vProvable(p»,

where the interpretation of 'Provable' is just the notion of provability for propositions hypothesized to exist. I will assume that Provable(p) is verified just in case one can prove p in the logic of naive propositions. Provable(p) is refuted just in case there is no proof of p in that logic. This interpretation of the provability predicate seems reasonable to me, but notice it establishes a limited sort of bivalence--viz., vProvable(p) v -, VProvable(p) is valid--even if the logic of naive propositions is a partial logic! So assume provable(p) and that the logic of naive propositions is consistent. Then p is false but provable, which contradicts our assumption. But assuming -, v provable(p) verifies p, and this shows that there is a true proposition that cannot be shown to be true in the logic of propositions. Intentional frames contain a variety of DRS predicates--in particular a truth predicate, a fact predicate, and a variety of attitudinal predicates, for which there are certain natural definitions. The interpretation of the truth predicate and the specification of the set PROP in an intentional frame sketched in the next section will give us: PROPOSITION 5: In every intensional model '.M and for all w, t in '.M, \tp E

PROPw, t, ('.M, w, t) 1= vTrue(p) vFact(p) ++ v p .

++

Vp) and \tp

E

PROPw, t, ('.M, w, t) 1=

It immediately follows from proposition 5 together with reasoning familiar from Tarski that the set PROPw, t is not definable within an intentional frame for all '.M and any w, t in '.M. PROPOSITION 6: PROPw, t is not definable within an intentional frame for all '.M

and any w, t in '.M. PROP is definable just in case there is a formula

(6) 3p (-,(v
401

Suppose p E PROPw , t. Then
403

CHAPTER TEN

MODEL THEORY

can generalize any of these approaches to handle any number of predicates that apply to abstract objects like facts or propositions. A theory that identifies propositions, facts and other saturated abstract objects with sentences is not ideal, however. Because of arguments like Church's translation argument discussed in chapter 3, it is better to identify propositions with nonlinguistic structured partial models like DRSs. But one can also apply model-revision approaches in a very straightforward way to DRSs or other DR-theoretic structures, should one so desire. The reason is that DRSs are objects in the domain of a DRS model; one can revise the extension of a DRS predicate as long as the DRSs are objects in the domain of the model whose existence is independent of the assignment of extension to predicates at worlds. Also crucial is that such structures are assigned an evaluation by the model. Thus, we can coherently compare the evaluation of such a structure in one model (at some world) with the extension of a predicate at the same other model in the sequence. On the other hand, it is far from obvious how to use model-revision techniques if one identifies abstract objects simply with sets of possible worlds or DRS intensions. The essential point for applying the model revision techniques to intentional models generally is that DR-theoretic. intentional structures are independent of intensions in the way required for these techniques to work. That is, even though such structures are not linguistic items, we can apply the techniques of Kripke, Gupta and Herzberger to them. Model revision constructions give rise to many possibilities. Within the framework of the model theory for DRT, the general approach is this. I extend the embedding definition in the appendix of this chapter to all DRSs. Embedding functions will map proposition discourse referents onto DRSs and concept discourse referents onto predicative DRSs, as before. The model theory will now, however, consist of two main parts. First, one constructs a model-structure for the DR-theory fragment without an interpretation of DRS (or predicative DRS) predicates. A model structure M is a tuple of the form <WM , TM, DM , {Qp, M}PE 1t, [D>, where WM is a set of worlds, TM a set of times, DM a domain, {Qp,M}PE 1t a set of alternativeness relations (one for each DRS predicate in 1t), and [D an assignment function for the non-DRS predicates. A model for the full DR-theory fragment discussed here extends a model structure with an interpretation of the truth predicate (a function from worlds to extensions) and other DRS predicates. This interpretation may be partial, as in the case of Kripke's (1975) inductive construction, or total in the case of Herzberger's (1982) and Gupta's (1982) semi-inductive construction. The total interpretation uses the classical valuation rules for the connectives and quantifiers, while the partial interpretation uses valuation rules like those known as "strong Kleene. " The second main component of a model theory for naive propositions is a revision rule which defines a sequence of models that revise and improve upon the initial interpretation of the DRS predicates. A very general characterization of a revision rule can be found in the appendix. Define an inte.cpolation function on a set A to be any function f from go (A)2 into go (A) such that whenever A I, A2 !: A and A I n A2 = 16 then f(A I , A2):::! Al and f(Ab A2) n A2 = 16. A revision rule is a function 1(

defined on the class of all limit ordinals such that for each limit ordinal A, 1((A) is an interpolation function on the set K of DRSs. Given a model IJv( and a revision scheme !l(, the revision sequence starting from IJv( according to 1( for a I-place DRS predicate P is the sequence {IJv(U,!l{.}UE On' such that: lJv(u,!l{. = <W'M ' T'M' D'M ' !)P,'M , [Du,!l{.>, where [ODU,!l{. = [OD'M for all nonlogical constants 0 other than P, and [pDa.,!l{. is defined as follows. Let A!l{.w ~ Dw and A!l{.w ~ K. Finally, let Qp be a selection function from W to go (W) "appropriate" for the predicate P.

402

i) [PDO, ~ = A~ ii) [PDu+l, ~ = {KE A: 3glJv('" FW',g K for all w' E Qp(w)} iii) Where A is a limit ordinal, [PDA,!l{.'M,w = 1((A)(P+W' P-w), where p+w = {K E A: (3'Y
404

405

CHAPTER TEN

MODEL TIIEORY

chapter. One desideratum, however, for any interpretation of such structures, which all of the model revision procedures, meet is that the semantics for paradoxical structures should not "infect" with unintuitive predictions the unproblematic parts of language. 27 A judicious application of a revision procedure does not lead to any obvious violation of the desideratum that we keep the logic of ordinary, unproblematic propositions intact. Where these methods diverge from our intuitions is only with paradoxical sentences and propositions. That is precisely the point where they should diverge, because our intuitions get us into trouble. So in general we can use anyone of these schemes to define PROP and to get possible intensions for DRS predicates. For instance, the Herzberger scheme entails the existence of an enclosure point in a revision sequence beginning with a model ']v[, a point in the revision a such that for every predicate P, K E [PDa'!/{.M,w iff K E [PD~, !/{.M,w for all ~:2: a. [PDa'!/{.M,w contains all the P-stable DRSs, those that remain within the extension of P throughout the rest of the revision process. Conversely, we may consider the set of those DRSs that remain stably outside the extension of P throughout the rest of the revision process. These stable DRSs have a desirable nonparadoxical character, and we may use them to define PROP. We may stipulate for an intentional frame together with a classical model ']v[:

