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JOURNAL OF SEMANTICS AN INTERNATIONAL jouRNAL FOR THE INTERDISCIPLINARY STUDY OF THE SEMANTICS OF NATURAL LANGUAGE MANAGING EDITOR : PETER BoscH(IBM Germany) REVIEW EDITOR: BARTGEURTs(Univ.ofTilburg) EDITORIAL BOAR D : PETER BoscH(IBM Germany) StMON C. GARROD (Univ. of Glasgow) BARTGEURTS (Univ. ofTiJburg) PAUL H OPP R (Carnegie Mellon Univ.,Pittsburgh) LAURENCE R. HoRN (Yale University) STEPHEN lsARD (Univ. of Edinburgh) HANS KAMP (Univ. of Srungart) LEO G. M. NOORDMANN (Univ. ofTilburg) RoB A. VAN DER SANDT(Univ. of Nijmegen) PtETER A. M. SEUREN(Univ. ofNijmegen)
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JOURNAL OF SEMANTICS Volume 9 Number
1
CONTENTS
]ENS ALLWOOD,jOAKIM NIVRE AND ELISABETH AHLSEN On the Semantics and Pragmatics ofLinguistic Feedback
I
KEES vAN DEEMTER Towards a Generalization of Anaphora
27
MICHAEL B. KAc A Simplified Theory of Boolean Semantic Types
53
CHRIS BARKER Group Terms in English: Representing Groups as Atoms
Journal of&mantics
\):
1-2.6
© N.I.S. Foundation ( 1992)
On the Semantics and Pragmatics of Linguistic Feedback JENS ALLWOOD, JOAKIM NIVRE and ELISABETH AHLSEN
University ofGoteborg
Abstract This paper is an exploration in the semantics and pragmatics of
linguisticfeedback, i.e. linguistic
basic communicativeJunctions, such as contact, perception, understanding, and artitudinal type ofreaction con veyed by feedback utterances, the communicative status of the information conveyed (i.e. the level of awareness and intentionality of the communicating sender), and the contextsensitivity of about
reactions to the communicated content. Special attention is given to the
feedback expressions. With regard to context sensitivity, which is one of the most characteris
tic features of feedback expressions, the discussion focuses on the way in which the type ofspeech
act
(mood), the factual polarity, and the
information status of the preceding utterance influence
the interpretation of feedback utterances. The different content dimensions are exemplified by data from recorded dialogues and by data given through linguistic intuition. Finally, two different ways of formalizing the analysis are examined, one using atttibute-value mattices and one based on the theory of situation semantics.
1
PUR PO SE
The purpose of this paper is to present a sketch of a semantic/pragmatic account of linguistic feedback mechanisms in spoken interaction. After an initial account and exemplification of the relevant semantic/pragmatic features has been made , two attempts at formalizing these are presented and discussed.
2 BACKGROUND
2.1
Analytic components ofcommunication
Direct human face-to-face communication can be seen as the product of analytically separable, interdependent functional subsystems. In Allwood, Nivre and Ahlsen
(1990), it was suggested that, at least for some purposes, the
following three overriding functions might be fruitful to consider for speech production and speech perception.
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mechanisms which enable the participants in sp�ken interaction to exchange information
2 On rhe Semanrics and Pragmarics ofLinguisric Feedback
Speech management, interactive functions and focused/main message functions can further be analytically subdivided into subsystems and sub systems of subsystems, characterized by different functions. Interaction func tions can, for example, be subdivided into mechanisms for: (i) sequencing (of activities and subactivities, communicative acts and/or topics) (ii) turntaking (iii) giving and elicitingfeedback. The literature on conversation analysis and discourse analysis (see e.g. Levinson I983 or Brown and Yule I983) contains much discussion of the former two types of mechanisms, whereas there has been less discussion of feedback (c£ Allwood I988a, I988b). This paper is intenged as a contribution to the further exploration of linguistic feedback mechanisms, especially with regard to the semantic/pragmatic functions of such mechanisms.1 2.2
Linguisticfeedback: basicfunctions
The term feedback originates in cybernetics (Wiener I 948), where it is used to denote processes by which a control unit gets information about the effects and consequences of its actions. Here we are concerned with linguistic (interindividual)fe�dback (Allwood I979, I988a, I988b, 1988c), i.e. linguistic mechanisms which enable the participants of a conversation to exchange information about four basic communicative functions, which are essential in human direct face-to-face communication. These functions are:
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(i) Speech management functions, i.e. the linguistic processes and mechanisms whereby a speaker manages his or her own linguistic contributions to a communicative interaction. involving phenomena that have sometimes been described as 'planning', 'editing', '(self )repair', etc. (ii) Interactive functions, i.e. linguistic processes and mechanisms whereby the speakers manage the flow of interaction. (Feedback mechanisms, the topic of this paper, is an example of an interactive subsystem.) (iii) Focused or main message functions, i.e. linguistic processes and mechanisms whereby speakers manage to communicate information which is not immediately connected with management of their own speech or the interaction at hand. Focused or main message functions thus include most of what is commonly described in grammatical theory and can be operationally def ined as that which is contained in an utterance when those parts that are devoted to speech management or interactive functions have been subtracted.
J. Allwood, J. Nivre and E. Ahlsen
3
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(i) contact (i.e. whether the interlocutor is willing and able to continue the interaction) (ii) perception (i.e. whether the interlocutor is willing and able to perceive the message) (iii) understanding (i.e. whether the interlocutor is willing and able to under stand the message) (iv) attitudinal reactions (i.e. whether the interlocutor is willing and able to react and (adequately) respond to the message, specifically whether he/she accepts or rejects it). These four basic functions of linguistic feedback arise from four basic require ments of human communication. First, communication requires that at least two agents are willing and able to communicate. Second, communication requires that the receiving agent is willing and able to perceive the behavioural or other means whereby the sending agent is displaying or signalling informa tion. Third, communication requires that the receiving agent is willing and able to understand the content that the sender is displaying or signalling. It is also often helpful if the receiver can perceive and understand various types of indicated information.2 Finally, communication requires that the receiving agent is willing and able to react attitudinally and behaviourally to various aspects of the content that the sender is displaying or signalling. Again, it is sometimes beneficial for communication if the receiver also reacts to indicated information. Certain conventional features of the displayed or signalled content here seem particularly important for the interpretation of the content of feedback expressions. Among these are polarity (positive or negative) and mood (conventionally signalled evocative intention; c£ Allwood 1978). Every language appears to have conventionalized means (verbal and prosodic means as well as body movements) for giving and eliciting information about the four basic communicative functions. Linguistic feedback mechanisms on a primary level usually involve very short morphemes (yes, no, m ), or basic mechanisms such as repetition, simple body movements (head nods, head shakes) in combination, on a secondary level, with fairly simple phonological, morphological and syntactic operations for modifying and expanding the primary feedback expressions. Earlier studies that have discussed feedback and related phenomena include Allwood (1976, 1979, 1988a, 1988b), Anward (1986), Clark & Schaefer (1989), Ehlich (1986), Fries (19 52), Hellberg (1985), Heritage (1984), James (1972), Schegloff (1982), Severinson-Eklundh (1986), Sigurd (1984), Yngve (1970). Allwood (1988b) gives a taxonomy for the structure of linguistic feedback and, in particular, describes the Swedish system. In the present paper, we want to focus on the content features of linguistic feedback.
4 On the Semantics and Pragmatics of Linguistic Feedback
3 CONTENT FEATURES OF FEEDBACK
3.1
Introduction
Although simple feedback words, like
yes, no
and m , are among the most
frequent in spoken language, a proper analysis of their semantic/pragmatic
content seems to be fairly complex and involve several different dimensions. One striking feature is, for example, that these words involve a high degree of context dependence.
data from recorded dialogues and by data given through linguistic intuition. The examples from recorded dialogues are all in Swedish (with English trans
lations). In addition to this, Swedish is used to exemplify distinctions which cannot be found in English. The four dimensions we will discuss are: (i) Type of reaction to preceding communicative act (ii) Communicative status
(iii) Context sensitivity to preceding communicative act, with regard to: A Type of speech act (mood) B. Factual polarity C. Information status
(iv) Evocative function.
3.2
Type ofreaction to the preceding communicative act
The raison d'etre of linguistic feedback mechanisms is the need to elicit and give information about the basic communicative functions, i.e. continued contact, perception, understanding and emotional/attitudinal reaction, in a sufficiently
unobtrusive way to allow communication to serve as an instrument for
pursuing various human activities. The linguistic feedback system is, in this way, an essential instrument for successful communication of any type.
Especially, it is an essential instrument for the incrementality of cohllnunica
tion, i.e. the step-by-step build-up of consensual joint understanding and atti
tudes. Feedback mechanisms are thus a means for communication which in its
turn is a means for pursuing a variety of other human activities.
In our analysis of the content of feedback we are assuming that what we have
called the basic functions also define four basic dimensions in the reactions that interlocutors have to each other's contributions in conversation. Feedback
utterances therefore give information about one or several of the following types of reaction:
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Below, we will first discuss four of these dimensions and exemplify them by
J. Allwood, J. Nivre and E. Ahlsen
s
{i) contact-willingness and ability to continue interaction
(ii) perception-willingness and ability to perceive expression and message (iii) understanding-willingness and ability to understand expression and message (iv) (other) attitudinal reactions-willingness and ability to give other attitudinal reactions to expression, message, or interlocutor.
(I)
men efter tre ar va de ju3 en harlig mylla (but after three years you-know it was a lovely mould) B: ja (yes) A:
We can compare this to example (2), where B's weaker feedback utterance mm has the same content with respect to contact, perception and understanding, but does not necessarily convey the attitudinal reaction of acceptance of the veridicality of A's statement.
(2)
. . . ja kan fa sana/ /aah kontakter . . . kontakter rna universum jaa (. . . yes I can get such//eeh contacts . . . contacts with the universe yes) B: mm (mm) A:
One might, however, claim that mm still signals acceptance in the weaker sense of accepting to continue, accepting the information in the preceding utterance as perceived and understood and possibly also of accepting to take a stand on this information.
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Category (iv) has the word other in brackets since contact, perception, and understanding also involve attitudes, albeit of a very fundamental cognitive and volitional sort. Category (iv), which we will mostly just refer to as attitudinal reactions without other, is supposed to cover other attitudes such as acceptance, non-acceptance, belief, disbelief, surprise, boredom, disappointment, enthu siasm, etc. When it comes to the words yes and no and their synonyms, we believe that the attitudes acceptance and non-acceptance are in focus and form a basis which can be modified by added attitudinal reactions. We can thus accept with regret or with enthusiasm by uttering the word yes with different types of prosody. In general, we can say that feedback words differ from each other mainly with regard to what attitude they signal, e.g. yes-acceptance, no non-acceptance, great -appreciation/enthusiasm, etc. In example {I) below, ja (yes), has the functions of conveying continued contact, perception and understanding as well as the attitudinal reaction acceptance.
6
On
the Semantics and Pragmatics of Linguistic Feedback 3·3
Communicative status
Like any other information communicated, feedback information concerning the basic communicative functions can be given on many levels of awareness and intentionality. This is so, whether the information is communicated by verbal or bodily means. Although levels of awareness and intentionality almost certainly are a matter of degree, in order to simplify matters somewhat we here distinguish three levels from the point of view of the communicating sender {c£ Allwood I976):
The fact that linguistic expressions by convention are taken to be signals does not, however, imply that they are always actually used as signals. A symbol can also be used to indicate and/or display its conventionally signalled content or some other content. Compare the example discussed by Searle {I 969), where an American soldier, captured by the Italians in the Second World War, by quoting 'kennst Du das Land, wo die Zitronen bliihen' (do you know the land where the lemons bloom), intends to display to the Italians that he is German. In order to illustrate the application of the dimension of communicative status to linguistic feedback utterances we will consider the communicative status of some examples from the recorded dialogues. In examples {I) and (3) below, the communicative status of the feedback utterances produced by B is not quite the same. In both cases the preceding utterance (produced by A) is a declarative statement with positive polarity (i.e. it is not negated) and in both cases the feedback utterance signals the acceptance function by use of ja (yes), while it indicates continued contact as well as per ception and understanding of the preceding utterance. In example (I), however, the simple Ja (yes), can merely be said to indicate the attitude of belief, while in
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(i) Indicated information is information that the sender is not aware of. or intending to convey. This information is mostly communicated by virtue of the receiver's seeing it as an indexical (i.e. causal) sign. (ii) Displayed information is information that the sender is intending to 'show' the receiver. The receiver does not, however, have to recognize this inten tion. Display of information can be achieved through any of the three main semiotic types of signs (indices, icons and symbols, c£ Peirce I9Ss). (iii) Signalled information is information 'that the sender is 'showing' the receiver that he is displaying and thus intends the receiver to recognize as displayed. Signalling can also be achieved through any of the three main semiotic types of signs. In particular, however, we will regard ordinary linguistic expressions (verbal symbols) as being signals by convention. Thus, a linguistic expression like It's raining, when used conventionally, is intended to evoke the receiver's recognition not merely that 'it's raining' but that he/she is 'being shown that it's raining'.
J. Allwood, J. Nivre and E. Ahlsen
7
example (3), the more elaborated feedback utterance rather signals belief, expressed through the indicative mood of the sentence de e de ju {it is you know).
(I )
A;
men efter tre ar va de ju en harlig mylla (but after three years you-know it was a lovely mould) B: ja {yes) (3) A; de e ju valdit faalit me karnkraft (it is very dangerous you-know with nuclear power) B: ja!/de e de ju (yes//it is you-know)
3.4 . 1
Context sensitivity with regard to the preceding communicative act
Introduction
One way of analysing the meaning of linguistic feedback expressions and mechanisms is to say that they are characterized by a very abstract conventional type content in combination with high degree of context sensitivity. For example, the conventional-type content of the three expressions yes, no, m, and ok can perhaps be characterized in the following way:
yes -acceptance no-rejection m -confirmation ok-agreement The conventional occurrence content of the three expressions is, however, always also a function of prosody and context. The function of prosody is mainly to modulate attitudinal information. In some cases (c£ example 5 below), this can affect the presupposed truth of the preceding utterance. Prosody will, however, not be treated in any detail in this paper. As for context, �;tble I below demonstrates the influence of mood and polarity of the preceding utterance. We can see how context can change the occurrence content both with regard to attitudinal reaction (from acceptance to non-acceptance) and with regard to attitudinal object (e.g., from statement to offer). The table is some what unnatural in that simple feedback expressions without pronominal indications of the objects of acceptance and nonacceptance (yes it is, no it isn't) have been used. In the case of yes, this leads to ambiguity after a negative state ment (ambiguous between acceptance of a negative statement and acceptance of the positive counterpart of the negative statement- rejection) and unclarity after a negative request (yes I will(?), yes I won't(?)).
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3·4
Table I Functions of yes, no, m, and ok in relation to the mood and polarity of the preceding utterance Preceding utterance
Listener's response
no
m
ok
Acceptance of statement (indicated belieQ
Rejection of statement
Confirmation of understanding (indicated acceptance of statement)
Ambiguous berween rejection of statement (yes it is) and acceptance of statement (yes
Acceptance of statement (indicated belieQ
Confirmation of understanding
Agreement (acceptance of what has been said as a point of departure, more or less stipulatively) Agreement (acceptance of what has been said as a point of departure . . .)
Commitment to positive fact
Commitment to negative fact
Commitment to positive fact
Commitment to negative fact
Open the door!
Acceptance of request
Refusal of request
Neg request
Unclear
Acceptance of request
Acceptance of offer
Rejection of offer
Confirmation of understanding (indicated commitment to positive fact) Confirmation of understanding (indicated commitment to positive fact) Confirmation of understanding (indicated acceptance of request) Confirmation of understanding (indicated acceptance of request) Confirmation of understanding (indicated acceptance of offer)
Acceptance of offer
Rejection of offer
Pos statement
It's raining
Neg statement
It isn't raining
you are right) Pos yes-no question:
Is it raining? Neg yes-no question:
Isn't it raining? Pos request
Don't open the door! Pos offer:
Would you like some tea?
Neg offer:
Wouldn't you like some tea?
Confirmation of understanding (indicated acceptance of offer)
Agreement (acceptance of implicit suggestion) Agreement (acceptance of implicit suggestion) Agreement
Agreement
Agreement (indicated acceptance on the grounds of what has been said) Agreement (indicated acceptance on the grounds of what has been said)
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yes
J. Allwood, J. Nivre and E. Ahlsen
9
We seem to have a sort of semantic field constituted by terms like yes, no, m ,
and ok supported b y attitudinal dimensions o f meaning like agreement,
confirmation, acceptance and commitment. Each term is primarily focused towards one or several of these dimensions, but can, depending on context, simultaneously indicate or display other compatible dimensions or even, with a change of focus, signal other dimensions. The latter might happen, for example, in language acquisition, when a language learner who is yet not very proficient in the language he/she is learning uses the vagueness of the notion of acceptance connected with the word yes in order to signal acceptance of continued communication rather than acceptance of perceived and understood content. What is really being signalled
is willingness or agreement to con
tinue communication rather than the more stereotypical full-bodied notion of accepting the evocative intention of the preceding utterance (communicative act). If the receiver of the yes is not fully informed about the learner's non proficiency, there is a clear risk that what the learner is signalling (displaying, indicating) will be misunderstood. Just like deictic expressions
(1, you, here, there, now, then ,
etc.), feedback
expressions are thus highly dependent on context for a precise determination of their meaning. However, just as is the case with deictic terrns, this dependence is not random, but in fact triggered by specific contextual parameters. As can be seen from the discussion and examples above and further from the examples to be discussed below, among the most important of these parameters are various features of the immediately preceding communicative act: (i) Type of speech act (mood) (ii) Factual polarity (iii) Information status.
3-4.2
Type of speech act (mood)
Table 2, which is extracted from Table 1, illustrates the status of yes in different contexts. More precisely, we can see that the object of acceptance is determined by mood and speech act status. In the examples, we are making the assumption that mood and speech act status are in harmony. When mood and speech act
Table
l
Effects of speech act status (mood) on feedback
Preceding utterance
Listener's reply
Function
It's raining Is it raining? Open the door! Would you like some coffee?
yes yes yes yes
Acceptance of statement Commitment to positive fact Acceptance of request Acceptance of offer
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(displayed or indicated, as the case may be)
10
On the Semantics and Pragmatics of Linguistic Feedback
status differ, increased degrees of freedom are introduced and context seems to determine which is chosen. We also see that the speech act status of the preceding communicative act can trigger a change in the attitude signalled. A yes-no question can, at least in some cases, be analysed as a request for a commitment on the part of an interlocutor as to the veridicality of some state ment. A reply using yes or no will therefore indicate a positive or negative com mitment to an indicated fact and not merely acceptance of this fact. If we contrast examples (I) and (4), we see the partially different functions of jaljaa (yes) after a statement (example I}, where it conveys acceptance of the statement and after a question (example 4), where it conveys commitment to a positive fact. A:.
men efter ere ar va de ju en harlig mylla (but after three years you-know it was a lovely mould) B: ja (yes) (4) A:. e ni klara da (are you finished then) B: jaa (yes) The vowel reduplication in jaa is one of the means whereby a speaker can show increased commitment. Further, if we take the meaning of yes and no to be acceptance and non acceptance (rejection), it might be tempting to assume that they, when follow ing a statement, as in the case above, always directly indicate acceptance or non-acceptance of this statement. This is, however, an oversimplification as is shown by the example below:
(s)
A:. it's raining B: oh no
Here, oh no, if pronounced in a short, matter of fact way, can indicate denial of the statement. But consider instead the possibilities of pronouncing oh no with a disappointed or surprised intonation. In such cases, B would presuppose the truth of A's statement in order to signal his emotional non-acceptance of some thing he, all the same, believes to be true. The object of acceptance or non-acceptance contextually signalled by yes and no therefore does not merely depend on the status of the preceding communicative act but also on what type of attitudinal reaction the feedback utterance signals. Attitudes such as disappointment or surprise are factive and presuppose some fact towards which they are directed. This presupposition seems to be upheld in the cas� above and the non-acceptance instead to be used as an underpinning of the unpleasantness or unexpectedness signalled by the
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{I)
J. Allwood, J. Nivre and E. Ahlsen word
oh
II
in conjunction with the prosodic expression of disappointtnent or
surpnse.
3-4·3
Factual polarity
If we look at examples (6) and (7) below, we can see how the factual polarity of the preceding communicative act affects the function of the feedback utterance. Consider the use of na/nej (no) in examples (6) and (7) below.
(6)
negative polarity and the function of the negative feedback utterance is acceptance. In example (7), on the other hand, In example (6) the preceding statement has
Table 3 Effects of the factual polarity of the preceding utterance on feedback Listener's response
Preceding utterance
Pos statement:
It's raining Neg statement:
yes (it is)
no (it isn't)
Acceptance of statement (indicated belieQ Rejection of statement
Rejection of statement
Commitment to positive fact
Acceptance of statement (indicated belieQ Commitment to negative fact
Commitmeilt to positive fact
Commitment to negative fact
yes (I will)
no (I won't)
Acceptance of request
Refusal of request
Rejection of request (defiance)
Acceptance of request
yes (I would)
no (I wouldn't)
Acceptance of offer
Rejection of offer (declination)
Acceptance of offer
Rejection of offer (declination)
It isn't raining Pos yes-no question:
Is it raining? Neg yes-no question:
Isn't it raining?
Pos request:
Open the door! Neg request:
Don't open the door!
Pos offer:
Would you like some tea? Neg offer:
Wouldn't you like some tea?
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A; de kan ju inte va for fiskarnas skull va (it couldn't be for the sake of the fish you-know) B: na (no)
1 2 On the Semantics and Pragmatics of Linguistic Feedback the preceding statement has feedback is non-acceptance.
(7)
positive polarity
and the function of the negative
A: sa gar naturen under me tekniken (like that nature perishes with technology)
B: NE]IIde vaxer upp annat da vet du
(no//other things grow up you know)
Table 3, which is also extracted from Table 1, illustrates ·the role of the factual polarity of the preceding utterance. As we can see, the polarity of the preceding utterance affects the attitude expressed by a yes or a If a statement preceding a
yes
is positive, the
yes
no.
signals acceptance of the
function has to be supported by the positive pronominal reformulation it is. Likewise a no following a positive statement signals rejection of the statement, but following a negative statement it signals acceptance. The polarity of the preceding utterance thus �eems to have a particularly drastic effect on the atti tude signalled by a yes or a no. If we look a little more closely at Table 3, we see that statements and requests seem to pattern one way and yes-no questions and offers a slightly different way with regard to the effect of their polarity on the content of yes and no. In the case of statements and requests, positive polarity results in acceptance (yes) and rejection (no), while negative polarity results in the converse rejection (yes) and
acceptance (no). What seems to be accepted or rejected in the case of requests is the task of carrying out the request, while following statements, acceptance (yes and no) ambiguously can concern what might be termed provisional accept ance or it might concern a more full-bodied acceptance and integration into one's own system of belie�s. Rejection following statements seems in the case of both yes and no to signal commitment to fact with a polarity opposite the one indicated by the statement. In the case of preceding yes-no questions and offers (which in the examples given here also have the form of yes-no questions), change of polarity does not seem to have the same effect, so that yes signals commitment to positive fact and no signals commitment to negative fact, regardless of the polarity of the preceding utterance. In order to maintain the same analysis for all four contexts we could say that the yes, where it follows a negative yes-no question or offer (since negation to be relevant seems to presuppose a positive expected state of affairs which is denied), signals acceptance of this expected positive state of affairs. A no would signal rejection of this expected positive state of affairs. Another alternative to maintain the same analysis for all four contexts would be to claim that yes always involves commitment to positive fact and
no
com-
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statement. If the statement, however, is negative, the yes can signal objection and rejection of the proposed negative statement. Normally, however, this
J. Allwood, J. Nivre and E. Ahlsen
13
·
(8) A:. nie idjot dozhd (isn't it raining) B: da (yes)
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mitment to negative fact. This analysis would, in fact, also work for yes and no following statements and requests, where, for example, a yes signalling com mitment to positive fact following a negative statement would indicate objec tion or rejection of the claim made and when following a positive statement would indicate acceptance or agreement Even if the analysis of yes and no as signalling commitment to positive and negative facts, respectively, perhaps seems somewhat simpler than the acceptance/non-acceptance analysis, it runs into problems with the case discussed in example (s), i.e. where no is preceded by oh and pronounced with an intonation conveying disappointment. Such a response seems to presuppose the correctness of the speaker's claim, but signal the listener's emotive, conative non-acceptance. Whichever analysis is chosen, it is, however, clear that the attitude expressed by a yes or a no requires consideration of the polarity of the immediately pre ceding utterance in order to be determined. In some languages, such as Swedish and German, the analysis just proposed for yes and no in English would have to be made somewhat more complicated in order to accommodate the fact that these languages have a special morpheme jo (Swedish) and doch (German) which is used instead of yes in all the cases following an utterance with negative polarity. So for Swedish and German one could therefore suggest that the meaning of ja (the same word in both languages) is to accept to carry out what the evocative function of a preceding positive utterance signals. In the case of statements, yes-no questions, and yes no offers, the ja furthermore often 'delivers the goods', i.e. provides a commit ment to one of the indicated alternatives. In the case of requests, this is usually not possible since mostly non-verbal action going beyond a simple yes is required to 'deliver the goods'. The function of jo and doch would, when following an utterance with negative polarity, instead be to assert commitment to a positive corresponding state of affairs opposite to that indicated by the preceding utterance. The Swedish and German distinction between ja-jo and ja-doch would thus separate acceptance of a positive state of affairs from commitment to a positive state of affairs as a reaction to an utterance where this state of affairs has been given negative polarity. In English, yes is instead polysernic with regard to these functions. Other languages, such as Russian, offer a further modification of the analysis. The acceptance function of da (yes) has been extended so that not only positive facts can be accepted, but also negative facts. Consider the following example.
14
On the Semantics and Pragmatics ofLinguistic Feedback
B's utterance in the Russian example (8) signals acceptance of the fact that it is not raining. Negative questions, requests and offers seem to function similarly, so that
da
can be used to signal acceptance of a negative state of affairs. In
English, the word mm can be used in a similar way, the difference being that mm indicates rather than signals acceptance.
3·4·4
Information status
A third feature of an
utterance preceding a yes or a no that seems important both for the actual morphological and phonological realization of yes or no and for their interpretation is the information status that the utterance has for the
(9)
)
( 10
(I I)
A:. det regnar (it's raining) B: ja det gor det ja (yes it does it yes) A:. det regnar inte (it's not raining) B: na det gor det inte na (no it does it not no) A:. det regnar (it's raining) B: "'na det gor det inte na (no it does it not no)
In example
(9), the 'sandwich' positioning of
the ja before and after the pro
nominal reassertion of the preceding statement serves to signal that the listener has been reminded of something he/she already knew. The corresponding 'sandwich' construction with no can therefore be used after a negated state ment, as in example 10 , only when it signals that B is reminded of a negative
( )
fact that he accepts as true. It cannot be used in order to object to a positive statement, as in example I I .
( )
·
If, in example (9), B had responded by ja ja, which could be regarded as an abbreviated version of ja det gor detja , the signalled meaning would have been something like yes, I know, without the indication of having been reminded. IfB had responded by jasd (oh (really)), this would instead have signalled that the fact mentioned by A was new to B, thus not something he was reminded of or already knew. In fact, this feature of jasd (oh) can be ironically exploited in Swedish by speakers who say jasd in order to indicate to their interlocutor that what they are hearing is perhaps not so new and interesting as their interlocutor would like to imagine.
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( )
listener, i.e. for the person giving the feedback. Compare examples (9), 10 , and
( u ).
J. Allwood, J. Nivre and E. Ahlsen 1 s Another operation on information status can be achieved by the use of jaha (oh) which in example says
(9) could have been used to signal that B accepts that A det regnar as a fact, which is ambiguous between taking A's uttering some
thing as a fact and taking the state of affairs indicated by A as a fact. This
ambiguity is brought out in examples such as jaha, det iir vad du sager (oh, that's
what you say), jaha det iir vad du tror (oh, that's what you think), or jaha, daflr vi ta
med oss paraply (oh, then we have to take an umbrella).
( 12)
A:. sa ja har tomadador dar a ja brukar fa ett par hundra tomater (so I have tomato boxes there and I usually get hundreds of tomatoes)
B: nae
(no) Another example where the information of the preceding communicative act is
(
perceived as new by virtue of the feedback utterance is example I 3) below.
3·5
EvocativeJunction
Feedback utterances conveying that the listener (B in our examples) is surprised and that the information in the preceding utterance is new to him/her often also have an evocative function, i.e. they place an obligation on the current speaker (A) to react, in his turn, and give feedback to B's feedback. Thus, B's
jassa, in example ( I 3), displays surprise which leads A to reaffirm.
( I 3)
A:. a karamellpapprena dom kommer i i//i den dar papperskorgen sen (and the candy papers they get into into//into that waste paper basket then) B: jassa (really) A:. jaa
(yes)
B: de va ovanlit (that's unusual)
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As we have seen, there are various means for making a feedback utterance indicate, display or signal the information status of the preceding utterance in relation to the person who gives feedback. In example ( 1 2) below, the use of the negative morpheme nii (no), as a reaction to a preceding positive statement, as well as the lengthening of the morpheme nii (no) by the added vowel-e, makes the utterance display an attitude of surprise and thereby indicate that the infor mation status of the preceding utterance is new rather than given or known. In particular, as already discussed in section 3.4.2, B is not denying the veridicality of A's statement
16 On the Semantics and Pragmatics of Linguistic Feedback
4 F O RMALIZI NG C O N T E N T F E AT U RES O F FEE DBAC K 4· r
Introduction
In this section, we will explore the possibility of formalizing the analysis of content features presented in section 3· In doing this we will develop two different kinds of formalization, one using attribute-value matrices and the other based on the theory of situation semantics. 4. 1.1
Attribute-value structures
The fir st kind of formalization simply consists in using attribute-value matrices to represent bundles of content features associated with linguistic expressions. Besides offering a compact and yet perspicuous notation, the use of attribute value matrices (or feature structures, as they are sometimes called) potentially gives us a unification-based formalism! which may be useful if you want to describe how the occurrence content of a particular feedback utterance is consttucted by combining a type content with features of the context. (This is a problem that we will not really pursue in this paper, however.) 4.1.2
Situation semantics
The second attempt at formalization is couched in the framework of situation semantics (Barwise & Perry 1983, 1985; Barwise 1989). Within that theory, the occurrence content P of a linguistic utterance is regarded as a function of two parameters: the expression (type) S which is used, and the embedding circum stances (or context) c in which S occurs. This is expressed in the following semantical 'equation' (cf Barwise 1986b):
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The word jassa (really) displays surprise and indicates that the preceding utterance contains new information. An additional rising intonation can make this function even sttonger. As we can see, A responds with a feedback utterance jaa (yes), where the added -a gives the utterance emphasis, i.e. A reaffirms his own preceding utterance. B then continues de va ovanlit (that's unusual), which displays her continued attitude of surprise. In a somewhat wider sense of evocative, of course, every utterance contain ing only a single feedback word could be said to evoke the continuation of the conversation. Consideration of the evocative function of feedback thus connects it to the basic function we have above referred to as ability and willingness to continue a communicative interaction. By uttering a feedback word a speaker simultaneously indicates willingness and ability to continue and willingness and ability to let the other speaker continue.
J. Allwood, J. Nivre and E. Ahlsen
( 14)
I7
qs, c)- P
The occurrence content of an expressionS in a context c (as well as the content of any other information-carrying event) is generally taken to be the infor mation that there exists a (real) situation of a certain type (i.e. that a certain type of situation is realized). The content is therefore modelled in situation semantics with a
situation type (c£
Barwise
1986a,
Israel
&
Perry
1988).
A
situation type T is defined by a (possibly parametric) infon (or state ojalfoirs) i, which is called the conditioning infon ofT. A particular situation s is of typeT if and only if it supports i (or an instance of
i, if i is parametric), i.e. if and only if i is a fact i n s . A situation-type T with conditioning infon i is represented as in
(r s), where sis a situation variable and the whole expression is read as 'the type (rs)
[sli]
For example, if an utterance of the sentence It is raining in a certain context c has the content 'it is raining at a certain spatiotemporal location /' (say, the utterance location), then we may express this as follows: (
r6 )
qit is raining, c)= [s I «at/; raining; 1 »]
The picture sketched so far is oversimplified in (at least) one important respect. In reality, the content of a linguistic utterance is not a function of two but of three parameters. In addition to the expression used and the embedding circumstances, we have to consider the set of constraints (law-like regularities such as linguistic conventions) with respect to which the utterance interpreted, as the examples in
(r7)
(r7) make clear:
a. qswedish, /n;r./, c)- 'no' b. qGreek. /n;r./, c)= 'yes'
Since we will only be concerned with one language (Swedish) in the formalized examples below, we will generally suppress the constraint parameter in the representations and continue to represent the content of linguistic utterances as a function of only two parameters: expression and content. It is important to keep in mind, however, that the content we artribute to particular utterances is always dependent on a particular set of constraints (especially linguistic conventions).
4.2
Type ofreaction to the preceding communicative act
Information about the basic communicative functions (contact, perception, understanding, attitudinal reactions) can be represented in attribute-value format using the four attributes CONTACT, PERCEPTION, UNDERSTANDING and
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of situations where i holds'.
1 8 On the Semantics and Pragmatics ofLinguisric Feedback ATTITUDE,
where the attribute AlTITUDE, as noted above, can be read as short for
since CONTACT, PERCEPTION and UNDERSTANDING also involve attitudes (c£ section J.2).
OTHER AmTUDE
The first three will be treated here as binary fearures (with possible values+ and -) , although this is an oversimplification. The AmTUDE feature, by contrast, takes as its value a complex fearure sttucrure containing information about the attitudinal reactions which are present in different cases. This complex feature structure thus contains a selection from a set of binary features ACCEPT, REJECT, BELIEF, AGREEMENT, SURPRISE, etc.
5
In sum, then, we need at least the following collection of features to repre sent type of reaction to preceding communicative act: Type of value
Feature CONTACT
BOOLEAN
PERCEPTION
BOOLEAN
UNDERSTANDING
BOOLEAN
AmTUDE
COMPLEX
ACCEPT
BOOLEAN
REJECT
BOOLEAN
BELIEF
BOOLEAN
AGREEMENT
BOOLEAN
SURPRISE
BOOLEAN
(
( (r9)
The content of the feedback utterances Ja and mm in examples r ) and 2) (repeated below for convenience) can now be (partially) represented as in
(
and 20), respectively. ( 1) A: men efter tre :ir va de ju en harlig mylla (but after three years you-know it was a lovely mould) B: ja (yes)
(19) [CONTACT [PERCEPTION [UNDERSTANDING [AmTUDE [ACCEPT
(2)
+] +] +] +]]
A; . . . ja kan fa sana//aah kontakter . . . kontakter rna universum jaa ( . . . yes I can get such!/eeh contacts . . . contacts with the universe yes) B: mm {mm)
(20) [CONTACT [PERCEPTION [UNDERSTANDING
+]
+] +]
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( r8)
J. Allwood, J. Nivre and E. Ahlsen
19
If we turn to situation semantics, we must remember first that the content of a feedback utterance will be represented as a situation type (c£ section 4.1.2). In most cases, the conditioning infon of this type will be a complex one, consisting ii' to of a conjunction of atmnic infons (we will use the notation '& i 1, denote the conjunction of the infons i 1, i i)· For example, the content of the feedback utterances in example (1) and (2) can be represented as in (21) and (22): .
•
•
•
•
•
We see that the conditioning infons in both cases are conjunctions of (possible) facts about the speaker Bi and his willingness to continue, his perception of the preceding utterance ui, his understanding of the content Pi of the preceding utterance ui, and (in 21 but not in 22) his acceptance of the communicated content Pi. So far, we have not made any attempt to capture the influence of context in the interpretation of feedback utterances. For example, in (21) there is no indication of how the location /1, individual Bt, Utterance U 1 and COntent p 1 (which are constituents of the conditioning infon) are picked out from the context (and the context itself is only represented by the symbol c1). We will return to this problem in section 4·4 below. 4·3
Communicative status
Communicative status can be introduced into our attribute-value notation by means of three complex-valued attributes INDICATE, DISPLAY and SIGNAL, which take as their values feature structures representing the information which is indicated, displayed or signalled, respectively. Their use is illustrated in (23), which is a richer representation of the content ofja in example (1) than the one given in the preceding section, and (24), which represents the content of ja de e deju in example (3), repeated below for convenience.