As a possible basis of choice among these alternatives, let me present two paradigms about how to understand revision rules. According to the first, the (semi-) inductive definition of the extension of a predicate builds up an appropriate extension supervening upon the base model structure. That is, a revision rule is simply a way of extending initial assignments of a model structure to get a full interpretation of the language. It is of a piece with model theory traditionally construed, and it is perhaps the most natural way of defining the truth set for extended Frege structures or the set PROP for intentional frames. 30 According to the second conception, a revision rule reveals something of the way we reflect about the particular property at hand and the way those reflections may tend to change the extension of the predicate. The second conception of a rule of revision is essentially doxastic or attitudinal; it tries to capture the way our own cognitive activities may affect the contents of cognitive states. These two conceptions of a revision rule fit DRS predicates differently. The second conception is quite natural for the attitude predicates. But attitudes are quite different from other DRS predicates; in reasoning about our own attitudes, we acquire new beliefs, desires, intentions, etc. Some of our attitudes may become unstable during our reasoning about them, in the sense that we may on reflection come to hold a belief, for instance, that we did not formerly have and then upon further reflection reject that belief and so on. 31 The revision rules for the belief predicate in Asher and Kamp (1986), Asher (1988), and Asher and Kamp (1989) attempt to capture this dynamic aspect of belief--viz. how our beliefs change under reflective reasoning,32 Another important point about attitudinal predicates is that the starting points of the revision procedure for the attitudinal predicates should reflect the pre-reflective cognitive states of agents. The semi-inductive schemes seem better able to do this. For instance, one may pre-reflectively believe a paradoxical proposition and only come later to realize through reasoning that it has an unstable truth value. This is impossible to model within an inductive scheme; an inductive scheme requires that paradoxical propositions, like the proposition that claims of itself that it is not believed, remain outside of both the extension and the "anti-extension" of the belief predicate. 33 For other DRS predicates like truth, facthood and especially application, however, the second conception is perhaps less felicitous. That a statement like It is true that Isis the cat is washing herself is true should not have much to do with how an agent might reflect on truth. On the semi-inductive schemes of Herzberger, Gupta and Belnap, it will. The instabilities or gaps in the truth predicate due to paradoxical sentences like (1) might only arise because agents reason about propositions containing the truth predicate in a particular way, as Gupta has argued. But equally plausible is the first view concerning the truth predicate. A plausible suggestion is to establish the, appropriate extensions for the truthlike predicates using an inductive scheme to reaoh the minimal fixed point, and then to use a semi-inductive revision procedure on the attitudinal predicates. To capture all the truths that result from having altered our attitudes--viz., truths of the form Vtrue(believe(a,
PROPw, t = {a E {DRS}: a has a proper embedding at w and t in the enclosure point of the Herzberger revision sequence beginning with ']v[}.

The inductive schemes entail a fixed point of the revision sequence beginning from a partial model ']v[. We may stipulate for an intentional frame together with a partial model ']v[: PROPw , t = {a E {DRS}: a has a proper embedding at wand t in the minimal fixed point of the inductive revision sequence beginning with ']v[}.

According to either of these choices, we have established that the intentional structures of DRT are nontrivial in the sense that they have a non-empty set of elements on which the first order quantifiers, connectives, and propositional predicates have their familiar meaning. Extending the technique of inductive and semi-inductive definitions to attitudinal DRS predicates has in principle already been done. 28 But such studies typically only apply the technique to one predicate--belief or knowledge. In the present more general setting, the interpretation of many predicates requires caution. A large number of alternatives arise, and at least some merit discussion. Should we, for example, revise all the DRS predicates together, or should we make a distinction between attitudinal predicates and non-attitudinal predicates? The techniques developed by Kripke, Herzberger, Gupta, and Belnap yield many different, possible revision rules. Should some predicates be revised according to one rule, others according to another? The rules are not all independent, so that the effects of one revision rule for one set of predicates might affect or conceivably even wipe out the logic of another.29

406

407

CHAPTER TEN

MODEL TIIEORY

The initial extension for the truth and truthlike predicates will reflect the independence of certain truths from attitude reflection (those that remain within the extension of the truth like predicates during subsequent revisions of both attitude predicates). A number of nice details emerge. The Liar sentence or any simple truth paradoxical proposition or application paradoxical proposition, like the one saying that the Russell property does not apply to itself, is stably not believed; doxastically paradoxical sentences would have an additional layer of complexity.34 This approach would underscore the considerable difference between the interpretation of attitudinal predicates and non-attitudinal predicates. Non-attitudinal predicates like the truth predicate could best be characterized at a particular point in the model revision sequence (like the fixed points of the inductive revision scheme). On the other hand, the revision process for attitudinal predicates should reflect the dynamics of those cognitive states. Thus, no single model in the revision sequence represents the "right" model for the attitudes; the sequence as a whole is what is important. One could combine the two constructions by doing a fixpoint construction for the truth like predicates that begins with a metastable model for the attitude predicates--such a model represents a stable cycle of revisions as in Asher and Kamp (1989).35 These fixpoints would then define PROP. For an intentional frame a model ']v[ and for each world w and time t in ']v[, one could stipulate:

stable truth conditional content. Alethically paradoxical propositions--which includes propositions like those expressed by (1 )-(2) and (4) of the last section--end up lacking a truth value altogether, because of the inductive scheme chosen. Attitudinally paradoxical propositions never get a stable truth conditional content. All paradoxical propositions never acquire determinate truth conditions in the following sense: if p is paradoxical, then it is never the case that p stabilizes to truth or falsity.

= {a E {DRS}: (']v[A. w, t) ~ a, and ']v[A. is the minimal fixed point model for the truthlike predicates constructed from the enclosure point of ']v[~ for the attitude predicates} .