(2 3) [INDICATE [cONTACT [PERCEPTION [UNDERSTANDING [ATTITUDE [BELIEF
+] +] +] +]]]
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(21) C(ja , c1)- [s I & «at 11; willing-to-continue, B1; 1», «at 11 ; perceive, B1, u1; 1 ))' «at /1; understand, B1, u11 P1; 1», «at /1; accept,B1, P1; 1»] {22) C(mm, c2) = [s I & «at 12; willing-to-continue, B2; 1», «at 12; perceive, B2, u2; 1 )), «at /2; understand, B2, u2, P2; 1 ))]
20
On
the Semantics and Pragmatics ofLinguistic Feedback
[siGNAL
In situation semantics, the notion of communicative status can be captured in different ways. Here we approach the problem simply by dividing the con tent of an utterance into three parts, namely indicated content, displayed content and signalled content, which we will represent as C1(S, c), CD (S, c), and C5(S, c), respectively. Thus, we assume that the following equation holds (for arbitrary . expressions S and contexts c): (2 5 ) C(S, c) - Ct(S, c) + Cn (S, c) + Cs(S, c) Given this assumption, we can characterize the contents of the feedback utterances in examples (r) and (3) as in {26) and (27): (26) C1(ja, c1) = [s I & «at I 1; willing-to-continue, B1; 1 », «at 11; perceive, B1, u1; b >, «at 11; understand, B1, u1, P1; 1 », «at 11; believe, B1, P1; 1 » ] Cs(ia, c1) - [s I & «at 11; accept, B1, P1; 1 » ] (27) C1(ja de e deju, c3) - [s I & «at 13; willing-to-continue, B3; 1 », «at /3; perceive, B3, u3; 1 », «at /3; understand, B3, u3, P3; 1 » ] Cs(ia de e deju, c3) - [s I & «at 13; accept, a3, P3; 1 », «at 13; believe, a3, P3; 1 » ] 4·4
Context sensitivity with regard to the preceding communicative act
In this section we will discuss one kind of context sensitivity in relation to the formalizations developed so far, namely sensitivity with respect to factual
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[AlTITUDE [ACCEPT +] ] ] (3) A: de e ju valdit faalit me karnkraft (it is very dangerous you-know with nuclear power) B: jal/de e de ju (yes/ /it is you-know) (24) [INDICATE [coNTACI' +] [PERCEPTION +] [UNDERSTANDING +] [siGNAL [AlTITUDE [ACCEPT +] [BELIEF +] ] ]
J. Allwood,J. Nivre and E. Ahlsen
21
polarity. In section 3·4·3· we discussed two different analyses ofthe way in which the factual polarity of the preceding utterance influences the content of words like yes and no, one based on the notions of acceptance and rejection, one b ased on the notion of commitment to facts. The formalizations suggested here are based on the first analysis throughout. In attribute-value notation, the occurrence content of na/nej in examples (6) and (7) can be represented as (28) and (29), respectively. (6)
A:.
(28) and (29) differ only in the value they assign to the path [siGNAL [ATTITUDE [REJECT]]]. In both cases, the value is the same as the polarity of the preceding statement We can capture this generalization in a set of constraints on the attribute-value structure C representing the content of an utterance of the type nej in the context of a preceding statement represented by the attrib ute-value structure PS (where the notationJ:path designates 'the value assigned to path in feature structure f): (30) C:[INDICATE [coNTACT]] - + C:[INDICATE [PERCEPTION]] = + C:[INDICATE [UNDERSTANDING]] = + C:[siGNAL [ATTITUDE [REJECT]]] - PS:[POLARITY]
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de kan ju inte va for fiskarnas skull va (it couldn't be for the sake of the fish you-know) B: na (no) (7) A:. s:i g:ir naturen under me tekniken (like that nature perishes with technology) B: NE]IIde vaxer upp annat d:i vet du (no//other things grow up you know) . (28) [INDICATE +] [cONTACT [PERCEPTION +] [UNDERSTANDING +]] [siGNAL [ATTITUDE [REJECT -] ] ] (29) [INDICATE +] [cONTACT [PERCEPTION +] [UNDERSTANDING +]] [SIGNAL [ATTITUDE +] ] ] [REJECT
22 On the Semantics and Pragmatics of Linguistic Feedback
Using situation semantics the contents of nii/nej in examples (6) and (7) can be represented as in ( 3 I ) and ( 32), where, for the first time, we try to give a little structure to the contexts. The context in example (6) is characterized as a situa tion c6 where it is the case that a person A6 addresses B6 at a location 16_1 (temporally preceding the location /6 where the feedback utterance occurs), making an utterance u6 with content P6, which has the polarity o. In a similar way, the context of example (7) is characterized as a situation c7 where it is the case that a person A7 addresses B7 at a location /7_ 1 (temporally preceding the location /7 where the feedback utterance occurs), making an utterance u 1 with content P1, which has the polarity 1 .
( 3 I ) C1(nej, c6) = [s I & «ar l6; willing-to-continue, B6; 1 »,
We can generalize over ( 3 I ) and (3 2) by means ofparameters and obtain ( 3 3), which is a characterization of the content of nej in a context of type c. (We use boldface for parameters; note especially the polarity parameter I.)
( 3 3 ) C1(nej, c) = [s I & «at I ;; willing-to-continue, B; 1», «at I ;; perceive, B, u; 1», «at I ;; understand, B, u, P; I» ] Cs(nej, c) = [s I & «at I;; reject, B, P; I» ) where cl=«at I;_1; address, A, B; I» Cl=«at I;_1; utter, A, u; I» Cl=«at I ;_1; content, u, P; I» Cl=«at I;_1; polarity-of, I, P; I»
Since we have not yet worked out a formalized way of capturing the systematic dependency offeedback content on the speech act (mood) and infor-
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«at /6; perceive, B6, u6; 1 », «at /6; understand, B6, u6, P6; 1 » ] Cs(nej, c6) = [s I & «at 16; reject, B6, P6; 0» ] where c61=«at /6_ 1; address, �. B6; 1 » c6 1=«at /6_1; utter, �. u6; 1 » c61=«at /6_ 1 ; content, u6, P6; 1 » c6 1=«at /6_ 1 ; polarity-of, 0, P6; 1 )) ( 32) C1(nej, c7) = [s I & «at /7; willing-to-continue, B7; 1 », «at /7; perceive, B7, u7; 1 », «at /7; understand, B7, u7, P7; 1 » ] Cs(nej, c7 = [s I & «at /7; reject, B7, P7; 1 » ] where c71=«at /7_1 ; address, A7, B7; 1 » c71=«at /7_ 1 ; utter, A7, u7; 1 » c71=«at /7_ 1 ; content, u7, P7; 1 » c71=«at /7 _ 1; polarity-of, I , P7; l »
J. Allwood,J. Nivre and E. Ahlsen
23
marion status of the preceding utterance, we will not discuss formalization with regard to these features of context sensitivity here. 4·5
EvocativeJunction
5
C O N C L US I O NS
In this paper we have argued, discussed and at least partly demonstrated that what we have called 'the linguistic feedback system' of a language should not be regarded as an area of hopeless complexity and confusion. Rather, linguistic feedback systems seem to be describable subsystems of the interactive mechanisms available in the spoken form of any language. We have further argued that such systems can not only be described phonologically, morpho logically and syntactically, but also semantically and pragmatically. In order for such a description to be possible, feedback expressions and feedback mechanisms must, just like deicric expressions and deicric mechanisms, be regarded as highly context-dependent. Specifically, we have argued that an account of the meaning of feedback utterances involves considering at least the following dimensions of content. Type of reaction to preceding communicative act. 2. Communicative status of various aspects of the content conveyed by the feedback utterance. 3- Context sensitivity with regard to the preceding utterance in at least the following respects: (i) Its evocative function (type of speech act) (ii) Its factual polarity (iii) Its information status. 4· Evocative status of the feedback utterance. 1.
Our attempts at formalizing these features of the meaning of feedback utterances using attribute-value matrices and situation semantics are, naturally,
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Adding evocative functions to the representations used so far requires nothing new in principle. For the attribute-value representations we simply add a complex-valued feature EVOCATIVE, which takes as its value feature structures representing different evocative functions. For the situation semantic approach we simply extend the situation-types representing the content of feedback utterances with more conditioning infons corresponding to the evocative aspects of the utterances. However, since we have not yet worked out a precise and detailed account of the evocative functions we also abstain from giving any formalized examples here.
24 On the Semantics and Pragmatics of Linguistic Feedback only first attempts but, we hope, sufficiently precise as to convince other linguists that the area of feedback might be worthy of their attention.
Department ofLinguistics University ofGiiteborg Renstriimsparken S-142 98 Giiteborg Sweden
N O TE S &;
can be seen, we are here making no attempt to distinguish semantics from pragmatics. This is so because we believe that such a distinction runs into serious practical and theoretical difficulties (c£ Allwood 1981 ). 2 For the distinction between indicated, dis played and signalled information, see section 3 ·3 below. 3 The Swedish word ju appears in some of the examples in this paper. ju has no exact translation into English. It has the function of making what is stated appear as mutually known information. This 'might depending on context variously be rendered as 'you know' or 'we know'. For reasons of idiomaticity, we have chosen to use the hyphenated expression you-know in our ttanslations although this is not always
a good equivalent. It should also be observed chat ju is less salient and weaker chan you-know. 4 For an introduction to unification-based formalism; and their use in syntax and semantics, see Shieber 1986, Pollard & Sag 1987,johnson 1 988. Here ir is even more of an oversimplifica tion co use simple binary fearures, and for two reasons. First, the object of rhe atti rudes may be differem from one case co another, although it will be assumed here chat the object is always some fearure ofthe content of the preceding utterance. Second, the strength of the attitudes may vary; surprise, for example, may be expressed in different degrees, although it will be tteated here as a simple yes-no matter.
RE F E RE N C E S
Ahlsen, E. (198 5}. 'Discourse patterns in aphasia', Gothenburg Monographs in Linguis tics, 5, University of Goteborg, Dept. of Linguistics. Allwood, J. (1976), 'Linguistic communica tion as action and cooperation', Gothenburg Monographs in Linguistics, 2, University of GOteborg, Dept. of Linguistics. Allwood, J. ( 1978), 'On the analysis of com municative action', Gothenburg Papers in Theoretical Linguistics, 3 8, University of GOteborg, Dept. of Linguistics.
Allwood, J. (1979), 'Ickeverbal kommunika rion: en oversikt', Papers in Anthropological Linguistics, 2, University of GOteborg, Dept. of Linguistics. Allwood, J. ( 1981 ), 'On the distinctions between semantics and pragmatics', in W. Klein & W. J. M. Levelt (eds), Crossing the Boundaries in Linguistics, Reidel, Dordrecht. Allwood, J. (1984}. 'Finns det svenska kom munikationsmonster? In 'Vad iir svensk kulrur?', Papers in Anthropological Linguis-
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1
J. Allwood,J. Nivre and E. Ahlsen 25
·
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tions and shaken attitudes', Linguistics and tics, 9, University of GOteborg, Dept. of Linguistics. Philosophy, 8: I So-61. Allwood, J. (I985). 'Tviirkulturell kommuni Brown, G. & G. Yule (I98 3), Discourse Analy sis, Cambridge University Press, Cam kation', in J. Allwood (ed.), 'Tviirkulturell bridge. Kommunikation', Papers in Anthropological Linguistics, I 2, University of GOteborg, Clark, H. & E. F. Schaefer (I989), 'Contribut ing to discourse', Cognitive Science, 13, 259Dept. of Linguistics. 94· Allwood, J. (ed.) (I988a), 'Feedback in adult second language acquisition', Final Repon Ehlich, K. (I986). Interjektionen, Niemeyer, Tiibingen. II, Ecology of Adult Second Language Fries, C. (I 952), The Structure ofEnglish, Long Acquisition (ESF). man, London. Allwood, J. (1988b), 'Om det svenska systemet for spr:i.klig aterkoppling'. in Hellberg, S. (I985), 'Scandinavian sentence types', University of GOteborg, Dept. of P. Linell, V. Adelswiird, T. Nilsson & P. A. Nordic languages. Pettersson (eds), Svenskans beskrivning, I6, SIC 2Ia, University ofLinkoping, Dept. of Heritage, J. (I984), 'A change-of-state token and aspects of irs sentential placement', in Communication Studies. J. M. Atkinson &J. Heritage (eds), Structures Allwood, J. (I988c), 'Aterkoppling i vuxnas of Social Action, Cambridge University spr:ikinliirning', in K. Hyltenstam & Press, Cambridge. I. Lindberg (eds), Svenska som andrasprak, University of Stockholm, Centre for Bi Israel, D. & J. Perry (I 988), 'What is informa tion?', paper presented at The Conference lingualism Research. on Minds, Brains and Language, Van Allwood, J. (I 990), 'Synopsis of a method for couver, BC, February I988. conceptual determination', paper presented at the Twelfth Scandinavian James, D. (I972), Some aspecrs of the syntax Conference of Linguistics, Reykjavik. and semantics of interjections. Papersfrom the Eighth Regional Meeting of the Chicago Allwood, J., J. Nivre & E. Ahlsen (I990), Linguistic Society, I62-I72. 'Speech management: on the non-written life of speech', Nordicjournal ofLinguistics, Johnson, M. (I 988), Attribute-value Logic and 13: I-48. the Theory ofGrammar, CSLI Lecture Notes Anward, J. (I 986), 'Emotive expressions', in I 4, CSLI Publications, Stanford. 0. Dahl (ed.), Papers from the Ninth Levinson, S. (I983), Pragmatics, Cambridge University Press, Cambridge. Scandinavian Conference of Linguistics , University of Stockholm, Dept. of Lin Peirce, C. S. (I9S S). Philosophical Writings of guistics. Peirce, edited by J. Biichler, Dover, New York. Barwise,J. (I 986a), 'The situation in Logic-ll: conditionals and conditional information', Plunkett, K. & S. Stromqvist, ( I990), 'The acquisition of Scandinavian languages', in E. C. Traugott, C. A. Ferguson & J. S. Gothenburg Papers in Theoretical Linguistics, Reilly (eds), On Conditionals, Cambridge University Press, Cambridge. 59· University of GOteborg, Dept. of Linguistics. Barwise, J. (1 986b), 'On the circumstantial relation between meaning and content', Pollard, C. & I. Sag (I987), Information-based Syntax and Semantics, CSLI Lecture Notes Versus, 44: 23-39· I 3, CSLI Publications, Stanford. Barwise,J. (1989), The Situation in Logic, Csll Lecture Notes 17, CSLI Publications, Searle, J. (I969). Speech Acts, Cambridge University Press, Cambridge. Stanford. Barwise, J. & J. Perry (I983). Situations and Severinson-Eklundh, K. (I986), 'Dialogue processed in computer-mediated com Attitudes, MIT Press, Cambridge, Mass. munication: a study of letters in the Barwise, J. & J. Perry (I98 5). 'Shifting situa-
26 On the Semantics and Pragmatics of Linguistic Feedback COM-system', Universiry of Linkiiping, Sigurd, B. (1984), 'Om Jasa, Bra, Precis och Dept. of Communication Srudies. andra rerurord', Sprdkvard, 3: 3-8. Schegloff, E. (1982), 'Discourse as an inter Wiener, N. (19481!961), Cybernetics; or Control actional achievement', in D. Tannen (ed.), and Communication in the Animal and in the Analyzing Discourse: Text and Talk (George Machine, MIT Press, Cambridge, Mass. town Universiry Round Table on Yngve, V. (1970), 'On gerring a word in edge Language and Linguistics, 198 1 ), George wise', in Papers from the Sixth Regional town Universiry Press, Washington, DC. Meeting, Chicago Linguistic Sociery, Shieber, S. M. (1986), An Introduction to PP· 56 7-77 Unification-based Approaches to Grammar, CSLI Lecrurc Notes 4, CSLI Publications, Stan�ord. Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Journal ofSemantics 9: 27-51
© N.I.S. Foundation (1992)
Towards a Generalization of Anaphora KEES VAN DEEMTER
Intitutefor Perception Research (IPO), Eindhoven
Abstract
r
I NTRO D U C T I O N
Anaphoric reference has always been a busy area of linguistic research. Traditionally, theories of anaphora have concentrated on situations in which the anaphoric element is a definite Noun Phrase, most often a pronoun. Accordingly, the relation between anaphor and antecedent was construed as a relation of identity. an anaphor and its antecedent were, loosely speaking, considered to stand in a relation of coreftrence . 1 . Gradually, however, a shift in perspective has arisen. Especially since the 1970s, questions of text coherence have come into focus (e.g. Clark & Haviland 1977; see Carter 1 987 for an overview) in artificial intelligence as well as in psycholinguistics and, along with this new perspective, pronominal anaphora has come to be viewed as merely one symptom of text cohesion (Halliday & Hasan 1976), rather than as an isolated phenomenon. The cohesive viewpoint was given a linguistic follow-up in the work of Grosz (1 977) and Sidner (198 3 ), among others. Sidner, for instance, viewed anaphora primarily as a way to keep hold of the focus of a text. Now in this wider perspective of text-cohesion, the restriction to 'identity anaphora' has litde to commend itsel£ For example, consider the following text (c£ Heim 1982): ( 1) John read A BOOK ABOUT ScHUBERT. He wrote a letter to THE AUTHOR.2 If the pronoun he is anaphoric because its interpretation (i.e. its reference) depends on the cohesion between the two sentences, then why should not the author be anaphoric for the same reason? In cases such as this, where the anaphoric relationship does not depend on equality of anaphor and antecedent,
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This paper deals with anaphoric properties of both pronominal and nonpronominal Noun Phrases within the framework of Discourse Representation Theory (DRT). A generalized notion of anaphora is advocated, in which the notion of anaphora is extended to cover relations between anaphor and antecedent other than referential identity. This paper tries to make insights gained in DRT, as well as in other theories of anaphora, applicable to a wide range of 'new' phenomena in the area of context dependent interpretation.
28 Towards a Generalization of Anaphora
we will speak of 'non-identity', or 'bridging' (Clark & Haviland 1977), anaphors. D. Carter included the bridging phenomena in his tentative definition of what we will call generalized anaphora : Anaphora is the special case of cohesion where the meaning (sense and/or reference) of one item in a cohesive relationship (the anapbor) is, in isolation, somehow vague or incomplete, and can only be properly interpreted by considering the meanings of the other item(s) in the relationship (the antecedent(s)). (Carter 198 7)
Associated specification: the anaphor names an element that is, as a mater of word meaning (i.e. 'analytically'), associated with the antecedent (A meeting . . . The participants). 2. Inferred specification: as above, but the association is non-analytic, in that it does not hold as a matter of word-meaning. (The dead heiress . . . The murderer). J. Set-element specification : the antecedent denotes a set; the anaphor is singular and has the same head as the antecedent plus at least one additional modifier; in such cases, the anaphor specifies an element of the antecedent-set (A herd ofelephants . . . The elephant with the 1.
limp).
However, Sidner's theory does not offer a fully general and rigorous perspective on generalized anaphora. Not only is it a long way from her semantic nets to the determination of truth-conditions; more disturbingly, the conditions under which generalized anaphora is allowed in her proposals go unexplained. To concentrate on set-element specification, why is this type of anaphora restricted to singular NPs? Why should the head of the anaphor be the same as that of the antecedent? And why are additional modifiers obligatory? Moreover, why are all anaphors restricted to definite NPs? Apart &om the question of explanation, at least some of these restrictions are not in agreement with the linguistic facts. For instance, in (2), the Noun Phrases two sick elephants and all sick elephants (with accent on sick) make for perfectly grammatical anaphors. (2)
A herd
of elephants was visible in the rear window. Two/All sick elephants were lying somewhere in the middle,
but Sidner's rules do not allow these NPs to be anaphoric, since both are plural instead of singular, and one of them is indefinite and the other quantificational.
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Carter shows that something like this extended notion of anaphora is implicit in much earlier research. Of course, a theory has to specify the conditions under which generalized anaphora can obtain, and how the meaning of an anaphor depends on the meaning of the antecedents. So far, no fully general treatment of generalized anaphora has been proposed, to the best of my knowledge. Heim's proposals to deal with (1), for instance, are strictly limited to defiriite NPs.3 Some steps in the direction of a more general account were taken by Sidner (1979), whose inventory of anaphors includes the following types of non identity anaphors:
K.
van
Deemter 29
Somewhat more controversially, we would claim that even proper names can be anaphoric (c£ Weijters 1989). For even though a proper name can sometimes4 introduce a previously unknown entity, the more common situation seems to be that a proper name selects an entity from an earlier intro duced set. Consider
(3 ) Yesterday, PSV had great difficulty in winning the cup final. Only five minutes before the end of the match against FC Utrecht, KIEFT scored the winning goal. (Weijters 1989)
2
C O NST RAI NTS O N F U L L NP ANAPHORA
Much of the effort in modem anaphora research has gone into finding structural constraints on the anaphoric relation. For instance, �e tradition that has originated from Reinhart ( 1976) has formulated syntactic constraints on the coreference relation, and the accessibility constraints in DRT serve a similar purpose. Which of all the traditional constraints carry over to full NP anaphora? Some time ago, H. Lasnik conjectured that all do: 'The correct
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·
Weijters notes that even readers who have not the slightest idea which players ate in the PSV team, are able to deduce on the b asis of (3) that Kieft is one of them. Henceforth, we will, lacking evidence to the contrary, assume that all NPs can be anaphoric. Although subsequent treatments have expanded the work of Sidner,5 they inherit its main weaknesses. In order to arrive at a comprehensive and explicit treatment of anaphoric phenomena, and to formulate and explain adequate restrictions, we will sketch an account of generalized anaphora along the lines of Kamp's Discourse Representation Theory (DRT; Kamp 198 1).6 As a result, further justification is provided for the idea that there is one notion of generalized anaphora which applies to pronouns and definite descriptionS as well as other Noun Phrases, and possibly even to other categories-and also for the idea that the mechanism of DRT is powerful enough to account for this broad area ofanaphoric phenomena. The organization of this paper is as follows. In section 2, we will investigate the structural constraints on full NP anaphora. In section 3, a simple variety of DRT that deals with singular and plural NPs is sketched. In section 4, our own proposal for the treatment of anaphoric full NPs is presented. In section s, possible extensions of our proposal are briefly discussed, such as the extension to categories other than the Noun Phrase. Throughout, familiarity with existing theories of anaphora will be taken for granted except for some brief explanatory remarks. The basic technicalities of Generalized Quantifier theory are explained in a technical Appendix.
30 Towards a Generalization of Anaphora generalization appears to be that in any structural configuration in which co
reference between two NPs is precluded, overlap in reference is also precluded' (Lasnik I 976). However, this is not exactly what we find. The deviations from Lasnik's
conjecture are most clear in the case of Reinhart's constraints on anaphora. Let us, for the moment, stick to entrenched (pre-Reinhart I 98 Ja) terminology. As is well known, the
Disjoint Reference Rule (DRR)
forbids that a non-reflexive
anaphor has an antecedent within its 'minimal governing category', a specified syntactic domain that may be simplified, for current purposes, to be the S or NP node most immediately dominating the anaphor. (See, for instance, Reinhart I983b for details.) Now this rule fails to hold in the new situation. For example,
(4) THE LEFT envisaged A NEW FOOTHOLD, if we interpret the foothold as an anaphor, namely as a foothold for the Left. For in this case, no S or NP node separates the anaphor and the antecedent.
Likewise, the
Noncoreference Rule
(NCR) is violated in the sentence
(s) A FE� SPECIMENS were enough to conclude that ALL PAPERS were censured, for NCR enforces noncoreference between a nonpronominal NP and any the specimens c-command the apers? �,-commanding NP, whereas in
( s) ,
p
� However, the non-application of these rules in the area of full NP anaphora can be understood if one takes the pragmatic viewpoint of Reinhart 1 9 8 3 a where there is, within the broader area of coreference, one preferred relationship between a pronoun and an NP, namely the binding relationship. Binding
implies a c-command relation as well as a few other structural requirements.
Now Reinhart's central idea-in the style of Grice's axiom of Manner-is that deviations from this preferred situation ought to be motivated. In other words, a Preference for Binding principle ('Preference Principle', for short) is in force which says:
Preference Principle : Whenever a sentence is uttered in which rwo NPs fail to stand in the binding relation, whereas a minor change in wording (without a change in meaning) would
have resulted in a binding situation, rhen the rwo NPs are nor intended to corefer.
This principle, together with a definition of binding, replaces specific rules such as NCR and ORR. To start with ORR, structural rules say that (6)(a) is a case of binding, while (6)(b) is not (6)(a) ZELDA bores HERSELF. (6)(b) ZELDA bores HER.
Therefore, if a speaker utters (b), he or she 'avoids' the binding variant (a), and consequently no coreference between Zelda and
her is intended. This reasoning
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DRR is violated in
K. van Deemter
31
applies to full NPs with the same cogency. For instance, the Preference Principle forbids full NP anaphora in (7):
(7)
ZELDA
bores THE WOMAN,
for it is plausible that the woman can be replaced by the pronoun her without a change in meaning. The application of the principle to NCR is analogous, and can, in principle, also be applied to full NPs. For instance, anaphora in (8) The SOLDIER thinks that THE OFFICER is competent is forbidden, since replacement of the officer by he results in binding. By contrast, coreference in (9) is allowed, As HERODOTUS had
tO be in Athens by nightfall, THE HISTORIAN had tO hurry up (example from Van Eijck, personal communication).
for replacement of one of the two NPs by a pronoun can never result in binding, since neither NP c-commands the other. We think that these predictions are borne out by the facts. However, the (real or purported) full NP anaphors in (7), (8 ) and (9 ) are all of a special kind: they are identity anaphors. It is easy to see that the applicability of the Preference Principle, and therefore also the validity of ORR and NCR, is limited to identity anaphora. For replacement of an anaphoric full NP by a pronoun will always change meaning-so that the Preference Principle cannot apply-except when we happen to deal with identity anaphora. This explains why (4) and (s ) violate constraints on coreference. For instance, a newfoothold in (4) cannot without a change in meaning be replaced by itself, neither can aJew specimens in (s ) be replaced by they. The situation for the DRT constraints on anaphora is even subtler. As is well known, Kamp ( 198 I) predicts that quantifying NPs create anaphoric 'islands' that are inaccessible for anaphors outside the NP. Now full NP anaphors violate this constraint, but plurals do so as well.8
( 10)
wants a moped. (a) HE/THE BOY lifeS tO show off (b) ONE SMART GUY �ants to rent one. (c) THEY like to show off EVERY SCHOOBOY
While anaphoric readings �re impossible in (w)(a), anaphoric readings of (w)(b) and (c) seem acceptable. We will see later how slight modifications in DRT predict precisely this pattern of observations. Another central tenet of DRT is the novelty constraint on indefinites. DRT makes indefinite NPs the mirror image of definite NPs: while definite NPs must always be anaphoric, indefinites can never be anaphoric. Indefinite NPs introduce new material-encoded in a so-called Reference Marker (RM)-and
8
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(9)
32 Towards a Generalization of Anaphora
this material can be referred to by a subsequent definite NP. This idea cannot be upheld without modification, however, since indefinite NPs can be anaphoric in our sense of the word, as we have seen.9 Yet, it is true that indefinites cannot normally have identity anaphora. For instance, the indicated reading of (I I) is ungrammatical: (I I)
THE MAN
walks; A MAN talks.
3
A
S I M PLE THEORY O F S I N G U L A R A N D PLURA L N P S
Given that our proposals in the area o f anaphoric NPs come on top o f a DRT based semantics for non-anaphoric NPs, and since our account will include plural NPs, a variant ofDRT has to be adopted that included plural NPs. So far, however, no definitive treatment for plurals has been forthcoming. We will keep matters simple and stay away from such complexities as are involved in the treatment of mass NPs (Link 1 983), conjoined NPs (e.g. van Eijck 1 983) and intensionality (Landman 1 989). Instead, we will rely on a simple theory of plurality that combines some useful features of Roberts (1 987) and van Eijck ( I98 3)· A good starting point to explain our own proposal is the trea!ITient put forward in Roberts (1 987). Roberts extrapolates Kamp's distinction between quantificational and other NPs to the realm of plural NPs, calling an NP
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However, one need not describe this as a residual novelty constraint on indefinites; for although an indefinite anaphor cannot pick up an antecedent as a whole , neither can a non-anaphoric indefinite NP of the form DET CN (a Determiner followed by a Common Noun) be used to denote the entire set {XI �CNJI � X). Both phenomena can be explained along the lines of Horn's scalar implicatures (Horn 1972). For example, according to Horn, all is stronger than some, and therefore the sentence Some people walk has the scalar implicature that it is not true that All people walk . In Gricean terms, the strongest determiner is always preferred. Now, assuming that the is stronger than a , 1 0 it follows that a square of5 equals 25 is awkward, given that it is also true that the square oj5 equals 25 . Likewise, in ( r I), an anaphoric reading of a man talks is awkward, since it must also be true on this reading that the man talks . In combination with a Russellian analysis of definiteness, indefinites have non uniqueness as an implicature. The impossibility of indefinite identity anaphora follows immediately from this proposition. To sum up, the current tendency towards pragmatic explanation of structural constraints is confirmed by our findings in the area ofNP anaphora. For both the novelty constraint for indefinites and the limitations of c-command constraints can be reduced to pragmatic laws.
K. van Deemter 3 3
individual denoting
(ID, for short) if i t can have a collective reading, and
quantificational otherwise. Normally, ID NPs are read collectively, but if an implicit or explicit adverbial operator ('each') intervenes, they are interpreted individually. In the latter case, they are treated on the same pattern as quantifying NPs. In this way, the commonalities between distributive ID NPs and quantifying NPs are adequately reflected. For instance, Roberts' theory explains w hy the distributive reading of
( I 2)
The men lifted a piano
cannot precede It was heavy, since the Reference Marker that is introduced by the NP
a piano -which
appears quantified now-is inaccessible to discourse
in our own account, but other aspects will be left aside. In particular, we will use sets rather like lattices, as Roberts does. More crucially, we will replace conditions of the form CN{X) {meaning X � IICN]I) by conditions in the Generalized Quantifier format NP{X) (c£ van Eijck
I983),
primarily because
our treatment of anaphoric full NPs in section 4 needs to have all NP information available in one condition.11 The resulting representation for {I2) runs as depicted in Figure 1 . Note that the RM y ranges over individuals, while
X
and
Z
range over sets. The condition 'The , men {X)' can be glossed
'X
contains all the men in the universe of discourse, but nothing else'. In general, DET CN{X) holds if X contains DET elements oqCNJI, and nothing else. This informal characterization will be made precise below.
X The men (X) z
y a
y element X
piano (Z) lifted (y,Z)
Figure
1
Finally, we want to allow discourse anaphora to quantifying NPs, but only for plural pronouns and for nonpronominal NPs (section 2). Therefore, quantificationalNPs introduce a quantified individual RM and a set RM in the principal DRS. Roberts's conditional structure b I '*
DET
b 2 , which took a different value for each determiner, is replaced by Kamp's b I '* b 2 (i.e. For example, the sentence Many men walked is represented in b I '* EVERY '*
h).
'*
Figure 2. Thus we arrive at the following DRS construction rule, that applies to both singular and plural NPs:
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anaphors in a subsequent sentence. These features of her proposal will be used
34
Towards a Generalization of Anaphora
Many men (X)
X
y y elemen t x __,
--�
'------__
Figure
E
2
,
(Here ; [1p: - x ] abbreviates the result of substitution of x for 1/J in the condition ; .) To illustrate the intended meaning of conditions of the form a (X), consider
( I 3 ) Some men lifted a piano, and more specifically the condition 'Some men (X)' in its representation. X has to fulfil two requirements: the standard GQ condition II(some men )II(X) meaning that X contains some men and any number of other objects in addition-and the requirement that X contains only men. For if the men were assisted by any number of gorillas, their athletic accomplishment cannot be reported by the quoted sentence.13 Therefore, we will follow Van Eijck in defining
Set predication (preliminary): J verifies DET CN (X) iff IJDetJJQJCNJJ, f(X)) & f(X) � JJCN]J. However, in this clause, the meaning of NP(X) is specified not in terms of the meanings ofNP and ofX, but in terms of the meanings ofDet, CN and X. This departure from compositionality becomes a drawback in the case of syntacti cally simplex NPs (e.g. all in the sense of all people, who , proper names, pronouns). To remedy this defect, we will use the smallest witness set (Thijsse 1985) of an NP denotation (abbreviated: K QJNPJD ) as a proxy for the CN denotation (Appendix, ii.). Therefore, a slightly more general version of the definition runs:
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NP-introduction : Suppose a is a monotonically increasing NP (see appendix, i.), while p is a VP. When a sentence y of the form ap is processed, a novel set RM say X, is introduced in the principal DR along with the condition a (X). lf a is a collectively interpreted lD NP, then the condition y [a: = X] is entered in the principal DR If a is a quantificational NP or a distributively interpreted ID NP, a condition of the form b I => b 2 is entered, where b I consists of a newly introduced individual RM y and the condition y e X. The box � 2 consists of the condition y [a : = y ] .12
K.
van
Deemter 3 S
Set predication (final):f verifies NP (X) iffiiNPII(f{X)) &j{X) � J<j]NP�.
4
A TREA T M E N T O F F U L L N P A N A P H O R A W I T H I N D RT
Imagine a sign in a supermarket saying ALL PRICES REDUCED. This is not naturally taken to concern all prices of all commodities in the world. Rather, the domain of the statement may be restricted to prices in the supermarket. Only a small part of the world functions as the domain of our utterances, a different part on each occasion. In cases such as this-cases of full NP deixis -the domain is restricted by the utterance situation. In the case of full NP anaphora , it is the linguistic situation that causes the restriction. We can apply this idea to DRT by interpreting conditions relative to the temporary domains that are provided by antecedent RMs. The default domain, so to speak, is the normal universe-of discourse of the model, bur during processing different domains become active. Anaphoric resolution becomes the problem of finding the right domain. If one NP is anaphoric to another, their respective RMs stand in a certain relation. Which relations qualify? First, there are highly general relations such as the relation of subsumption (subset of a set, part ofa quantiry, substructure of a given structure). Presumably, this relation is so basic that it can be exploited without mention: speaking about a crowd, the NP the men can be understood as denoting the men in the crowd without explicit mention of the subset relation. The same thing may hold for a few other, highly general relations such as the relation berween cause and effect. For simpliciry, we will assume that all relations other than the relation of subsumption (for us mostly: the subset relation) can only be activated by the use of certain so-calledJunction nouns . For instance, although all articles have authors, the NP thepeople in
(14)
THE ARTICLES were
interesting. THE PEOPLE really liked them.
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Thus, ifNP1 is simplex and NP2 complex, and both denote the same quantifier (for instance, NP 1 = many and NP2 - many people), then both NP1(X) and NP2(X) are restricted to the CN-denotation of NP2• This a priori plausible prediction seems to be borne out by the facts. a Consequently, the smallest wimess set can be used both for complex and for simplex NPs. The treatment that we have outlined in the present section is basically rich enough to serve the purposes of this paper, although a number of additions are needed to make it fully adequate. In particular, provisions are needed to deal with NPs other than those which are monotonically increasing (see van Eijck 1983 and Appendix, iv.) and in order to deal with unbound anaphora to indefinites (Evans 1977; van Eijck 1983; van Deemter 1989).
36 Towards a Generalization of Anaphora
cannot denote the authors of the articles. In order to refer to these, the relevant relation ('author-of) must be indicated by means of the function noun author:
( I 5)
THE ARTICLES
were quite long. THE AUTHORS really liked them.
Whenever this is the case, we will speak of relational anaphora. I will sketch a treatment for relational anaphora in section 4.2, after concentrating first on subsectional anaphora (section 4.1). In section 4.3, we will adress the resolution problem for full NPs and reflect briefly upon the validity of familiarity based theories of definiteness.
Subsectional anaphora
How can our ideas concerning the interpretation of conditions relative to shifting domains be implemented within the theory of section 3 ? Given this set RM-based framework, context-dependent interpretation of conditions of the form NP(X) is crucial, so we will concentrate on relativization of these conditions.15 We stipulate that a condition of the form NP(X) can be relativized to any accessible RM Y, written NPY(X). Conditions of this form are interpreted roughly along the lines of Westerstahl (198 s), who interprets conditions of the form IIDetiiYQICN!D{X) as .meaning IIDetll( CNjl n Y)(X). For Westerstahl, Y is a set variable to be instantiated by a 'context set', which is somehow provided by the context.16 It is roughly a Westerstahl-style 'General ized Quantifier plus relativizations' theory that we want to add to DRT, in order to combine the virtues ofboth theories. In particular, DRT contributes its anaphoric mechanism to instantiate Westerstahl's variable over context sets. Suppose an earlier sentence has given rise to an antecedent RM Y, denoting a set of policemen, for instance, then the sentence Two tough guys smashed the door may lead to the representation in Figure 3, where the anaphoric link between the tough guys and the policemen is reflected by the relativized condition (2 tough guys)Y(X). As a result, DRT's predictions about possible pronoun antecedent pairs will be inherited by full NP anaphors. This idea will be made more precise in the next sections.
X
(2 tough guys)Y(X)
u smashed
.u u element X
Figure 3
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4· r
K. van Deemter
4. 1 . 1
37
The meaning of relativized conditions
The most direct way to combine Westerstahl's relativized NP conditions with DRT is to define interpretations of such conditions in the following way:
Subsectional Relativization (preliminary): If an NP is of the form (Det CN), then fverifies (NP )Y(X) iffj(X �f(Y) &j(X) � KIINPII & 11Detl!'ll1 ( K �NPII, (f(X ))).
(r6)
HUNDRED POLICE OFFICERS went in. THE MEN/THE BASTARDS ruined everything,
A.
it is predicted that the men among the officers ruined everything; but if all the . officers happen to be men (bastards), then all the officers are to be blamed, of course. So identity anaphora comes out as a special case of subsectional anaphora. Unaccented use of an NP induces identity anaphora. For instance, if the men is unaccented in speech, it will tend to be interpreted as denoting the entire set of officers. Reversely, an accented occurrence may either denote a subset of the officers, or a different set altogether. This fits the well-known rule that new information is accented in speech (Halliday 1967), provided that a real part of a given set counts a5 new information. Technically, this direct accommodation of Westerstahl's idea is not completely satisfactory yet. Not only is the compositional formulation of subsectional relativization-in which the determiner interpretation is recovered from the NP denotation-problematic in view of syntactically simple NPs such as all and many , but since we want to treat proper names and pronouns in the same way as other NPs, their treatment will become problematic also. Worse, Westerstahl's approach is limited to Noun Phrases, offering little promise for the relativization of Verb Phrases, Adjectives, etc. (section s). Therefore, we turn to relativizations in a more directly logical sense. A semantic definition of tht; relativization of a formula ¢ to a set A runs Here we assume that M is a model (E, I), where E is the universe of the modeL and I the interpretation function. M r A (the restriction ofM to A) is defined as (E n A , I '), where for n-ary relations R, I '(R) - I(R) n A". Finally, the
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The last conjunct incorporates Westerstahl's basic ideaP The second conjunct is needed for the same reason as the corresponding clause in Set Predication (c£ section 3). Further, we will assume that The men lifted a piano is false with respect to a domain Y, not only if the men were assisted by gorillas (c£ section 3), but also if they were assisted by men outside Y. This is why we requireJ(X) � f( Y). Sometimes, it follows automatically thatf(Y) - j(X). For example, in
38 Towards a Generalization of Anaphora treatment of free variables requires a slightly more complex version of relativization:
llf411M.£ = de£lk61k rA ,£ fA Here f rA is defined as follows: for arbitrary Z and x, where Z is a variable over sets and x a variable over individuals,
f rA (Z) = de£f(Z) II A f rA (x) = de£f(x) if X E A ; undefined otherwise.