PROPw , t

This definition of PROPw, t can be shown by the combination of semi-inductive and inductive constructions, together with a model structure with a suitable interpretation of DRT predicates, to yield a non-empty set of objects on which the connectives and quantifiers as defined in intentional frames have their standard first order definitions. It will also suffice to verify proposition 8, a slightly extended version of proposition 5. 36 PROPOsmON 7: There is a model ']v[ for an intentional frame on which for all w, t in ']v[, PROPw , t i= 91. PROPOsmON 8: Vp E PROPw , t (']v[, w, t) ~ vtrue(p) _ vp; Vp E PROPw , t (']v[, w, t) ~ vfact(p) _ vp; VCfNa (3p E PROPw , t such that
I have correlated naive propositions with certain information theoretic structures, which have (but are not identical to) truth conditional contents. The truth conditional content of naive propositions is represented in the' theory by the set of worlds and times at which the correlated DRSs have proper embeddings. Unproblematic propositions will eventually acquire, according to the procedure of model revision, a

4. TWO ARGUMENTS FOR A REPRESENTATIONAL THEORY OF ABSTRACT ENTITIES The previous sections have put in place the outlines of a mechanism sufficient to interpret the DR-theoretic structures in this book. But the metaphysical ramifications of the mechanism and of the approach in general remain largely unexplored. This is my task in the last two sections of this final chapter. The first advances two arguments for the sort of representational semantic theory I have built; the other looks at some of the implications for real metaphysics. Three general concerns have guided the development of my analysis of abstract entities: solutions to the paradoxes, the expressive power of the propositional fragment, and the semantics for natural language constructions denoting abstract objects, in particular the attitudes. I have argued for a DR-theoretic, representational account of the attitudes in chapter 3. In chapters 7- 9, I developed SDRS theory, my theory of discourse structure, which relied heavily on structured representations for discourse. A principal feature of my semantics is that embedding functions map abstract entity discourse referents onto DR-theoretic structures in the domain of the model. This is not the only way one might have treated abstract entities in DRT. The model theoretic machinery of the simple fragment suggests many possible values for discourse referents of abstract type: functions from indices to appropriate extensions, or sets of embedding functions, as well as DR-theoretic structures)7 In this section I examine the reasons for choosing representations as the values of abstract object discourse referents. I consider two new arguments about how strong representational theories offer a superior solution to the self-referential paradoxes. This discussion leads to philosophical questions about the reduction of abstract objects. I distinguish three sorts of representationalism. Weak Representationalism: (i) There exists a distinct level of semantic representation between syntactic structure and functions from indices (worlds, times, contexts, etc.) into truth values. (ii) The interpretation of a natural language fragment proceeds via the interpretation of representations. Strong Representationalism: (i) Weak Representationalism

diM! ERI EN

408

(ii) The representations posited by ordinary representationalism are themselves objects in the models that can be in the extension of various predicates-namely, the attitudinal predicates. (iii) The interpretation of representations makes reference to objects in the domain. Metaphysical Representationalism: Representations are mental constructs. Metaphysical Representationalism is part of the reductive claim that a conceptualist would make,38 While DRT is often interpreted as only weakly representational, my version is strongly representational. Many philosophers and psychologists have also adopted strongly representational theories-- for instance, Fodor (1975) and JohnsonLlaird (1982). There are theories, however, that are not representational in any of the senses above. Theories that reject strong and weak representationalism are Montague Grammar and more fine-grained versions thereof like Cresswell's (1985) structured meanings. These theories, unlike the situation theory of Barwise and Etchemendy (1987), or Bealer's (1982) or Chierchia and Tumer's (1988) property theories eschew any intermediate levels of objects--for instance structured propositions or situations-that might serve the role of representations,39 But if situations are taken to be parts of the world, then situation theory also rejects strong and weak representationalism. I now give my case for strong representationalism. As competitors to the representational theory, I will consider only the more refined theories of attitudes needed to get around the difficulties of substituting logical equivalents within belief contexts; the non-refined theories already suffer decisive and well-known drawbacks as general theories of propositions. Cresswell's theory is a paradigm of a refined nonrepresentational theory, though others, like versions of situation theory, might be considered as well. On Cresswell's theory, propositions are modeled by structured intensions, a sequence of intensions for each syntactic constituent of the sentence. I assume that a compositionality constraint applies to all such theories. Thus, the meaning even of self-referential sentences is to be accounted for in terms of the meanings of the sentences' constituents. One cannot then simply assign some arbitrary intension to paradoxical sentences, and one must calculate the intension corresponding to a sentence from the intensions of its constituents. The first argument for the representationalist position is that the representationalist can handle various forms of self-reference without resorting to non-well-founded sets. Of particular interest is the "designative" form of self-reference discussed in the previous section, of which (1.b) is an example: (1.b) This claim is not true. To express the self-referential (1.b) in the DRS language, we exploit the analysis of deictic reference and the device of extemal anchors. The DRS for (1.b) contains itself as an external anchor for the propositional discourse referent it introduces. This anchored DRS itself is well-founded and can be described in ordinary set theory. But the evaluation of the DRS in (1.b) will exploit the DRS itself; when embedded in a

MODEL THEORY

409

model, the DRS for (1.b) refers to itself. This is perfectly acceptable, since DRSs are not only intermediate structures but elements in the models as well. The representational view splits the problem of self-reference into two parts--first the construction of a proposition p and then an evaluation of p that makes use of p.40 Such anchored DRSs have the self-referential character that we expect of viciously self-referential propositions. They do not get a stable proper embedding in any model for the truth predicate using plausible revision rules for truth like those discussed in the previous section.41 What could a nonrepresentational theory like Cresswell's say about such paradoxical propositions? A nonrepresentational theory cannot split the problem of self-reference into two parts, as can the representationalist. What resources does the Cresswellian theory have? It simply has functions from indices to extensions. Let us now try to build compositionally the denotation of (1.b). The truth predicate must take a structured intension as an argument --a structured intension for (1.b) itself. But what is that? It is <-', [true], <-', [true], < ... >... >. The intension forms an infinite descending chain of intensions. Notice further that in this chain the intension [true] will have to contain itself--infinitely often. This is a non-well-founded set if functions and structured intensions are understood set-theoretically. This is, however, nothing new for the structured intensionalist. One well-known difficulty with Cresswell's view is that already iterated attitude reports lead to non-well-founded structured intensions; on such a theory even unproblematic nested attitudes look paradoxical. The proposition that John believes that Mary believes that Samantha is a mathematician is rendered by the structured intension: <[believe]([John], <[believe] ([Mary], <[mathematician] ([Samantha]»»» Here already we see that this intension forms a non-well-founded set. Within standard set theory, one cannot construct structured, Cresswellian intensions for any iterated attitude report or any sentence containing an occurrence of the truth predicate embedded within another. It is perhaps then no surprise that one cannot construct intensions for self-referential structures either. One can, however, model such complex structures in Aczel's non-well-founded set theory. The theory of non-well-founded sets allows us to represent self-reference directly without the two stage theory of the representationalist. Aczel's non-wellfounded set theory, AFA, makes heavy use of the notion of a graph.42 A graph is a collection of points and directed edges, while a decoration of a graph G is a function from terminal nodes in G (no directed edges going out from the node) to atoms including 16. The important axiom of AFA set theory is this: AFA Axiom: Every graph has a unique decoration. From this it follows that non-atomic objects a and b are identical just in case they may be depicted by the same graph. All the graphs below, for example, denote the same non-well-founded set, Q.

o

1 1

1_

Aczel's AFA has been shown to be consistent relative to standard set theory, but it has certain defects when used to model propositions in a straightforward way. Consider the discourses:

1

(6.a) (6.b)

1

1 1

This proposition is true. A: Proposition B is true. B: Proposition C is true. C: Proposition A is true.

On the left is the graph for [p] = <[true] , <[p]»; on the right is the graph for the set of equations [PI] = <[true] ,<[P2]», [P2] = <[true] ,<[P3]», [P3] = <[true], <[PI]».

The reason that this is true is that all the nodes in the graphs above can be labeled with n, and by AFA this decoration must be unique. Assume now that structured intensions are AFA sets. Structured meanings for sentences like (1.b) above plausibly take the form of a fixed point equation of the following form. p = <-', [true],
= <-',

[true], < p». A theory of non-well-founded objects modeled as non-well-founded sets, identifies many intuitively different self-referential situations--simple I-element selfreferential loops, n-element loops, and infinite descending chains. The representational approach developed here distinguishes these varieties of selfreference. A proposition that refers to itself or contains itself as a constituent like the Liar is identified with the following anchored structure like the one given in (K1.b). A cyclic sequence of objects al ... an, where each ai contains an abstract entity discourse referent Pi, will be represented by the following set of anchored objects:

A similar noncyclic set of anchored objects represents an infinite descending chain of propositions. Any proposition, even a self-referential proposition, can be modeled by a sequence of atoms in AFA. This proves to be the undoing of a theory of propositions relying on AFA.

Since we can tag each node with the same element in the above two graphs, the two "discourses" in (6) express the same proposition, according to AFA. But this is unintuitive. An agent might understand these discourses yet doubt that they had the same meaning or the same self-referential properties. One might believe that the proposition expressed by (6.a) was self-referential, without believing the proposition represented by an extension of the graph on the right into an infinite descending chain is self-referential. But we can give a much stronger argument against the structured intensionalist. Consider the following "discourse": (7) A: Proposition B is false. B: Proposition C is false. C: Proposition D is false. D: Proposition A is false. (7) yields the equations: [PI] = <[false] ,<[P2]», [P2] = <[false] ,<[P3]», [P3] = <[false] , <[P4]», [P4] = <[false], <[PI]». These equations give us the same

"~------------------------

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solution as the Liar. But there is a consistent assignment of ordinary intensions to p 1P4· [PID: W -+ 0; [P 2 D: W -+ 1; [P 3 D: W -+ 0; [P4D : W -+ 1. There is no consistent assignment of ordinary intensions to the Liar as we have already seen. So this seems to violate the requirement of the structured intensionalist that the ordinary or crude intensions are compositionally determined by the fine-grained view. Even if the intensionalist gives up his principle of compositionality or changes his definition of what the crude intensions are in (7), there is a clear way of distinguishing between these discourses to which an agent might appeal--one is consistent and the other is not in a two valued scheme. Yet the structured intensionalist tells this agent that he cannot distinguish them. AFA thus forces us to collapse together naive propositions that can be easily distinguished, and this is unacceptable both on intuitive grounds and since we can easily generate attitude reports where the theory will go wrong. 43 Thus, a nonrepresentational theory, even when it helps itself to powerful, new set theories like AFA, does not handle self-reference as well as my DRT semantics. The second argument for strong representationalism is much briefer but equally important. According to the well-foundedness constraint of chapter 7, every anaphoric identification must be well-founded. This led to some non-trivial constraints on discourse updating and anaphora resolution. Given the representational treatment of self-reference of the sort I developed earlier, one could claim a deep semantic motivation for this constraint. There are no non-well-founded semantic structures. To allow anaphoric reference by a discourse referent to a DRS in which it is declared would result in a non-well-founded discourse structure. Even selfreferential propositions, on my analysis, do not violate the well-foundedness constraint. Notice that this is a constraint specifically against non-well-foundedness. The structures that result from anaphoric identifications like the one just mentioned might very well be interpretable without paradox. The prohibition applies simply to a certain type of structure. The difficulty is for the nonrepresentational approach is that it is in any case committed to the existence of non-well-founded structures, even for simple embedded attitude reports or claims of truth. How then do we distinguish between the non-wellfounded structure that results from a discourse referent being identified with the DRS in which it is declared and the non-well-founded structure that results from identifying the variable introduced by the pronoun inside an unembedded belief context with a structured proposition containing a belief intension? On the structured intensions view, there seems to be difference that is not ad hoc between the following two cases of non-well-founded propositions resulting from the anaphoric process.

perfectly unproblematic. The structured intensions view or other nonrepresentationalist theories, committed as they are to the possibility of non-wellfounded propositions, approach the data in the wrong way and fail to explain certain important asymmetries, such as the one in (8.a) and (8.b). The strong representationalist account of paradoxical propositions, on the other hand, has the resources to distinguish between (8.a) and (8.b); it also suggests the possible linguistic universal against non-well-founded linguistic structures.