Subsectional Relativization (final):J verifies NPY(X) in M ifff(X) s; f( Y) & f(X) s; K IINPIIM & II(NP(X)) YJ!M.r The last conjunct can be expanded: II(NP(X)) YJIM.£ = defiiNP(X )IiM r f(Y).frf(Y) = IINPIIM r f(Y)(IIXII£ rf(Y) - IINPilv r f( Y)(f( Y) 11 f(X )) = IINPI!M r f(YJ,{(X ) ). To illustrate, take the sentence All people shouted , where the NP all people is anaphoric to the RM Y. Let the universe E of M equal {a , b , c , d }, while fM - f b , c , dJ; now ifiJpeopleJI = fa , b , c}, then llallpeoplei!M - f fa , b , c}, fa , b , c , d} }. and llall peoplei!M r £(Y) - { { b , c}, {b, c , d) }. Consequently, All PeopleY(X) is verified by J if f(X) s; f( Y), f(X) s; K (IINPID - {a , b , c }, and IIall people liM r f( Y)(f(X) ). Consequently,f(X) = { b , c }. As a result, this reading of the sentence All people shouted is true if b shouts and c shouts. Questions of 'stability' under relativizations are most conveniently investi gated for the logical relativizations themselves (i.e. for NP(X)Y), rather than for all three clauses governing relativized conditions (i.e. for NPY(X)). The most general son of question, for given NPs a and ,8 and for domains X, X ', Y, Y' is: ifwe know the truth-value of (a (X)) Y, then what can we deduce about the truth-value of (,B(X '))Y'? For instance, an obvious generalization of a mono tonicity property would be the property of
Model Anti-persistence: IfNP(X)Y and Y' s; Y then NP(X)Y', saying that models may be decreased without loss of truth. Now, since E of M, a 'non anaphoric' reading of an NP can be viewed as the limiting case of anaphora in which the entire universe E is the antecedent. Consequently, Model Anti persistence is equivalent to Stability under restrictions: the property that NP(X )E � NP(X) Y, for arbitrary ys; E . In the Appendix (Appendix, v.) we
IINP (X )IiM.£ equals IINpz(X )IiM.£ if Z denotes the universe
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Now that we have made relativization precise, we propose the following modification of the verification clause for relativized conditions, which is-in a sense to be made precise in the Appendix (Appendix, iii.)-'as compositional as possible':
K. van Deemter 39
will show that, given reasonable assumptions, it is precisely anti-persistent NPs ('All CN', 'Less than n CN', etc.) that have this property. 4. 1 .2
Pronouns as quantifiers
X z element Y
angry (z)
Figure 4 theyY(X) comes down to X Y . . Now there are several ways to accomplish this since the treatment of number and person features of pronouns is still a matter of some debate.18 Here, we opt for an approach in which both features are part of the semantic content, in order to account for the fact that certain violations of number agreement are semantically impossible, while other violations can be grammatically acceptable. For example, our account predicts that the indicated reading of (1 7)(a) is ungrammatical on semantic grounds, while ( I 7)(b) is left unaffected: =
(1 7)(a) (1 7)(b)
TWO BOYS EVERY BOY
want a moped. HE likes to show off wants a moped. THEY like to show off
It is plausible that, in addition to these semantic constraints on the number of a pronoun, there is a pragmatic-and therefore 'defeasible'-tendency towards complete number agreement between pronoun and antecedent, especially in
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So far, I have shown how subsectional anaphoric readings for NPs can be represented in DRT. I have not dealt separately with specific kinds of NPs (descriptions, proper names), but the treatment is analogous for all NPs and the reader will have little difficulty in working out the details for himself However, there is one exception, namely pronouns. If we compare our treatment of full NPs with the treatment of pronouns in Kamp (198 1), an asymmetry comes to ·the fore: our full NPs introduce RMs, bu� Kamp's pronouns only pick up old RMs. Symmetry is restored if we let pronouns, too, introduce RMs (see also Kamp 198 5 ) and add conditions of the form pronoun (RM). Given suitable pronoun meanings, relativization of pronoun (RM) to a different RM will amount to equality of the two RMs. To illustrate: assume that the RM Y is an available antecedent in the DRS, then the sentence They were angry is represented as shown in Figure 4· The meaning IITheyll has to guarantee that
40 Towards a Generalization of Anaphora
the case of bound anaphora (van Eijck I98 3). A possible semantics for the English plural pronoun runs
ll theyll - {Z : Z - E & lEI � 2}. As a result, theyY(X) implies the familiar DRT condition X - Y; for Subsectional Relativization species that jX � JY, and the clause ll(they (X) )YJI guarantees that JY � jX, as one may easily verify. the meaning of we must be s�ghcly more complex:
llwell = (Z : Z - E & lEI � 2 & Z � IIAnimatell & IISpeakerll e Z}.
llh4d - {Z :Z = E & E � liMa/ell & lEI I }. llhel�ub - {Z � E : I(E 11 IIMa/ell)l - I & E 11 11Malell � z & z� Male}. =
In the case of llhel�d• a relativized condition he Y(X) requires that Y equals the singleton X, while in the case ofllhellsub• Y consists of the only male entity in the possibly larger set X. According to this 'new information' reading, an NP the married couple can be antecedent to the anaphor he, which will now denote the male element of the couple. What counts is ·that, in the standard case where X is a singleton, the result is equivalent to the traditional DRT account,whereas the procedure followed is the same as the one proposed for full NPs. . This concludes our treatment of the ·semantics of subsectional full NP anaphora. As we have seen, identity anaphora comes out as a special case of a more general notion of anaphora. Our account makes it also plausible that definite descriptions can have identity anaphora by accident, while with pronouns, identity follows from descriptive poverty.20 Now we will return briefly to relational anaphora.
4.2
Relational anaphora
Relational NPs can be accommodated in our account of full NP anaphora by means of a mechanism of indirect relativization. Consider a relational NP such as the mother, two mothers , then the intended set of mothers can be restricted through a restriction of the set of their children. In order to make this idea precise, some notation is needed. Assume CN is relational; now if CN1 stands for the 'normal' meaning {xl 3 y:CNix, y)}, where CN2 denotes the relation involved in the CN, we propose the notation CN1 1Yl for the 'relational', or indirect relativization of CN 1:
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As a result, the relativized condition WeY(X) is true iff Speaker e 1 X - Y � IIAnimatell and lXI � 2. The pronoun he may, if we simplify, 9 denote either llhel�d• if it is taken to stand in the relation of identity to its antecedent; or, it may denote llhel�ub• if it is used subsectionally:
K. van Deemter
CN1 1 Yl
=
{m l 3 x e Y(CN2(m , x))}.
Suppose we are dealing with the CN mothers',
41
CN1 1 Yl
mother. Then if CN1 is glossed 'the set of
equals 'the set of mothers of elements in Y'. Using this
notation, we can deal with anaphoric readings of relational NPs by means of
Relational Relativization : (DetCN)Y(X) is verified QIDetii(CN1 1f(Y)I))(f(X)) &j(X) � CN1 1f(Y)J.
by an assignment J iff
For example, this definition provides acceptable verification conditions for the condition the motherY(X) in the representation of the sentence ( 1 8) If a farmer feeds his LAMBS he will pet THE MOTHER.
sheep that are mothers of lambs in Y. As stipulated in the introduction of section 4, this treatment is restricted to NPs containing a recognizably relational C� (such as mother, daughter, example). In all other cases, our approach forces .us to construe the anaphoric relation as a variety of the relation. Sometimes this may lead to a rather strained analysis. For
subsumption
instance, the anaphoric.relation in such notoriously problematic cases as (1 9)(a) When we arrived in THE VILLAGE, SEVERAL HOUSES were abandoned. (1 9)(b) MY DESK is a mess. MANY PAPERS are covered under cigar-ash. must be construed as a subsumption relation of some kind, since no overt relational element connects the houses with the village or the papers with the desk. In the final analysis, a more liberal approach that allows a wider range of 'associative' anaphoric relations may turn out to be most appropriate. In section
s. we will briefly discuss an approach that would make possible an alternative ('situation anaphora') solution to pieces of discourse such as (1 9)(a) and (b). But first we have some remarks about the relational) full NP anaphora.
4·3
resolution
problem for (subsectional or
Resolution and thefamiliarity condition
We have seen that a suitably extended version of DRT can be used to derive anaphoric readings for full NPs. In order to choose the
intended
reading, the
same resolution strategies can be used as for pronominal anaphors (e.g. Sidner 198 3; Carter 1 987). However, the descriptive information in full NPs-which is, as we have seen, not fundamentally different from, but much richer than the
number
and gender information in pronouns-c:in constrain the set of possible
antecedents drastically. Suppose the set of worlds
W
encodes the Common
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In particular, for the condition to be true, X must contain the unique sheep that is a mother of a number oflambs in the set Y, and X may contain nothing more. The indefinite NP Two mothers is treated analogously, with X containing two
42 Towards a Generalization of Anaphora
Knowledge21 of speaker and hearer, then a starting point for resolution would be the following constraint
Resolution Constraint: Suppose K(m] is a DRS, and K(m + I] is the DRS resulting from K(m] after processing NP, and suppose that NP introduces the RM a , with accompanying condition c Y(a ); then NP cannot take RM Y as its antecedent ifK(m + I] is false in all w e W in which K(m] is true. This admittedly uneventful constraint is highly general in that it applies to singular and plural NPs, subsectional and relational, bound and unbound. Note that it requires only that c Y( a ) makes sense in one , rather than all w e W. The following eX:unple shows why:
The description the son of . can relate to the film director, even though nothing is lr..nown about him.22 Further, the Resolution Constraint is merely a constraint, not a sufficient condition. Other constraints, of a pragmatic nature, are suggested by Maes. For instance, the description in (2o) is adequate, according to Maes, in so far as it can count as an explanation for the director's predilection. To exemplify the Resolution Constraint, suppose a discourse has led to the introduction of an RM Y, the non-singleton set of prisoners in a penitentiary institution. Let .... abbreviate 'can take as its subsectional antecedent'; then if we assume that Reinhart's constraints are fulfilled and that Y is accessible, our theory predicts that .
.
a. the old sailor Y if, in at least one w E W, there is exactly one old sailor among the prisoners. b. an old sailor .... Y if, in at least one w e W, there is at least one old sailor among the prisoners. -+
This example is worth reflecting upon, for it brings out that all the differences between definites and indefinites are accounted for by a Russellian 'uniqueness' analysis of descriptions (Russell I905) plus a Hornian theory of scalar implicatures (section 2). Otherwise, the two are treated equally. Where does this leave the principle offomiliarity (Christophersen I939; Heim I 982), here rendered as Heim's 'Extended Novelty-Familiarity;,..Condition' (Heim I 982)? For ; to be felicitous w.r.t. F it is required for every NP; in ¢ that (i) ifNP1 is [- definite), then i � Doni(F};(ii) ifNP1 is [+definite), then (a) i e Dom(F), and (b) ifNP1 is a formula, F entails NP1• (Heim 1982)
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(20) The first novel of THE UNKNOWN DIRECTOR FRANK VRIESAKKER deals with the themes of guilt and responsibility. In his films THE soN OF A CALVINIST PREACHER has already shown a predilection for those themes. (Maes I 990)
K. van Deemter
43
s C O N C L U S I O N : THE B O U N D S O F A N AP H O RA
In the introduction of this paper, we promised a theory of 'generalized anaphora'. In the sequel of this paper, we have somewhat discourteously stretched the time-honoured notion of anaphora to cover so-called subsectional cases of anaphora (as in sentence (2), for example) and we have even tried to apply it-even more controversially-to relational Noun Phrases (as in sentence ( I ) ). We hope to have demonstrated how theories that were designed to tackle problems in the area of pronominal anaphora can be used to deal with very similar problems in areas that are traditionally unrelated to anaphora. Thus, the notion of anaphora and many notions that are related to it (antecedent , accessi bility, resolution , etc.) were generalized considerably. Yet this article has at best provided a very partial answer to the question of how general a phenomenon anaphora really is. We will not attempt a definition of generalized anaphora in this paper.24 Instead, some possible extensions of the theory beyond the topics of the previous sections will briefly be pointed out below.
Vagueness. First, there is the extension towards an account of vague NPs. Our definition of model restriction (M f A) implies that, for all predicates P, IIPI!M r A - IIPI!M n A . For predicates which are more thoroughly context dependent, a more sophisticated definition ofl ' is needed in which E plays the role ofa comparison set. Consider the command Give me twofast horses! What can interpretation of this sentence against the background of an antecedent set of
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(F is a file and ¢ an English sentence, while F 'entails' an NP if the descriptive content of the NP follows from F.) We claim that the familiarity pnnciple is refuted, at least in this strong form. For (i) indefinites, we have seen, can be anaphorically related to familiar material. Further (iia), it has often been observed that definites need not refer to familiar material.23 Finally (iib), we have seen that definites need not entail their descriptive content (Maes forthcoming). In effect, our approach vindicates a unicity account (Kadmon 1987) of definiteness. However, we do not think that the property of'having an anaphoric reading' is a consequence of unicity, as Kadmon claims, since this is a property that is shared by all NPs, as we have stressed throughout this paper, while unicity is not. Of course, part (i) of Heim's familiarity condition remains valid for identity anaphora and part (ii) remains valid for pronouns, so a weakened version of the familiarity principle can easily be formulated. However, no separate statement of the principle is needed since this weakened version follows from indepen dent semantic and pragmatic principles, as we have seen.
44 Towards a Generalization of Anaphora
horses Y mean? Out of all the possible choices, two interesting ones are the following: (Subsectional :) Two fast horses Y(X) is verified by fiff fX � fY &}X � llhors�l & V x e X: x is faster than most elements of Y. ( Contrastive:) Two fast horses Y(X) is verified by f iff & }X � llhors�l & 'rJ x e X & 'rJ y e Y: x is faster than y . As ever, the contrastive sense-in which the speaker, tired of all the slow horses
Other categories. It seems that some degree of extrapolation to categories other than the Noun Phrase is justifiable as well. For example, consider VPs . There are relational verbs, such as stop or continue , that can be viewed as inherently anaphoric to a VP describing an activity. On an anaphoric reading of stopped in
(2 1 ) The computer WAS RUNNING THE PROGRAM but suddenly it STOPPED, the computer might go on running other programs; it stops running the one program mentioned in the text. An example of a subsectionally interpreted VP would be
(22) Mary went SWIMMING but after a while she stopped EXERTING HERSELF, which has a reading according to which Mary stopped swimming, leaving it open whether she continued doing other exerting things. The sentence may also be a legitimate category for anaphora. In this case, antecedent RMs would denote entire situations (places, times, worlds). For instance, in
(2 3 )
The crowd gathered in front of the castle. Only one man carried a key,
one understands typically that the man carried the key at the time of the gathering. A similar view was taken, among others, by B. Partee, who showed how an anaphoric mechanism could account for a number of facts in the area of temporal reference. This idea can be accommodated in the account of section 4 if domain dynamics is replaced by time dynamics. Interestingly, neither subsumption nor equality are the default anaphoric relations in this application of the anaphoric perspective. Rather, the default anaphoric relation is the relation of immediate succession ; all other relations, including equality of time, have to be enforced, as Partee shows.
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in Y, demands two really fast horses-requires contrastive intonation (Halliday 1967). This example suggests that the role of comparison sets in the interpreta tion of vague adjectives (Klein 1979) might be integrated in a theory of generalized anaphora by identifying comparison sets with anaphoric antece dents.
K van Deemter
45
Let us conclude. To hypothesize that context-dependent interpretation will be an increasingly important aspect of future semantic theories seems a safe bet. Theories of anaphora have proved their usefulness as a tool in a considerable part of this area, far beyond the facts they were originally designed to explain. How much further they will finally reign remains to be seen.
6 APPENDIX: TE RM I N OL O GY AND S O ME RE S ULTS FROM GQ -THE O RY
ii.
Recoverabllity ofA from QA. W is a so-called wimess set for quantifier QA if V B (B e QA - (B n W) e QA ). Now, in order to arrive at a composi tional verification clause for conditions of the form NP(X) and NPY(X),
we made use of the smallest wimess set 1e (QA ) of QA . 1e(QA ) n {XI V Y: Y e a - (Y11 X) e a ). The following theorem proves that the smallest wimess set of an NP denotation, where NP is of the form Det + CN, equals the CN denotation IICNjj: =
Theorem I : Assuming Conservativity, Quantity, Nontriviality and Finiteness , it holds that 1e ( QA ) - A . Proof25 Conservativity guarantees that A is a wimess
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Constraints on generalized quantifiers. It is a crucial observation of Generalized Quantifier (GQ) theory that natural language NP denotations, viewed as sets of properties (Montague 1973) (equivalently: relations between properties), observe certain semantic constraints (Barwise & Cooper 1981; van Benthem 1984). In particular, the truth of a relation QAB, where Q denotes the relation and A and B are subsets of the universe E may (Quantity) only depend on the cardinalities of the set-theoretic regions A n B , A - B, B - A , and E - (A v B )). Second (Conservativity), QAB may only depend on the two regions within A, namely A 11 B and A - B . Thirdly, a quantifier QA has to obey a Nontriviality constraint (also called Variety): IfA :F � then there are B, B ' , such that QAB, -. QAB ' . Also quite general are the constraints of(1) Continuity: If B � B ' � B ·, then ifQAB and QAB ·, then also QAB ' ; (2) Finiteness : natural language quantifiers Q are only defined on finite relata; and (3) Extension : QEAB o QE.AB , as long as A , B � E , E ' . In addition, a number of properties were formulated for classificatory purposes. For instance, a quantifier Q is upward monotonic in its second argument (also called monotonically increasing, or (-t)) if it holds for all A, B, B ' , that if QAB and B � B ', then also QAB '. Upward (downward) mono tonicity in the first argument is called Persistence (Anti-persistence). A quantifier Q is intersective if, for all A and B , Q(AB) o Q(A 11 BA n B ). L
46 Towards a Generalization of Anaphora
set for QA Ifwe assume that W is a smaller witness set for QA, we can derive a contradiction; for
(I ) We can remove any element x from any B for which Q(A, B) holds. This
iii.
Nonrecoverability of Q &om QA Conversely, the determiner denota
tion cannot be recovered from an NP denotation. This negative result can be proved simply, as Thijsse (I983) shows: suppose E is the universe of discourse, and take Q1 = II Two ll and Q2 = IIAllll, while lA I = 2. Then (relative to E) Q1A = Q2A = {X s; E : A s; X}, but the two determiner denotations are different. Note that the very same example also goes to show that not all NPs are model anti-persistent (and consequently, not all NPs are R-stable); for although Q1A = Q2A relative to E , the equality is easily destroyed through relativiza tion. Consequently, the denotation of a relativized condition NPX is not a Junction of the denotations ofNP and X. This is reflected in our own definition of 'f verifies NPXM', which defines the meaning of an expression in a given model M in terms of a different model M r X. No strictly compositional verification clause is possible, unless the model becomes part of the meaning: IINpX11£ equals the function h , such that
h(M) = {Z s;}X: z s; K(NP ) & Z e IINPIIM r fX}·
iv. Adequacy of the set.,.RM account ofNP semantics. We have limited
the way in which NPs introduce set RMs-basically borrowed from van Eijck (1983)-explicitly to monotonically increasing NPs. This can be argued as follows: call a quantifier QA directly DR-representable (DR) if all its elements are 'grouped around' a number of witness sets: QA is DR <> de£ '9' B: B e QA - 3 X s; A (X e QA & X s; B .)
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is trivial for x outside W n A, so suppose x e W n A. We have Q(A, B n A n W) (due to Conservativity and the fact that W is a witness set). Now assume that a e A - W (such elements exist, we have assumed), then if we define a permutation :n interchanging a with x, it must hold that Q(n(A ), n(B n A n W), due to Quantity , and Q (A , :n(B n A n W) n W), that is Q(A, B - {x }). (2) Conversely, we can also add arbitrary x to a set B for which QAB holds. This is trivial for x outside W n A, so suppose x e W n A. We have Q(A, B n W), so Q(A, (B n W) u {a )), for arbitrary a e A - W. So (compare ( I )) we have Q(A, :n( (B n W) u {a }) ), that is Q(A, B u {x}). (3) Combining these results with the requirement of Finiteness , we have that Q(A, U), for arbitrary U. But this is at odds with the Nontriviality constraint on NP denotations, so a contradiction has been derived.
K.
van Deemter 47
It is easy to see that, given DRT's embedding apparatus, quantifiers which are DR are representable in the box notation exemplified above. But direct repre sentability is coextensive with upward monotonicity in the right argument. Theorem 2 (given Conservativity ): QA is DR � QA is monotonically increasing (-t). Proof: The left-to-right implication is straightforward. For the other direction, suppose QA is - t. Then (I) if QAB then 3 X � A (X e QA & X � B) (take X: - A n B and use Conservativity); and (2) if3 X � A (X e QA & X � B), then X e QA. and therefore also B e QA. due to the left-to-right implication.
Theorem 3: A quantifier is continuous if and only ifit is logically equivalent to a conjunction of one -t quantifier and one -l quantifier. (Thijsse I983.) Consequently, all Continuous quantifiers are 'OR-representable via reanalysis'.
Stability. Let, as before, stability under restrictions (R-stability) be the requirement that, for a certain NP, ll(NP (X ) fll implies II(NP(X)) Yjl, for any X, Y � E . The following theorem equates this property to the familiar property of anti-persistence:
v.
Theorem 4· Given Conservativity and Extension , a quantifier Q is R-stable iff it is !-. Proof: Suppose Q is R-stable, while QAB and A ' � A . Now R-stability implies QA A n A 'B n A , and therefore QEA n A 'B n A (EXT), so QEA 'B n A ' , and QEA 'B (CONS). Conversely, suppose Q is !-, while QEAB. Then QEA n YB, and also QEA n YB n Y (CONS), and Q_e-.yA n YB n Y (EXT). '
'
Without the assumption of Extension , counterexamples against theorem 4 are easy to find. A case in point is the quantifier Q ('few') that is defined QEAB <>De£ jA n B I � I /2IE 1. which is � - but not R-stable. A Non-conservative counterexample is the quantifier Q, defined (for a given x ): QAB <>De£ x E A V x � B, which is R-stable but not � -. Here, total removal of objects from the model is innocuous, but removal of an object (the obj ect x , in this case) from A alone can turn a true statement into a false one.
Acknowledgements Among chose who helped shape chis paper, I wane co thank che following people in particular: Jan van Eijck, Marrin Scokhof, Jeroen Groenendijk and Elias Thijsse, who all commented
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Consequently, monotonically increasing NPs, such as every, or more than n are unproblematic. A monotonically decreasing NP can be 'reanalysed' as the negation of a monotonically increasing one (van Eijck I98 3). Moreover, if we assume Continuity (see above), then all NPs can be reanalysed as conjunctions of the earlier resolved cases:
48 Towards a Generalization of Anaphora extensively on earlier versions; Re�o Scha, for constructive disagreement; and, most of all, Johan van Benthem, for lots of suggestions and for encouragement. K.EES VAN DEEMTER
Institutefor Perception Research (!PO) PO BOX 51J 5600 MB Eindhoven The Netherlands
N O TES
innocently executed American .
6
7
8 9
10 II
I2
Cases in point are Hirst (I 98 I ) and Carter ( I 98 7). Carter, for instance, extends Sidner's approach to cover certain sorts of indefinite NPs. We trust that our proposals can be incor porated in other 'context change' theories I 3 of anaphora, such as Groenendijk & Stokhof(198 7 ) and Barwise (1985). The simplest and probably most viable definition says that a node a c-commands I 4 (for 'constituent-commands') a node {3 if and only if the node that immediately dominates a dominates {3 as well. See van Eijck (1983) for additional evi dence for our position. I5 A case in point is the two sick elephants
variety of example sentence (2). See also section 4·3· This is a highly plausible assumption, since on a standard truth conditional analysis, the is logically stronger than a . Although some anaphoric full NPs could be treated on the basis of a CN(X) format, this is not true for all NPs. For example, the identity between an anaphoric NP the men and an antecedent RM Y can be expressed by means of conditions (1) men(X) and (2) X - Y; but the subsec tional anaphoric relation between the NP all men and Y cannot be expressed by a condition (I) men(X) and, for instance, (2) X � Y. The CN(X) format works only for identity anaphora and for intersective NPs (Appendix, i.). In this simplified construction rule, as also in van Eijck (1983), RMs introduced by embedded NPs are not taken into account. Therefore, additional provisions would be needed to make sure that in sentences such as Everyformer who owns a donkey beats it the donkey-RM lands in the b 1 box. There may be cases where this restriction to the CN denotation is not in force, bur we will follow van Eijck in disregarding them. For example, collective readings ofboth (i) Some people lifteda piano and (ii) Some lifted a piano require that the lifting was done entirely by peop�e. rather than g�rillas-if we assume that Kllsome II - l�eople II· Still, context-dependent interpretation of conditions of the form CN(x) is required
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From the perspective of this paper, Heim's intended coreference (Heim I982) and Sidner's cospecification (Sidner I979) can be viewed as variants ofthe relation of identity. 2 In this paper, anaphoric links are often indicated by means of small capitals. This limitation is due to Heim's reliance on D. Lewis's mechanism of accommoda tion (Lewis I 979). Normally, a definite NP such as the author requires a pre viously mentioned author, so if no author is mentioned, accommodation is trig gered; but if the author in (I) is replaced by a hundred readers, accommodation doesn't come off the ground. 4 A characteristic syntactic construction in which a proper name .can be used to introduce an entity combines the name with an appositive NP: Earl Johnson, an
K.
for embedded NPs. For instance, in [All people who bought [raincoats ]NP]NP got wet , it is possible to understand the people but not the raincoats as relativized to a given
16
17
I9
20 ·
21
l�ab(X)
22 The fact that the speaker must know that the descriptive content of the anaphor holds follows from a Gricean sincerity ('Quality') condition that is not particular to anaphora. 23 For instance, such definite descriptions as John's father and the weather need not be anaphoric, as Heim is well aware (Heim I 982: Ill. 5-2). Also relevant is the phenomenon of 'forward' (i.e. kata phoric) reference, in which an anaphor relates to an antecedent to its right. In such cases, even the familiarity of ana phone (kataphoric) antecedents becomes problematic. See van Deemter (1 990) for a discussion. 24 In particular, I feel that D. Carter's defini tion of anaphora (c£ the introduction of the present paper) is somewhat overly general in counting all cases of context dependent meaning as anaphora. For instance, the well-known phenomenon of contextual disambiguation obviously involves context-dependent meaning, but seems to obey rules that are very different from those that govern the interpretation of pronouns. Similar reservations would apply to the inclusion of other context dependent phenomena such as gapping and VP deletion . 25 Thanks are due to J. van Benthem for parts of this proo£ A closely related theorem is proved in Thijsse (1983).
RE FERE NCES Barwise,J. (1 985), 'Noun phrases, generalized quantifiers and anaphora', CLSI Stanford, informal note. Barwise, J. & Cooper, R. (198 1 ), 'Generalized quantifiers and natural language', Linguis tics and Philosophy, no. 4· Benthem, J. van ( 1 984). 'Questions about quantifiers', journal of Symbolic Logic, 13,
JOJ-49·
Carter, D. (1 987), Interpreting Anaphors in
Natural Longuage Texts, Ellis Horwood, Wiley & Sons, New York. Christophersen, P. (I939), The Articles: A Study ofTheir Theory and Use in English , Munks gaard, Copenhagen. Clark, H. H. & Haviland, S. E. (1977), 'Com prehension and the given-new contract', in R. 0. Freedle (ed.), Discourse Production and Comprehension , Ablex Publishing Corp., Norwood, NJ.
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18
antecedent. For a brief discussion of other categories than the Noun Phrase, see section 5· Westerstahl adds that he leaves 'the (more difficult) question of how context sets are chosen to more ambitious semantic theories', such as the present proposal aims to be. For the use of KIINP II in this clause, see section 3 and Appendix, ii. Westerstahl's clause is needed for nonintersective determiners such as all (see Appendix, i.). See, for instance, Roberts (I987) for a discussion of the number feature. For simplicity, linguistic gender is identi fied with natural gender, although this is not completely appropriate for most languages. See e.g. Lyons (I 968): 281-8 for a discussion. For instance, a nonanaphoric occurrence of would only be applicable if the iihe entire universe of discourse can be assumed beforehand to contain precisely one male entity (c£ section 4·3)· Common Knowledge (Lewis 1 969), also called Mutual Knowledge, may be defined as follows (Harman 1 977): 'A and B mutually know that p' <>De£ q , where q is defined selfreferentially as 'A and B know that p and that q '.
van Deemter 49
so Towards a Generalization of Anaphora Deemter, K. van (I989), 'Anaphora across the board', MS no. 684, Institute for Percep tion Research. Deemter, K. van (I990), 'Forward references in natural language', Journal of Semantics, 7. 3 ·
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Eijck,J. van (I98 3), 'Discourse representation theory and plurality', in A. ter Meulen (ed.), Studies in Mode/theoretic Semantics, Foris, GRASS-I, Dordrecht. Evans, G. (I977), 'Pronouns, Quantifiers and relative clauses', Canadian Journal ofPhilo sophy, 7, 467-536. Grice, H. R (I97S). 'Logic and conversation', in Cole & Morgan (eds), Syntax and Seman tics, Vol. m: Speech Acts, Academic Press, New York. Groenendijk, J. & Stokhof, M. (I987), 'Dynamic predicate logic: towards a com positional and non-representational dis course theory', MS, ITLI, University of Amsterdam. Grosz, B. (I 977), 'The representation and use of focus in dialogue understanding', Stan ford Research Institute, Technical Note I s I, Menlo Park, Cali£ Halliday, M. A. K. (I967), 'Notes on conrrast ivity and theme',journal ofLinguistics, J. Halliday, M. A. K. & Hasan, R (I976), Co hesion in English , Longman, London. Harman, D. (I977), 'Review of Linguistic Behavior by Jonathan Bennett', Language, 53. 4I7-24. Heim, l. R. (I982), 'The semantics of definite and indefinite Noun Phrases', Ph.D. thesis, University of Massachusetts, Amherst, Mass. Hirst, G. (I98 I), 'Anaphora in natural lan guage understanding: a survey', Lecture Notes in Camputer Science, Springer Verlag, New York. Hom, L. R (I972), 'On the semantic proper ties of the logical operators in English', mimeo, Indiana University Linguistics Club. Kadmon, N. (I987), 'On unique and non unique reference and asymmetric quanti fication, PhD. thesis, University of Massachusetts, Amherst, Mass. Kamp, H. (I98I), 'A theory of rruth and
semantic interpretation', in J. Groenen dijk, T. Janssen, M. Stokhof (eds), Formal Methods in the Study of Language, Mathe matical Centre Tracts no. I 36. Kamp, H. (I98 5), 'Situations in discourse without time or questions', MS, University ofTexas, Austin. Klein, E. (I979), 'A semantics for positive and comparative adjectives, MS. Landman, F. (I989), 'Groups-l', Linguistics and Philosophy, no. I 2.5. Lasnik, H. ( I976), 'Remarks on coreference', Linguistic Analysis, 2., I -22. Lewis, D. (I969), Canvention: A Philosophical Study, Harvard University Press, Cam bridge, Mass. Lewis, D. (1979), 'Scorekeeping in a language game', in R Baeuerle, U. Egli, A. von Stechow (eds), Semantics from Different Points ofView, Springer, Berlin, New York and London. Link, G. (I983), 'The logical analysis of plurals and mass terms: a lattice-theoreti cal approach', in R Bauerle, C. Schwarze, A. von Stechow (eds), Meaning, Use and Interpretation of Language, De Gruyter, Berlin. Lyons, J. ( I 968), Introduction to Theoretical Linguistics, Cambridge University Press, Cambridge. Maes, A. ( 1 990), 'The interpretation and repre sentation of coreferential lexical NPs in expository texts', in journal ofSemantics, 7, 143-74· Montague, R. (I973), 'The proper treatment of quantification in English', in R H. Thomason (ed.), Formal Philosophy, Yale University Press, New Haven, Conn. Partee, B. (1984), 'Nominal and temporal anaphora', Linguistics and Philosophy, no. 7· Reinhatt, T. (I976), 'The syntactic domain of anaphora', PhD. thesis, Massachusetts Institute ofTechnology, Cambridge. Reinhart, T. (I 98 3a), 'Coreference and bound anaphora: a restatement of the . anaphora questions', Linguistics and Philo sophy, no. 6. Reinhart, T. (1983b), Anaphora and Semantic Interpretation , Croom Helm, London. Roberts, C. (I987), 'Modal subordination,
K. van Deemter 5 I Thijsse, E. (1983), 'Laws of Language', MA thesis, Filosofisch Instituut, RU. Gronin gen. Thijsse, E. (I 98 5), 'Counting quantifiers', in J. van Benthem and A. ter Meulen (eds), Generalized Quantifiers in Natural Language,
Foris, GRASS-4, Dordrecht. Westerstahl, D. (1985). 'Determiners and context sets', in J. van Benthem and A. ter Meulen (eds), Generalized Quantifiers in Natural Language, Foris, GRASS-4, Dordrecht. Weijters, A. (1989), 'Denotation in discourse, analysis and algorithm', Ph.D. thesis, Katholieke Universiteit Nijmegen.
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anaphora and distnbutiviry, Ph.D. thesis, University of Massachusetts. Russell, B. (1905), 'On denoting', Mind, 14, 479-93 · Sidner, C. (1979), 'Towards a computational theory of definite anaphora comprehen sion in English discourse', MIT Artificial Intelligence Lab. TR-537Sidner, C. (1983), 'Focusing in the com prehension of definite anaphora', in M. Brady and R Berwick (eds), Computational Models ofDiscourse, MIT Press, Cambridge, Mass. Stalnaker, R. {I979). 'Assertion', in P. Cole (ed.), Syntax and Semantics g: Pragmatics, Academic Press, New York, 3 I s-32·
Journal ofSemantics 9: 5 3-67
© N.l.S. Foundation (1992)
A Simplified Theory of Boolean Semantic Types M I C H A E L .B . K A C
University ofMinnesota
Abstract The theory of semantic types in Keenan and Faltz ( 1 98 5 ) is insufficiently constrained in the sense that it requires denumerable categories to be interpreted under certain conditions via nondenumerable algebras. An ontologically more austere version of the theory is proposed in nonetheless possible to treat an infinite language by providing an inductively defined hierarchy of such algebras, each representing a stage of an expanding knowledge base. Some apparent obstacles are considered and disposed of and some advantages discussed, having to do with the alethic modalities and referential opacity induced by predicates of propositional artirude. Finally, it is shown that a weaker version of Keenan and Faltz's central mathematical result, the Justification Theorem, suffices for the revised system and a simple, inruitive proof for it is given.
0
A BOOLEAN syntactic category, in the sense ofKeenan and Faltz (1985) (herein after 'BSNL'), is one whose members include expressions formed by combina tion with not, and and or; for any such category K, the associated semantic type T(K) is so defined as to have the internal strucrure of a Boolean algebra. Among the desirable consequences of treating the Boolean categories in this way are the following: (i) There is a uniform semantics for not, and, and or, which are interpreted as Boolean complement, product and sum respectively and thus have the same interpretation regardless of the category of expressions with which they are combined. (ii) It becomes possible to define a notion of GENERALIZED ENTAILMENT such that for arbitrary x, y E X, X Boolean, x � y iff[x] � [y]. The appeal of (ii) can be seen from the following example. Let X, Y E NP and Z be a monadic predicate. Then X and Y Z � X or YZ. But the basis for this entailment can be 'localized' in the coordinate NP's, the logical relationship between the entire sentences being clearly due to the fact that their subject NP's stand in an analogous relationship. If T(NP) is defined as a BA then the desired results are assured, since:
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which expressions are always interpreted in terms of finite algebras and it is shown how it is
54
A Simplified Theory of Boolean Semantic Types
[X and Y] - [X] · [ Y] ill and] is Boolean pr:oduct); [X or Y] = [X] + [ Y] ill or] is Boolean sum); for all x, y in a BA, x · y :::;; x + y, hence [X and Y] :::;; [X or Y]; [X and Y] [X or Y] (definition of generalized entailment). �
·
In an earlier development of the theory, Keenan and Faltz (I978)1 proceed from standard model-theoretic assumptions in first positing a universe of discourse
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What the Keenan-Faltz approach ultimately amounts to is treating the whole range ofBoolean categories in the same way mathematically as sentences in classical propositional logic-an extremely powerful but also entirely natural cross-categorial generalization. The only difference between sentences and subsentential expressions involving not, and, and or is that whereas the former are (classically) interpreted in terms of the algebra {o, I } , members of other Boolean categories must be interpreted in terms ofBA's of other kinds. This in turn naturally gives rise to the question ofwhat constraints, if any, can be put on the BA's required. One way in which BA's differ is in regard to the cardinality of their domains, which may be finite or infinite, denumerable or nondenumerable. For reasons to be discussed in the next section, it would appear prima facie as if at least one class of expressions, namely monadic predicates, must under certain conditions be associated with a nondenumerable type; the purpose of this paper is to show that this is not so-indeed, that monadic predicates can always be interpreted in terms of finite BA's. Since there appears to be no obstacle to extending this restriction to all Boolean categories, a version of the theory even more constrained than that envisaged in BSNL seems possible. Bu_t the particular manner in which the constraints are implemented will be seen to have some other attractive properties, most particularly in regard to certain types of opaque contexts. The organization of the discussion is as follows. We first review the essential features of the Keenan-Faltz framework and place the central problem to be addressed in the context provided thereby (section I ), after which we present a proposed solution (section 2). In section 3 a number of apparent difficulties are addressed and disposed of, and in section 4 it is shown that the proposal enables us to interpret modal operators without recourse to alternative possible worlds (indeed, without recourse to anything not already ,in the system for other reasons) and to solve a well-known problem involving predicates of proposi tional attitude. Finally, we show how a weaker version of Keenan and Faltz's central mathematical result, the Justification Theorem, suffices for the new system and present a simple proof for it.