412

(8.a) [John does not believe thisj.]j (8.b) [John believes that Mary is going to leave himL, but Mary does not believe thisj. Both of the propositions that result from identifying the variable introduced by the pronoun with the structured intension for the material inside square brackets produce non-well-founded structures. But one is clearly ungrammatical, while the other is

5. MET APHYSICAL REPRESENTATIONALISM AND METAPHYSICAL REDUCTION In the previous section I argued for strong representationalism. In this last section, I consider metaphysical representationalism. The consequence of metaphysical representationalism for real metaphysics is a reduction of abstract objects to mental constructs. It is a conceptualist's view of abstract objects, a position in metaphysics at least as old as Peter Abelard in the Western philosophical tradition. The novel part of my argument consists of a new way of making the conceptualist thesis precise; my semantics for abstract nominals has rendered empty the apparent ontological commitments of natural language to abstract objects. I will look at two paradigmatic types of abstract entities--propositions and facts--and propose a reduction of these entities. The view of properties, on my analysis of them as propositional functions, stands or falls with the view of propositions. Given the interpretation of "" and the fact that abstract entity discourse referents map onto DR-theoretic structures under embedding functions, my theory suggests that propositions and properties are equivalence classes of DRSs and predicative DRSs respectively.44 In effect, however, whenever we intuitively quantify over propositions or other abstract entities as in the many examples of this book, my analysis requires only that we quantify over DRSs. In the model theory, propositions and their properties supervene upon their constituent DRSs. Propositions, (complex) concepts, facts, and other abstract entities are not properly speaking elements of the domain of our models but rather constructions out of elements of the models using a particular equivalence relation (alphabetic variance or perhaps in certain cases a functional equivalence of some kind). We don't quantify over propositions or other abstract objects, just over DRSs. My semantic analysis thus supports a reductive claim. There are no propositions, facts, etc.; there are just DR-theoretic structures. Further, these structures are just constructs of mental states. DR-theoretic structures are at bottom designed to tell us something about the structure and contents of cognitive states. The characterization of abstract entities in terms of equivalence classes of DR-theoretic structures suggests the following strategy: any fine-grained notion of abstract entity is entirely dependent on structural properties or features of cognitive states, which I take DRSs to characterize. The reduction I propose aims to eliminate fine-grained propositions, finely-individuated facts, and the like as independent entities. We are left only with

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constructions of cognitive states and the basic contents provided by the conception of possible worlds, which Stalnaker has adroitly defended. 45 We can think of propositions and the like as constructions--useful for characterizing the behavior and mental states of agents. The highly structured abstract objects of natural language metaphysics, to which we appeal in the semantics of the attitudes and other constructions, are mental constructs. The conceptualism I advocate is, however, very modest. I retain a possible worlds apparatus to explain contents. Over and above the modal facts of our world (modal facts that can be modeled by thinking of a space of possible worlds or how the world might be), we need nothing in the way of mind independent abstract metaphysical objects to get a semantics for abstract entity characterizing constructions. Many philosophers, for instance Bealer and Monnich (1989), might object to this proposal. The objector might claim: these objects are mind independent after all. They are elements of your models and are not tied to agents at all. But it is easy to make the dependence upon mental activity explicit in the model. We may postulate that a model in which there are no agents at any world has no DR-theoretic structures in its domain. In a model there may be worlds with no agents, but this should be no cause for alarm; agents can clearly communicate and think about such a world, and so a model in which one world has an agent should be a model in which DR-theoretic structures are postulated as elements of the domain. The objector might still not be satisfied, for he might reply: in what sense are these mind dependent objects? Does an agent have to actually think one of these structures? Complex objects like DRSs and DDRSs are freely generated from infinite sets of other types of objects. So my conceptualist owes an account of how a finite mind can contemplate or construct an actual infinity. None of this is reflected in his models or his postulates. The DR-theoretic structures in the models represent possible mental constructions by possible agents. Any of the possible constructions can be thought, indeed constructed, by anyone mind; none can think all of them. But there are many agents. In fact there are infinitely many ways the world might be, and so indeed infinitely many ways agents could have thought (for instance). Thus, we can imagine the entire range of intentional structures being generated as possible thoughts. Further, the conceptualist may simply assert that we can countenance such infinite sets. The natural numbers, constructive set theory, the set of all possible thoughts, the set of all possible grammatical English sentences are examples of infinite structures that the conceptualist countenances. It's not as though he actually has to count each sentence to come to the conclusion that a natural language yields an infinite number of sentences! The set of all intentional structures is needed when we talk about quantification. But quantification over intentional structures does not seem from the logical point of view different from quantification over numbers, for which there are a number of constructivist approaches to which the conceptualist can appeal. Another argument of Bealer and Monnich (1989) is "the argument from necessary existence." If I understand it, the argument purports to saddle the conceptualist with an unfair notion of propositional existence. The argument is this. It is surely true that

it is possible that there are no finite minds. We are contingent beings. Now, they note, the proposition that there are no finite minds is true only if there are no minds to think it. But the proposition must exist in order to be true or false. The only situation in which it could be true is one in which it does not exist. So it must be false. Consequently, finite minds necessarily exist. The argument is unsound. The missing premise is that a proposition can exist at a world only if mind exists at that world. But a conceptualist could reject this premise in favor of the following: a proposition like the proposition p, that there are no finite minds, exists only if there are [mite minds to think it in some world. But there are finite minds in some worlds (ours), so the existence of this proposition is not at issue. p might be true only in a world in which there are no finite minds--a possibility which a [mite mind can contemplate from some other world. These counterfactual possibilities are not really problematic; they are part and parcel of a robust notion of possibility, to which my modest conceptualist can help himself. Remember, my modest conceptualist is interested in getting rid of structured propositions and other abstract entities as independent objects while keeping an adequate account of the semantics of language and natural language metaphysics. He is not committed to ridding himself of possible worlds talk as well. The conceptualist's claim that abstract entities are conceptual constructions rests, of course, on being able to fumish some procedure of construction. The conceptualist's construction procedure should guarantee that speakers can communicate about abstract entities and thus it must be a procedure that fits into an overall theory of communication and information transfer. The construction procedure must be a computable procedure. If the construction procedure were not computable, then it would remain very unclear in what sense it was a procedure that humans could reliably use or whose outputs humans could recognize as being outputs of a particular construction procedure. 46 The "proof" of the computability of the construction is to produce implementable rules for the construction and manipulation of structures defining various abstract objects. Such computable constructions specify semantic information, at least in part.47 This has been precisely the task of chapters 4-9. Platonism is an alternative to conceptualism. According to the Platonist, the types of natural language metaphysics correspond one to one with the entitites of real metaphysics. No reduction of the types of natural language metaphysics is possible. On such a view, each type of abstract object would have a wholly mind-independent existence. This is a quite drastic form of Platonism. Several philosophers, Barwise and Perry (1983), Bealer (1982), Bealer and Monnich (1989), and Zalta (1988), have appeared to advocate something like this position recently. They assert that properties, propositions and perhaps other abstract objects have a mind independent existence, much like that of concrete objects like people, rocks, and trees. Such a position brings with it a host of epistemological and metaphysical difficulties that any theory should avoid. For instance, it is inappropriate to postulate any causal powers for some types of abstract entities. But if this is the case, then it is very difficult to give a reasonable account of how human epistemological agents, who acquire most of their information by interacting causally with their environment, might