M. B. Kac 5 5
U (an arbitrary nonempty set) and then defining the set P( U) of PROPERTIES on U as u•. (P( U) is then taken to be T(N), the type for common nouns.) T(NP) is then shown to be P( U)*; by virtue of being a power set algebra, T(NP) is accordingly a BA. as desired. (Thus, in our example, [X and Y] is actually [X] n
=
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[ Y] and [X or Y] is [X] u [ Y].) In the LTNL system, an individual name is taken to denote not a member of U but rather a member of P( U)* consisting of a singleton property (that is, a singleton whose sole member is an element of U) and all supersets thereof Intuitively, each such set �x) consists of exactly the properties possessed by the member x of the singleton element of �xJ· For example, in a universe with exactly two members a and b, �·I � {{a}. {a, b }}. This is essentially the way indi vidual names are interpreted in Montague semantics, though with a different motivation. In Montague semantics, an individual name is translated by a A. abstract denoting the characteristic function of the set ofproperties of the asso ciated element of the universe so as to make it possible to interpret NP's as functions applied to properties; in the Keenan-Faltz system, the primary moti vation is to provide for NP-denotations on which Boolean functions are defined.2 Continuing with the example of our two-membered universe, if we interpretJohn as I( a ) and Mary as �b)• then Uohn and Mary] - I(• } n I( b) - {{a, b }}. the set consisting ofjust the universal property, and e.g. John and Mary sing is true iff sing is interpreted as that function from P( U)* into {o, I} which yields I on all arguments with U as a member. Let x e U. Then �x) is termed the INDIVIDUAL GENERATED BY {x}. There is a small terminological problem here in that it now becomes necessary to have a different designation for x itself; the term ENTITY is reserved for this purpose. It will be readily noted that in the LTNL system, individual names refer not to entities directly but only to the associated individuals. This in turn leads to two undesirable consequences, the first being that the universe of discourse U is essentially duplicated by the set of individuals (which is a subset of P( U )* and in I : I correspondence with U). The second has a more metaphysical character, namely that the LTNL system requires noumenal entities-that is, the members of U are not denotable by any expression of the object language (all else held constant) and are thus 'ontologically mysterious'. Following a proposal originally advanced in Keenan (1 982), BSNL obviates these difficulties by reversing the relationship of the universe of discourse and the set of properties, deriving the former from the latter.3 Recall that in LTNL the properties form a power set algebra. The BSNL strategy is to let the properties be any BA whatsoever as long as it is isomorphic to some PSA (that is, complete and atomic).4 Let F denote such an algebra and a(F) the atoms thereof Then for each a e a(F), the individual I. = {p e F I a � p J. Put T(N) F and T(NP) = F* and both of the aforementioned difficulties are removed since there is no longer any need to posit a set of entities distinct from
56
A Simplified
Theory of Boolean Semantic Types
2 Imagine an abstract automaton M which interprets the sentences of a de numerable language L. Select an arbitrary moment in time, call it t0; to this moment-as at every subsequent one-M has encountered only a finite number of lexical expressions of any category K and there thus need be only a finite algebra of properties in terms of which to interpret the members of K seen thus far? Assume further that M has in memory an assignment of values to lexical elements ofK taking the form of a function whose range is sufficiently large. By T.(K) we designate the TEMPORALLY LOCAL SUBTYPE OF T(K) AT t., n ;;li: O, a finite BA (and hence provably complete and atomic) in terms of which all members of K encountered to this point are interpreted. Suppose now that at some sub sequent moment t 1 M encounters a previously unseen lexical expression of category K. At this point, there are two possibilities as to how the machine might 'update' its memory so as to take this new expression into account (which includes the expansion of T0(K) to a new algebra T1(K) and a concomitant redefinition of the assignment function).8 On the one hand, it might consult an oracle which simply instructs it as to how to redefine the assignment function
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the individuals. Insofar as it is necessary to make reference to a universe of dis course, this can be identified with the set of individuals wrt F. The mathemati cal structure of the theory in other respects is unaffected: for example, monadic predicates can be interpreted exactly as they are in the LTNL system, each such predicate denoting a function_{p, p a property, such that for any individual I,_{p(I) � r iffp e ].S A problem nontheless remains. Implicit in the Keenan-Faltz approach (in both its earlier and later guises)-indeed, in most approaches to the formal description of natural language-is the assumption that natural languages are denumerable.6 If we grant that this is the case then the theory ofBoolean types as developed in BSNL appears insufficiently constrained in that by requiring only that the set of properties be a ca-BA it allows for infinitely many atoms in a given type, whence the type is nondenumerable. Thus no matter how values are assigned to lexical members of the associated category there must be 'anony . mous' members of any such type, which in turn amounts to saying that it is larger than necessary. On the other hand, if we require that all Boolean types have finitely many atoms then all such types are finite-a cure that seems worse than the disease since it would then apparently be impossible to provide a type large enough for a category with infinitely many lexical members each with a distinct value. But NP must surely be such a category in a language rich enough to provide, say, a distinct name for eve·ry natural number. In the sequel I propose and motivate a resolution of this difficulty.
M. B. Kac
57
-
(i) For all c e C, if c is an atom of a given local subtype ofP, it is an atom of all subsequent local subtypes. (ii) All local subtypes of P have c0 as their zero element, hence P has C0 as its zero element. The atomicity ofP now follows. Each member of C is an atom ofP since for any p e P and c e C there is a local subtype whose domain includes both and in which c is an atom-from which it then follows that in that subtype, p � c iffp = c or p = c0; but if this holds within a subtype, it holds for the entire lattice. A similar line of reasoning establishes that for any p "" c0, there is an atom sub sumed by p since there is a subtype in which this is the case. Atomicity is an essential attribute ofP since there must be a property asso ciated with every nonempty finite set of individuals, and this in rum requires (given other assumptions of the theory) that each property be expressed as a
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in terms ofa new and larger range. On the other, it might have as part ofits pro gram a way of deducing from the form of the new expression how to carry out the required redefinition.9 The first option, while always available in principle (and necessary in some cases, since individual names may be arbitrarily assigned to referents), should not be abused; therefore we shall operate with the assump tion that it is to be employed only in those cases where the second is unavailable in principle. This restriction has an important consequence, as will be seen shortly. We now define T(K) as u. ,. 0T.(K). Note that as defined, T(K) is not a BA (since, inter alia, it lacks a unit element);10 it does, however, have at least one of the properties we desire, namely cardinality �0• Nor is its lack of a Boolean structure problematical since at every t. T.(K) DOES have the structure of a BA Let us now consider in somewhat more detail the structure of the set of properties, henceforth P.l l We begin by observing that although not a BA, P · nonetheless does constitute a lattice since for any x, y e P, there is a BA whose domain forms a subset ofP, hence x · y and x+ y exist and {x, y} has a glb and a lub. Further, the lattice, while not complete, is atomic, though we defer show ing this until the precise construction has been further elaborated.12 Let C {c0, c, c 2, • • •} be an arbitrary denumerably infinite set and for each natural number i > o define F; as the BA whose zero element is C0 'and whose atoms are { c , c 2, • • • cJ By [ e]; we denote the interpretation of the expression e in F;. Given any i we can then construct F;+, by building up the BA with atoms c, c 2, • • , c;, C;w The local subtypes thus form a strict hierarchy in the sense that the domain of each F, is a proper subset of the domain ofF;+, . The intent ofour conception ofP as a union of temporally local subtypes �ach obtainable from its predecessor is to identify the subtype at t0 with some F; and the subtypes at all subsequent moments with appropriately constructed F1, j � i. Observe further that:
58
A Simplified Theory of Boolean Semantic Types
sum of atoms. For each finite set A of atoms, the sum over A is associated with exactly lA I individuals, a given Ix being one of those in question j ust in case x
E A. Completeness, on the other hand, is not an essential attribute ofP since
the set of property-denoting expressions, while infinite, is only denumerably so; it is therefore unnecessary to make provision for sums over infinite sets of
atoms. However, every temporally local subtype ofP must be complete since to
each subset
A
of the set of atoms of the subtype there corresponds a property,
namely the one associated with the individuals
ipsofacto complete, so this is unproblematical.
I,, x E A. But all finite BA's are
This proposal for how to navigate between the Scylla of finiteness and the Charybdis of nondenumerability has three clearly definable aspects. First, it time coordinate (or, alternatively, that there be a family of such functions, one
for each time interval over which a given local subtype is in memory). Secondly, it is couched in automat;1-theoretic terms. Finally, it attributes to P a hierarchical structure. I shall consider each of these in turn. The view taken of the interpretation function involves nothing exotic,
amounting to little more than appropriating (albeit for a different purpose) the
machinery required for interpreting a tensed language. Further, it makes the semantics slightly more flexible-and, it should be noted, more realistic-in that
provision is now made for the possibility of a given name having different denotations at different times.
Identifying the local subtypes with successive memory states of an auto maton seems entirely natural in so far as knowledge is dynamic, expanding over time. Local subtypes ofP can thus be thought of as determining progressively
larger sets of individuals with which a language-interpreting being acquires familiarity, while the requirement that each subtype constitute a BA assures
that essential structural characteristics of the knowledge base remain invariant under expansion. Moreover, the perspective we have adopted is consistent with
the fact that there is more than one route to increasing one's knowledge base: certain things can be determined solely on the basis of what is already known,
without any 'outside' information, whereas others require some sort of inter action with the extra-mental world. It is precisely this distinction which is reflected in our two ways of interpreting individual names and sentences
containing them.O Further, the idea of identifying certain properties not with
elements of P but with the procedures by which the associated predicates are
evaluated is of a kind which has proven useful elsewhere-see especially van Benthem (1 986, chapter 8). The automata-theoretic perspective will be seen below to serve us well in other respects also.
We come finally to the hierarchical character ofP. To best understand why
it is natural to think in terms of a succession ofBA's each of which is a proper
superset of its predecessor differing from it only in those respects entailed by
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requires that the interpretation function be defined on indices containing a
M. B. Kac 59
3 We turn now to consideration of apparent difficulties. One is posed by proper ties such as that of evenness relative to the integers since in this scheme P has no element corresponding thereto. While we can, for any subset of the integers, provide an clement ofP corresponding to evenness relative to this subset, we cannot do so for the integers as a whole. This problem can nonetheless be skirted as long as we impose the requirement alluded to above that M's assign ment function always be updated automatically when possible, rather than via appeal to the oracle. In regard to evenness, this then means that the property-in its full generality-Is formally represented, though not via a member of P; rather, it is embodied in the recursive routine by which M, on encountering a new integer name, redefines the interpretation function and, in the process, reassociates even with the appropriate members of the new temporally local subtype. A second, and related, concern stems from the requirement that the proper tics form a denumerable set. Does this not then commit us to the apparently untenable claim that the set of all properties whatsoever is denumerable? No,
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the presence of an additional atom, observe first that the individuals are 1n I : I correspondence with the atomic properties and that the number of distinct individuals referrable to at a given moment is accordingly exactly the number of atomic properties of the associated local subtype. Now ask how a local sub type would have to be modified in order to make provision for exactly one more individual without loss of any of those already referrable to. The answer is obvious, namely that it is necessary to expand the set of atoms by exactly one (let a represent this new atom) and for each non-zero property p to add the new property p + a. The relationship between the earlier and the later subtype is thus exactly that obtaining between a given member of the hierarchy ofFi 's and its successor in the hierarchy. I conclude this section by considering an obvious question: why do we not simply revise the theory so that monadic predicates and common nouns are interpreted in terms of P rather than a succession of local subtypes? Put differently, why must the class ofpredicate (noun) interpretations form a ca-BA rather than simply an atomic lattice? The simplest answer to the question that I can think of is based on the earlier observation that P lacks a unit element. This in turn means that there is no universal property in P whereas there is such a property in each Fi. Such a property must be available for at least two reasons: first, it must be possible for certain lexical predicates (e.g. exist ) to be interpreted thereby; second, any predicate consisting of the disjunction of a VP with its negation (e.g. is even or is not even ) must be similarly interpreted.
6o
A Simplified
Theory of Boolean Semantic Types
.
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because what is at issue is not the cardinality of the set of properties taken as a whole (which must surely be maximally vast in the Langendoen-Postal sense) but only that of a largest set each ofwhose individual members is denotable by a I -place predicate in a denumerable language. If a language is denumerable then there is a perfectly valid sense in which it cannot have a nondenumerable domain of discourse, to wit whereas one can for any element of a non denumerable set assign a name to it, there is no way to define inductively a set of expressions sufficiently inclusive to allow all the elements of the set to be named. Insofar as this is true, there are elements of the set that cannot be 'talked about', whence the set as a whole fails to constitute a discourse domain in the commonly accepted sense.14 On this view the difference between a de numerable and a nondenumerable set, from the vantage point of semantics, is that the former is completely 'internally accessible' to the object language in a way that the latter is not. A third problem has to do with necessary truth. On the ordinary under standing, to say that a sentence is necessarily true is to say that there are no con ditions under which it comes out false; analogously, a necessarily false sentence comes out true under no conditions. Consider then an example like No natural number exceeds 1 relative to the local subtype F2: this is problematical since the sentence-ostensibly a falsehood under all conditions-is apparently true wrt the assumed local subtype. But this situation, though it forces us to complicate the picture slightly, is not fatal. We need merely adopt the restriction that a nontrivial monadic predicate is interpreted only in those local subtypes large enough to provide an individual not possessing the denoted property. A more troublesome example is Every natural number has a successor, which is necessarily true and yet would appear to come out false relative to EVERY local subtype since there is always an individual with the property ofbeing highest in the subset of natural numbers representable in the subtype. The way I shall suggest of dealing with this difficulty solves a problem which accrues even to the less constrained version of the theory. It will simplify matters somewhat if we restrict our attention temporarily to sentences such as 4 has a successor, i.e. sentences in which the subject term always denotes an individual. Consider then how we are to interpret the noun successor. In keeping with other facets of the Keenan-Faltz theory, we would expect the interpretation to be the sum of all atomic properties corresponding to natural numbers greater than o, this sum representing the property common to j ust those natural numbers each of which is one greater than another such number; it remains then to determine how has is to be interpreted. One requirement which the interpretation must satisfy is that it be a homomorphism from T(NP) into P (this is explained in section s); and this in turn means not only that we would expect 4 has a successor (relative to a local subtype in which the sentence is true) to be equivalent to 4 has 1 or 2 or . . but that we would also
M. B. Kac 61
"
[has]; (IpU)) - � xj j-• Then for every lx,• I :s;; k :s;; n, [ has ] ; (IpU)) (Ix) I , precisely as desired. Every natural number is interpreted as fl{ Ix, I I :s;; k :s;; n J, so for every F;, =
"
[Every natural number has a successor]; - rr [ has a successor];(J,,) k - •
I
(recall that predicate interpretations are homomorphisms). 4 Having disposed of merely apparent difficulties confronting the proposal, let us now consider some real advantages. The first of these is that it is possible to give a simple semantics for modal operators which requires no reference to alterna tive possible worlds-indeed, to nothing that is not already independently motivated in the system. Let F; be the least algebra in the hierarchy for which [ �] is defined, � a sentence of the object language; then to say that � is neces sarily true is just to say that it is true relative to every Fj , j � i. It thus immediately follows that
[Necessarily �] - llj ,. ; [ �]j The essential idea here is that as long as the interpretations of certain expres sions must be initially determined by M and, once established, cannot be changed either by the intervention of the oracle or by any subsequent action of M, it must then be the case that the truth values of certain sentences remain invariant no matter how many new individuals are introduced into the
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expect the sentence 4 has 5 to be true. I submit that this is a very odd outcome insofar as the sentences themselves are quite strange. I am also at a loss to see on what intuitive basis we could reasonably construe 4 has 5 to mean 5 is the succes sor of4 , as it apparently must on these assumptions. Alternatively, suppose that a noun like successor denotes not a property of natural numbers but rather the atomic property of the function which, for each natural number, gives the next one; we can in fact adopt an analogous strategy wrt to any common noun of this sort, e.g. square, cube, etc. LetJdenote any total function on the natural numbers and p(f) the associated atomic property. Observe now that there is exactly one individual possessing the property in question and hence that [a successor] (which, in the Keenan-Faltz theory is taken to be the union of all the individuals with [successor] as an element) is just Ipifr For each n � I , let x , , x 2, • • •, x, be the atomic properties of the individuals (wrt some F;) corresponding to the natural numbers representable in F; and define
62 A Simplified
Theory of Boolean Semantic Types
(i) (ii)
X X
believes that 2 + 2 is rational. believes that Jl6 is rational.
the complement clauses are not intersubstitutable s.v. on a de dicto inter pretation, and yet have the same intension. Suppose, however, that we decide to interpret such a complement clause de re as an object which in some way reflects the manner in which the automaton M goes about interpreting the clause. At a first approximation, let us suppose that a sentence cp in this type of context denotes (de dieto) the computational routine by which M interprets cp. Since different procedures would be expected to be invoked to evaluate '2 + 2' as opposed to JI6 the required distinction is made. Moreover, we would appear to have preserved the essential spirit of an intensional analysis in the sense that the procedures involved apply functions to arguments (intensions are functions) while capturing the generalization that opacity on de dicto inter pretations is in effect the same kind of opacity induced by direct quotation; thus, it seems reasonable to want to say that the nonequivalence of(i-ii) on a de dicto interpretation has exactly the same etiology as the nonequivalence of '
(i) (ii)
X X
',
believes '2 + 2 is rational'. believes 'JI6 is rational'.