414

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MODEL TIffiORY

come to know anything about these objects. The Platonist supposes that minds grasp in some way or other a wide range of mind independent, abstract entities to which we refer. But if such entities as propositions can be grasped, one would like to ask the Platonist, why can we not also grasp those properties of propositions like validity which have only to do with noncontingent, intrinsic features of those propositions? But if we do grasp properties of propositions like validity, in being able to judge whether a proposition expressible in a first order language or in the language of arithmetic is valid or not, then we attribute to ourselves capacities far beyond those that an algorithm or computable procedure could describe. The platonist has a dilemma: if he does attribute such capacities to minds that understand language, then we can neither explicate semantics nor human knowledge of semantics in computational terms; if he does not attribute such properties, then it makes all the more mysterious in what consists a language user's grasp of meaning. 48 The Platonist's general argument in the face of these difficulties usually relies on the commitments of natural language metaphysics. 49 The forms of natural language, in particular the sentential and verbal nominals, imply that properties and propositions exist. So in order to account for the semantics of natural language, one must (or it is most elegant) to assume the existence of such objects. Hence some version of Platonism, so the argument goes, must be correct. The Platonist's argument begins with the claims of natural language semantics and ends with the conclusion that there must be mind independent objects like facts and propositions. This argument is not compelling. I think it is invalid. The purpose of the last seven chapters has been to show that an account of the semantic and anaphoric behavior of chunks of discourse, verb phrases, nominals and noun phrases denoting abstract entities need not suppose that these forms of language denote metaphysically real abstract entities, only that they express the DR-theoretic structures for which I have outlined construction procedures. A closer look at propositions reveals that they are needed, neither in an analysis of attitudes, nor as theoretical, metaphysical entities in giving an account of natural language semantics. What philosophers have called propositions are various ways of classifying the structured contents of mental states. In some cases a very fine-grained notion of proposition emerges from our descriptions of cognitive states, as in our discussion of puzzles like those besetting Pierre and Peter of chapter 3. In the case of animals like cats and dogs also discussed in chapter 3, a much cruder notion is called for. This is of a piece with our conclusion about the propositional structure of a discourse in general; the individuation of propositions at the level of natural language metaphysics is highly context-sensitive and interest-relative. The natural explanation of why propositions behave in this way in natural language metaphysics is that they are not mind independent entities but rather mind dependent abstractions from the behavior of agents. From this perspective the debate between possible worlds theorists, NeoRussellians and Fregeans concerning the "true nature" of objects of belief--viz. propositions--is misguided. Many direct reference theorists have argued that their theory of structured propositions is the appropriate one. Possible worlds theorists

champion an even cruder notion of proposition, while Neo-Fregeans concentrate on fine-grained theories of propositions. Their debate misses the point; propositions are abstractions of bits of contents and structures of cognitive states (which DR-theoretic structures attempt to model); these abstractions don't have set identity criteria outside of a particular context of interpretation. Sometimes, crude propositions would have sufficed; at other times, only extremely fme-grained, context-sensitive ones may do. My approach to facts and possibilities parallels the one I have taken towards propositions. Based on the data in chapter 1, I suggested in chapter 5 that sets of logically equivalent DRSs could model possibilities, while the facts of a world w and time t could be modeled by sets of logically equivalent DRSs that had a proper embedding at w and t. The latter condition came from the factive presupposition of factive constructions. Further, it would appear that all we need to do in order to account for fact and possibility talk in natural language is to refer to DRSs. There is no need to refer to facts as independent entities to account for the natural language semantics of abstract entities, any more than there is to refer to propositions. The view that facts and possibilities are so characterized leads straightaway to a view of facts in which there are general facts, negative facts, and modal facts, as well as basic or atomic facts. An atomic fact consists of an n-ary relation applying to n objects, a negative fact is a class of DRSs each of which has at least one complex condition involving a negation and so on.50 We could reconstruct facts, possibilities and propositions by means of equivalence classes of DRSs. This does not of course imply that facts, possibilities and propositions are independent entities in the real metaphysics. Rather it shows that they emerge from the more basic DR-theoretic structures, which model contentful constructions of intelligent agents. The reconstruction of facts and possibilities makes them reifications of the contents of mental states without the structure. The facts of a world w are just sets of possible worlds that include w. Recall that a problem with facts was how to explain their causal powers. My reply is that facts have causal efficacy because of their factivity. A fact of w is a set of worlds that must include w, whereas a possibility of w is a set of worlds that need not include w. A major traditional metaphysical argument for the existence of facts is that a fact is the ground of truth of an atomic sentence. Could we use sets of DRSs or representative DRSs as models of facts to pursue this traditional sort of analysis? Let us look briefly at the use of atomic facts in the analysis of truth conditions. 51 Bradley (1932) argues that facts are necessary to give an appropriate analysis of truth conditions, given a commitment to properties. A necessary condition for an appropriate analysis of truth conditions assumed by Bradley is that it must be finitary. Suppose that we consider the simple first order language sentence 'Fa'. Anybody committed to properties will have a truth definition telling him that such a sentence is true just in case a has F. But, Bradley asks, what is it now for a to have F? It's not enough to say that in the world there is an unsaturated property F and an individual a; they have to go together. Thus, there appears to be another predication relation that must be invoked to explain the truth conditions for a's having F. That is, 'a has F' is true just in case there is some predication relation holding between a, the (first)

417

I'r------~~=~=~~-~-~~-=~~--------

418

_ _----~".-~-~---------------_ _

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MODEL THEORY

predication relation of having, and F. This now begets a familiar, infinite regress and a nonfinitary analysis of truth conditions. Bradley's claim is that there can be no appropriate analysis of the truth conditions of simple sentences without appealing to facts. That is, a proper, finitary analysis of the truth conditions of a sentence like 'Fa' must go something like this: 'Fa' is true iff 'Fa' denotes the fact that a has F and the fact that a has F obtains. As Russell points out, Bradley's regress is only telling if one wants to reduce facts to their constituent properties, relations, and individuals. I do not attempt to reduce facts to their constituent properties, relations and individuals. I am using DRSs to reduce facts. Let us, for a moment, treat facts as sets of logically equivalent DRSs K or, better yet, simply assume that a fact is represented by a choice of one of these DRSs--call it choice(K). My counterpart to the metaphysician's analysis of truth conditions is this: 'Fa' is true at w iff 'Fa' denotes choice(K) and choice(K) has a proper embedding at w. The notion of a proper embedding does not appeal to the metaphysician's conception of truth (though it does follow closely something similar to the Tarskian definition); so there is no circularity. An uncharitable philosopher might say that the analysis of the truth of sentences proceeds in terms of the notion of another sort of sentence, a DRS sentence, being true. That would be a misreading of the analysis; DRSs after all are not linguistic but information theoretic structures. Still, the objector may reply, DRSs are mental constructs, and our analysis of truth says that a sentence is true just in case the sort of mental construct it denotes can be properly embedded in the actual world; so now we want to know what it is for such a construct to be properly embedded. The DR-theoretic notion of an embedding of K is the counterpart of the metaphysician's notion of obtaining, so the traditional metaphysician should understand perfectly well what a proper embedding is, if he understands his own notion of obtaining. Even better, the DR-theorist has a proper recursive definition of what a proper embedding is. In conclusion, my analysis of natural language metaphysics favors a conceptualist real metaphysics. What does such a conceptualist interpretation give us? It yields a comprehensive theory of abstract objects that does better than simple possible worlds reconstructions of propositions; at least, it avoids the well-known problems of that view in connection with a semantics of the attitudes. But this view is also quite different in spirit from the Platonist theories of such abstract objects. It reduces many of the types of abstract entities we countenance in natural language metaphysics to constructions employing information structures and a possible worlds notion of content. This reduction is a plausible one, at least from the perspective of semantics; it allows us to make a lot of good predictions. The semantic theory permitted by such a reduction seems to be the equal of any Platonistic theory of abstract objects. It also at least indicates ways to avoid the epistemological problems that plague the Platonist's theory. The two level analysis of metaphysics implicit in the distinction between natural language metaphysics and real metaphysics undercuts a major Platonistic argument, what Jubien (1989) has called the "face value assumption." This is the argument that we should postulate the independent existence of abstract entities like propositions

and facts, because we talk about them in ordinary language. My natural language metaphysics allows the naive speaker of the language all the abstract entities he could wish for at the level of natural language metaphysics. It accommodates all the traditional Platonistic arguments that appeal to natural language usage or to naive intuitions based on such usage, by acknowledging that in the construction of semantic representations for such discourse, speakers do countenance entities that appear to stand proxy for abstract entities. But one may do that without giving in to the conclusion that because speakers do countenance such entities they should exist as independent elements of our real metaphysics. What our DRT analysis tells us is that Platonistic natural language metaphysics is compatible with a conceptualist's reconstruction of abstract entities. If the sort of semantics I have sketched for abstract objects is plausible, a modest conceptualism carries the'day.

419

6. TECHNICAL APPENDIX In this appendix, I first give a generalization of Aczel's Frege structures, which I call extended Frege structures. The DRS construction procedure, on the other hand, as defined in the Appendix to chapter 2, furnishes us with an intentional frame. I show that an intentional frame with its correctness definition is an extended Frege structure, and this will show that the construction procedure furnishes us with a model for the A-calculus and has the functional structure of the required sort. The second part of this appendix develops the homomorphism from a subset of the domain of the intentional frame to intensions, and shows in general how the . construction can be carried through. The definition of intensions corresponds to the definition of a truth set for the Frege structure.

6.1. Intentional Frames and Frege Structures

:r

= where Fn+ 1 ~ Fo ~ Fn is an explicitly closed family of functions iff (i) for every a E Fo, there is an f E FI such that f(b) = a for all b E Fo. (ii) for every E Fon, there is an f j E Fn such that f«ah ... , an» = aj for 1~ i~ n. (iii) for every f E Fm, g\, ... , gm E Fb and x E Fok, f 0 (gh ... , gm) E Fk and f 0 (gh ... , gm)(X) = f(gl(x», ... , gm(x».

DEFINITION:

In every closed family of functions '.J, for every expression '
E

Fn,

DEFINITION: A function F: Fnl X ... X Fnk ~ Fo is a linear functional on a family of

functions :riff for every m > 0 and functions fl in Fm+ nl ' ... , fk in Fm+ nk'

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CHAPTER TEN F(fb ... , fk ) E Fm.

F: Fn, X ... X Fnk --> Fo is a functional on a family of functions 1"'iff for every m > 0 and functions fl in F m, + n, ' ... , fk in F mk + nk'

DEFINITION: A function

F(fb ... , fk) E Fm' +...+mk

A-structure consists of an explicitly closed family J', together with two linear functionals on 1"' v: FI --> Fo and APP: Fo X Fo --> Fo, such that for each f E F I and a E Fo: APP(v(t), a) = f(a).

DEFINITION: A

Structure consists of a A-structure together with a set of linear functionals on an explicitly closed family 1"' where each linear functional corresponds to a logical operation.

DEFINITION: A Frege

One sort of Frege structure that we shall be interested in is a model of the A-calculus together with logical operations corresponding to those of first order predicate logic. Turner (1989) has generalized Aczel's basic notions and given a classical definition of the first order connectives and quantifiers. Here I will do two things. I will further generalize Frege structures to allow functionals on higher types. Then I will define a DRT intentional frame and show that the DRS construction procedure, specifically the operation of conversion and the DR-theoretic structures, together with the correctness definition, is an extended Frege structure.

Extended Frege Structure is a tuple< IF, J', 11>, where: (A) IF is a Frege structure <J', =, v, APP, -', &, "d>, where <J', v, APP> form a lambda structure and -', &, "d, are linear functionals on 'J, such that -,: 1"'0 --> 1"'0, =, &: 1"'0 2 --> 1"'0, and "d: 1"'1 --> 1"'0 are logical constants with the usual interpretation on PROP, where PROP C 1"'0. (B) l' is a set of functionals on :f. (C) IT is a set offunctionals on (1'X 1"'n) U (1"'X 1), for n = 1,2, etc.

DEFINITION: An

I

The DRS construction procedure furnishes us with an extended Frege structure. In order to avoid confusion in the notation, I will write the notion of DRS application, which is usually denoted by '(... )', using an explicit function, Conv+. In what follows I will assume that Predicative DRS n ranges only over greater than 0 place predicative DRSs. Predicative DRS, however, is the set of all predicative DRSs-including DRSs. I will use the list notation for a DRS with universe A and set of conditions B,, to save space. DEFINITION: A DR theoretic intentional frame is a structure I = <J', PARTIAL, v, A,+, -, $, L, /\, -', Conv+, Conversion, Conditions, Q>, where

(1) 1"'is a family of functions , defined in the following way:52 Fo = DRS U DDRS U DisGourse Referents U {*a: a EPredicative DRS n U Concept Discourse Referents}. /

MODEL TIIEORY

421

Fn+l = {Axa: a E Fn & x E Discourse Referents} U {Cj: c j is a concept discourse referent taking n+1 arguments} U {n+1-place DRS-Predicates}. (2) PARTIAL = U~ is; 4 PARTIALjis a collection offunctionals on 1"'that include all the Partial DRSs of chapter 2 that exploit elements of Q such that: PARTIAL I ~ {Fn+l --> Fn }; PARTIAL 2 ~ {Fn+l X Fm+l --> F n+m} PARTIAL 3 ~ {Fn --> Fn}; PARTIAL4~ {FnXFm --> Fn+m}; and: (a) For every cp E PARTIAL I and a E Fn+l n Predicative DRS, cp(a) = {X: X = Conversion(cp, a, u) for some u in a} ~ Predicative DRS n Fn. (b) For every cp E PARTIAL 2, a E Fn+l n Predicative DRS, p E Fm+l n Predicative DRS, cp(a, P) = {X: X = Conversion(X', p, u) for some u in p and for X' E {Y: Y = Conversion(cp, a, u) for some u r in a}} ~ Fn+m n Predicative DRS. (c) For every cp E PARTIAL 3 and a E Fn n Predicative DRS, cp(a) = Conversion(cp, a) E Predicative DRS n Fn (d) For every cp E PARTIAL4, a E Fn n Predicative DRS, p E Fm n Predicative DRS, cp(a, P) = Conversion(Conversion(cp, a), P) E Fn+m n Predicative DRS. (3) (a) A is a functional on J', A: Fo --> Fl. (b) v is a functional on F; v: FI --> Fo such that v(a) = *a, if a E {Predicative DRS} U {Concept Discourse Referents}; v(a) = 't, if a= AX't and 't E Fo - {Predicative DRS U Concept Discourse Referents} . (c) L: FI --> Fo and $, +, /\ : Fo X Fo --> Fo are linear functionals such that if cp E Fb and 01. 02 E Fo, then (i) Lcp is the set of all those objects a in Fo such that cp(a); (ii) 01 $ 02 is the pair set {oj, 02}; (iii) /\ is the SDRS join operation defined in the Appendix to chapter 7. (iv) + is the update function such that if u, v E {DRS}, u+v E {DRS} (update includes anaphora resolution); if u E DDRS, Y E DRS, then u + y is the DDRS update function described in chapter 3; if u E SDRS, Y E DRS then u + y is the SDRS update procedure. (4) Conv+: Fo X Fo --> Fo is a functional such that if AU 'Y E FIn Predicative DRS, p E Fo , then for any 8 E DRS Conv+(v(a), P) E Cono iff Y(P/u) is a part of 8. (5) Conversion is a functional on (PARTIAL X 1) U (PARTIAL X 1"'2) U PAR TIAL2 and is as defined in the appendix to chapter 2 when combining elements of PARTIAL and elements of Predicative DRS. (6) LIFT: 1"' --> l' is a functional on 1"' such that: for any AXh ... ,AXn K E Fn n Predicative DRS LIFT(a) = AP AXb ... ,AXn
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CHAPTER TEN

In addition, I stipulate the following conditions to hold of intentional frames. These specify the DR-theoretic structures we have been studying, and are mentioned above. (i) If '1' E Fn n Predicates and x" ... , Xn E Discourse Referents, then '1'(x" ... , xn) E Conditions. (ii) If '1' E Fn+ I n Predicates is associated with a verb, x" ... , xn E U and e is an eventuality discourse referent, then e-'1'(x;, ... , xn) E Conditions. (iii) If x" X2 E Discourse Referents, e" e2 E Discourse Referents are eventuality discourse referents, t E Discourse Referents a temporal discourse referent, then XI = X2, el < e2, el < t E Conditions. (iv) If CI is a concept discourse referent in F n, and x" ... , Xn E Discourse Referents then c I(x" ... , xn) E Conditions. (v) If e E Discourse Referents is an eventuality discourse referent, K E DRS, and el E UK an event discourse referent, then e = Lei K E Conditions. (vi) If K" K2 E DRS, 0 is a projective operator, e an event discourse referent, p a proposition discourse referent, and f a fact discourse referent, then f"" K" C "" Ail K" P "" K" OK" and e-KI E Conditions. (vii) If ~ E DRS and x E U~, then Ax~ E Predicative DRS n FI; and if ~ E Predicative DRS n Fn and x E U~, then Ax~ E Predicative DRS n Fn+l. (viii) (a) If ~I E DRS U Predicative DRS and

E DRS. (x) If K" ... , Kn E DRS, U' ~ Discourse Referents, Con' ~ Conditions where the arguments of ~ E Con' are among K" ... , K n, then < U', {K" ... , Kn}, Con'> E DDRS. (xi) If K" ... , Kn E DRS U DDRS, U' ~ Discourse Referents, Con' ~ Discourse Referents where the arguments of SE Con' are among K" ... , K n, then < U', {K" ... , Kn}, Con'> E DDRS. (xii) SDRSs are as defined in chapter 7. These definitions immediately imply that if