Note, however, that there is a vagueness in the proposal as it stands in that there is the following difficulty in interpreting the locution 'same procedure': do we say that the same procedure has been invoked in interpreting, say, '2 + 2' and '2 + 2 + 2'? The answer is affirmative insofar as what M actually does is to invoke the same program module in both cases, the evaluation of the two expressions differing only in the number of times the relevant procedure is applied; but the answer is negative if what we mean is that M goes through exactly the same sequence of states in evaluating the two expressions. Let us therefore remove. the vagueness by recasting the proposal as one to interpret
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universe of discourse or how the oracle chooses to redefine nonrigid designa tors. One appealing feature of this formalization of the notion of necessary vs. contingent facts is the extent to which it comports with the common-sense understanding of the distinction in psychological terms: actions of the oracle, which can change truth values of sentences from one moment to another, are the analogue of experience; actions of M which do not depend on those of the oracle correspond to the application of pure reason. A rather more interesting consequence of the proposal stemming from its automata-theoretic nature pertains to the well-known class of problems involving referential opacity induced by predicates of propositional attitude, e.g. believe-problems which are unsolvable even by recourse to intensions viewed as functions from possible worlds to extensions in those worlds. For example in
M. B. Kac 63
expressions in the relevant type of context as sequences of states of M (as repre sented by instantaneous descriptions) beginning with the point at which the reading of the expression begins and ending with the point at which the inter pretation of the expression has been obtained. With this step we not only make the proposal fully precise but solve another well-known problem, namely the one posed by sentence pairs like (iii) (iv)
X believes that woodchucks chuck wood. X believes that groundhogs chuck wood.
5
Ontological simplification of the sort that we have sought would be expected to contribute to a simplification of some of the mathematical underpinnings of the theory as well. In this final section we consider such a simplification in regard to the Justification Theorem which should be at least of some pedagogi cal utiliry. First, however, we present some further background. Keenan and Faltz impose as a constraint on predicates that they denote homomorphisms from their domain types into their range types. 1 5 This is required in order to a5sure equivalences such as those illustrated below: (i) John or Mary sang � John sang or Mary sang 6 (ii) [Every student [didn't sing]] � No student sang. 1 (iii) John saw Mary and Bill �John saw Mary and saw Bill (iv) Uohn [[didn't see) [every student]]) �John saw no student In order for the correct results to be assured in all cases, it is essential that the results of applying a predicate interpretation h to an arbitrary NP interpretation depend in a certain fixed way on the manner in which h is defined on the indi viduals. For example, if h is so defined as to yield I on at least one member L of a set I of individuals then it must yield I on every union of individuals with L as a term; similarly, if h is so defined as to yield I on all members of I then for each A E I*, h (nA) I . The Justification Theorem says, in effect, that this is assured as long as the domain and range of h are complete, atomic BA's. More formally: for any arbitrary functionf «P) B, P and B arbitrary ca-BA's and L(P) the set of individuals relative to P, there is exactly one complete homomorphism from -
.....
c
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Imposition of a requirement of intensional isomorphism does not help here since woodchuck and groundhog are structurally simplex; but the instantaneous description of M at the point at which it encounters the former will be different from the one at which it encounters the latter in just the required way, namely that the words currently being read are different.
A
64
Simplified Theory of Boolean Semantic Types
Lemma (BSNL, p. 51). For all p e P, P a ca-BA,
{p}'- fl {I E L(P) I P E I} fl{I I I E L(P) 1\ p � I}. ('I
I
A proof of the lemma is given in BSNL (p. 1 1 1); a somewhat simpler one follows. Observe first that
fl {I E L(P) I p E I} - { q I q � p} since on the one hand the presence of p in an individual assures the presence therein of all q � p, while on the other for any property r ';/: p, there is some atomic term x ofp such that x � r-whence r � !y· Suppose now that for some q
�p
.
q
E fl {I I I E �P) 1\ p � I}. I
Then if an individual fails to possess p, it fails to possess q . Suppose q � p; then for some atom x, x � q and x � p . It then follows that p � Iy and q e !y, a contra diction. To obtain the result sought, it now suffices only to observe that p e f1
{I I I E L(P) 1\ p � I}. I
We proceed now to a proof of the WJT. Define f L(P) -+ B in any way desired. We show first that there is at least one homomorphism agreeing withJ on the individuals, and then that there is at most one.
Existence. Let x be an atom of B and define
Px - L{y E a(P) 1./{Iy) � x}. It then follows that for all I e �P),J{I) � x iff Px e I. Define h : p• -+ B so that for arbitrary Q e P*, h(Q) � x iff Px e Q. Then h agrees with/ on all I e �P). To
show that h is a homomorphism, we shift temporarily to Sheffer algebra. Observe that for arbitrary Q, R e P*:
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p• into B which agrees with J on the members of L(P). Note that this in turn breaks down into two separate claims: that there is at least one homomorphism with the requisite properties, and that there is no more than one. It is thus sufficient to define a predicate interpretation j ust on the individuals and its definition on the remaind.er of T(NP) then follows automatically, furthermore, the interpretation can be defined on the individuals in any way desired. It will be noted that the JT, as formally stated, refers to COMPLETE homo morphisms, that is, ones whose definitions on products and sums extend to infinite products and sums. To prove so general a result is rather involved; if, however, we restrict attention to finite P then we need consider only finite homomorphisms, which ought to simplify things considerably, and it does indeed turn out that the result of replacing 'complete homomorphism' in the JT by 'homomorphism' (call this the 'Weak Justification Theorem') has a simple and intuitive proo£
M. B. Kac 65
. h(Q I R) ;?; X � Px � Q or Px � R � h(Q) ;/ x or h (R ) 'j x � h(Q) I h(R) ;?; x
Uniqueness. Let g be a homomorphism agreeing with h (and hence with}) on the individuals. Since any set is the union of its singleton subsets and h is a homomorphism, for all Q e P*, h( Q)
=
L:p
•
dTIP J{I) · np 1[/{I)] 1] g(Q). _
•
=
Alternate Proof of Uniqueness (by induction on IQI, Q e P*.) BASis: for
arbitrary p e P, h({p }) - h(fl {I E �P) I p E I}n fl(I II E t(P) Ap � I}) '
h ({p}) = np• I h (I) · npo[h (I)]
I
-
np. 1f(I) · np11[f{I)]
I
(f agrees with h on the individuals). Hence, for any homomorphism g agreeing
with h (and hence with}) on the individuals, h ({p}) g({p}). INDUCTION: suppose that h( Q) g( Q) for all Q e P* such that for some n ;?; I IQI n. Then for all p e =
=
=
P,
h (Q u{p})
=
h (Q) + h ({p}) = g( Q ) + g({p}) = g(Q u{p}).
Although more involved than the earlier demonstration of uniqueness, this proof depends in a more obvious way on the Boolean structure of P"' and also serves to emphasize that the proposed revision of the theory of types brings all Boolean types within the purview of mathematical induction.
Acknowledgements An earlier version of part of this paper was presented at the Parasession on formal Semantics of the
1989 Minnesota Conference on Language and Linguistics. The mathematical help of Linda
Seebach and the comments of two anonymous referees are gratefully acknowledged; respon sibility for any errors is the author's alone. MICHAEL B. KAC
Department oJLinguistics University ofMinnesota Minneapolis, MN 55455 USA
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(lemma). Further, since h is a homomorphism,
66
A
Simplified Theory of Boolean Semantic Types
NOTES amended to include an atom not present previously. 9 The machine, being purely hypothetical, is presumed to have infinite memory. IO Suppose there were a unit element, call it u. Then u would be an upper bound for every subset of the domain of each local subtype. But u is itself in the domain of a local subtype, and there is accordingly a larger subtype whose domain also con tains u and whose unit element w ,t. u . Hence, u is not an upper bound for { u , w) , a contradiction. I I Many of these observations extend m.m. to all 'open-ended' semantic types asso ciated with Boolean categories. I 2 That P is not complete-follows from the fact that the type, as a union of finite sets, is denumerable, whereas completeness would entail nondenumerability. The power set of the set of atoms is non denumerable, and in a complete lattice every member of the power set must have a lub; further, the lub's of all the members of the power set are distinct. I 3 The reader who suspects that this can be exploited in distinguishing alethic modalities is correct, as will be seen presently. I4 The fact that the set as a whole can be talked about is perfectly consistent with our approach since there is nothing to prevent us from taking this set as an individual, i.e. as corresponding to an atom ofP. 1 5 For monadic predicate interpretations, this follows automatically if we adopt the strategy suggested in note 5 · I 6 The intent o f the bracketing is to limit consideration to the 'VP-negation' inter pretation of (ii), in which not is applied to the predicate.
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I Henceforth 'LTNL'. For reasons which I will not discuss here, Keenan and Faltz argue for taking monadic predicate denotations as func tions applied to NP-denotations rather than the other way around, as in Mon tague semantics. See LTNL, pp. I 03 £ 3 This is the real effect of Keenan's pro posal, notwithstanding his beguiling reference to 'eliminating the universe'. 4 That the set of properties must be com plete and atomic follows, in the BSNL theory, from the presumption that there must be a property corresponding to each subset of the set of individuals, every property then being simply the sum of the atoms corresponding to the indi viduals in the set. In the revised theory, completeness is required only of certain subsets of the set of properties and not of the entire set. 5 A slight simplification in the theory can be obtained if we take advantage of the fact that any member x of a set A can be taken as that function from A • into {o, 1 } such that for any B e A •, x(B) - I iff x e B. We thus do not need to distinguish the types for common nouns and I -place predicates. 6 This assumption has been openly challenged by Langendoen ·and Postal (1 984). I take no position on their claim here, noting only that for most (and perhaps all) purposes of formal semantics it would appear unnecessary to accept it. 7 See Rounds et a/. (198 7) for a proposal with a similar spirit in the realm of formal syntax. 8 We must also allow for the possibility of the expansion of one subtype necessitat ing expansion of another, as will happen e.g. every time a new lexical NP is encountered since P will then have to be 2
M. B. Kac 67
RE FERE N C E S & L. M. Faltz ( 1985 ), Boolean Semantics for Natural Language, Reidel,
Keenan, E. L.
Dordrecht. Langendoen, D. T. & P. M. Postal ( 1984), The Vastness ofNatural Languages, Basil Black well, Oxford. Rounds, W. A., A. Mariaster-Ramer & J. Friedman ( 1987), 'Finding natural languages a home in formal language theory', in A Manaster-Ramer (ed.), Mathematics of Language, Benjamins, Amsterdam and Philadelphia, 349-59·
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Benthem, J. van ( 1 986), Essays in Formal Semantics, Reidel, Dordrecht. Keenan, E. L. ( 1982), 'Eliminating the uni · verse (a study in ontological perfection)', in D. P. Flickingt:r, M. Macken & N. Wie gand (eds), Proceedings ofthe First West Coast Conference on Formal- Linguistics, Depart ment of Linguistics, Stanford University, Stanford, CA Keenan, E. L. & L. M. Faltz ( 1978), 'Logical types for natural language', Department of Linguistics, University of California, Los Angeles.
Journal ofSemantics 9: 69-93
© N.I.S. Foundation (1992)
Group Terms in English: Representing Groups
as
Atoms
CHRIS BARKER Centerfor Cognitive Science, Ohio State University Abstract
r
C HA R A C TE R I Z I N G G R O U P T E R M S I.I
A syntactic diagnostic
Since the prototypical group term contains a group noun, we should begin by characterizing the class of group nouns. All group nouns happen to be morpho logically regular with respect to plural marking, so only nouns which take the plural are candidates for group noun status. For instance, we have group/groups, committee/committees, and army/armies. Since only count nouns take the plural morpheme, group nouns are a proper subclass of the count nouns. A count noun will be a group noun just in case it can take an of phrase containing a plural complement, but not a singular complement.
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What do terms such as the committee, the league, and the group of women denote? Pre theoretically, group terms have a dual personality. On the one hand, the committee corresponds to an entity as ideosyncratic in its properties as any other object; for instance, two otherwise identical committees can vary with respect to the purpose for which they were formed. Call . this aspect the group-as-individual. On the other hand, the identity of a group is at least partially determined by the properties of its members; for instance, a committee will be a committee of women just in case each of its members is a woman. Call this aspect the group as-set. Elaborating on suggestions in Link (1 984) and Lasersohn (1 988), I propose that group terms in English denote atomic individuals, that is, entities lacking internal structure. In particular, it is not possible to determine the membership of a group by examining the denota tion of a group term. The proposed account correctly predicts that group terms systematically behave differently semantically (as well as syntactically) from plurals such as the men and conjunctions such as John and Bill. Thus the atomic analysis advocated here stands in sharp contrast to previous proposals, including Bennet (197 5), Link (1 984), and Landman (1 989), in which group terms are considered of a piece semantically with plurals and conjunctions. Additional arguments come from the use of names of groups as rigid designators, from the parallel between group nouns and measure nouns, and from the distribution of group terms across two dialects of English.
70 Group Terms in English: Representing Groups as Atoms
the group of armchairs b. one committee of women c. an army of children 2. a *the group of armchair b. *one comrnittee of woman c. *an army of child 3- a. *the table of woods b. *one ball of yarns c. *a piece of cookies 4· a the table of wood b. one ball of yarn c. a piece of cookie 1.
a
a. a picture of horses b. an ocean of tears 6. a a picture of a horse b. an ocean of water
5·
However, the fact that these nouns also take of phrases with singular comple ments as in (6) distinguishes them from group nouns. Some nouns succeed or fail as group nouns according to which of several senses is intended.
7· a. *the book of pages 8.
b. *the book of page the book of matches b. *the book of match a.
The examples in (7) suggest that book is not a group noun, but the examples in (8) involving a different but closely related sense of book clearly is a group noun. Now we can give a first approximation at giving a more precise definition of 'group': a group is an entity which is in the extension ofa group noun. Note that this definition does not presuppose that a group entity is or is not atomic. In other words, a group is an entity which would be appropriate as the denotation of a definite description containing a group noun, such as the committee.
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We can call this use of of group-noun of These examples show that group, committee, and army are group nouns, while table, ball, and piece are not.1 Care must be taken with this test, however. There are count nouns which are not group nouns but which can take an of phrase with a plural complement, as in (s).
C. Barker 71
I .2
Distinguishinggroup termsfrom plurals and conjunctions
Group terms the committee that group the list of reasons
Plural terms the men those people the members of the group
Co�oined terms Bill and John the men and the women the chairman and the secretary
suggested by this chart, we will concentrate on simple noun phrases with lexical heads, sometimes modified with of phrases. In addition to these proto- . typical examples, later sections will treat names such as Committee A as group terms. Sometimes I will refer to plural terms and conjoined terms collectively as nonsingular terms. Most theories of plurals allow for definite descriptions involving plural nouns to have an extension identical to the extension of a conjoined noun phrase, and this makes sense. For instance, ifJohn and Bill are the only salient men, the extension of the phrase the men will be the same as the extension of the phrase John and Bill. This predicts that predicates sensitive only to extensions will not be able to distinguish between these two phrases, and we shall see that this seems to be so. Now imagine that the only salient committee has John and Bill for its two members. If the committee has the same extension as the plural phrase and the conjunction, then all three phrases should be intersubstitutable in extensional contexts without affecting truth value. In order to test this prediction, we need only find a purely extensional eredicate and test for entailment relationships.2 Although it is plausible that plurals and conjunctions can pattern together, group nouns behave differently. As
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The analyses of group nouns in Bennet (197 5), Link (1 984), and Landman (1 989) all class group terms semantically with a variety of nonsingular terms such as the men or John and Bill. The main empirical point of this paper will be to show that group terms systematically behave differently from plurals and co� unctions, at least with respect to entailments in extensional contexts. Later sections will explain how the formal analysis to be presented in section 2 will account for the observed pattern of facts. Here a 'term' is any noun phrase which is interpreted as a definite descrip tion, including some nonsingular noun phrases. Since we are primarily interested in denotation, I will have little to say about other occurrences of noun phrases, including intensional or non-definite uses. We will need to distinguish three kinds of term according to their syntactic structure and the nature of their head nouns.
72 Group Terms in English: Representing Groups as Acorns
9·
The men died. b. John and Bill died. c. The committee died. a.
10.
a. The men fathered two children. b. John and Bill fathered two children. c. The committee fathered two children.
It is difficult, if not impossible, to accept (we) as an entailment of(wa) or (rob). In general, the further the sense ofthe predicate from the prototypical activities or properties of the type of group in question, the more clear it becomes that groups in general do not automatically inherit the properties common to their members. In fact, a slightly more complicated example will block a group-distributive reading for all speakers. I
r . a. The men first met ten years ago. b. John and Bill first met ten years ago. c. The committee first met ten years ago.
The truth of(r ra) and (r r b) remains exactly equivalent, but the entailment for (r rc) becomes more remote. Even for people who conclude from the fact that John and Bill met that the committee also met (the group-distributive reading of meet), the entailment becomes more difficult in the presence of the modifier first. If it happens that the committee was formed several years after Bill and John first met, it becomes uncooperative at best to suggest that (r r c) is true whenever (I I a) and ( r r b) are.
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Clearly (9a) is true just in case (9b) is true, so long as John and Bill are the only men. But the status of(9c) is different. If committees are even capable of dying, it is only in an anthropomorphic sense in which dissolving a committee is compared metaphorically to the death of a living creature. In this sense, the truth of(9c) is independent of(9a) and (9b), since a committee can continue to operate even after losing all of its members, provided new members take their place in good time. Conversely, a committee can certainly die in the sense of dissolve at the same time that John and Bill remain healthy. However, some speakers allow another reading of(9c) on which (9a) and (9b) do entail (9c). For these speakers, the relevant reading is entirely literal, and would be appropriate if the committee were meeting in a war zone and were slaughtered together. For these speakers, die is a predicate which distributes over the members of a group. (See section 7 for a further discussion of group distributive readings.) For our purposes here, we need only note that the availability of this reading varies from speaker to speaker, and from situation to situation.
C. Barker 73
Furthermore, there are properties common to all of the members of a group which are never true of the group itself I 2. a The men are members of the committee. b. Bill and John are members of the committee. c. The committee is a member of the committee.
I 3· a. # The men had two members. b. #John and Bill had two members. c. The committee had two members. Even if(I 3a) and ( I 3b) are judged acceptable, surely they are false. In addition, notice that all of the (a) and (b) examples in this section are never grammatical with singular agreement marking on the verb, but the (c) examples are always grammatical with singular agreement. (In the examples as given above this contrast is neutralized by the use of the past tense for the sake of naturalness, but it can be revealed by attempting to insert perfective has/have immediately following the subject noun phrase in each example.) This difference in syntactic number is presumably related to the fact that group terms cannot appear as the complement to group-noun of (*the group of the committee), as well as to the fact that group terms cannot serve as the antecedent for each other (*the committeefought each other).3 To the extent that the agreement marking triggered by a definite description depends on its extension (see section 7), subject-verb agreement supports the claim that group nouns behave differently than plurals or group nouns. In any case, it is clear that group terms differ systematically from plurals and conjunctions in extensional contexts. I take these facts to motivate an analysis in which group terms differ in denotation from plurals and conjunctions.
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The sentences in (ua) and (ub) are contingent on the situation, but (uc) is a contradiction. Clearly, then, it is possible for the members of a group to have a property not shared by that group. In the other direction, it is possible for a group to have properties that the collection of its members do not. For instance, if the com mittee was formed (having different members) before Bill and John were born, then (I I c) can be true when (I I a) and ( I I b) are not, even without the modifier first. In general, any predicate which emphasizes the existence of a group as an individual independent of its membership can show this pattern. As an extreme example, some predicates can be rrue only of groups.
74 Group Terms in English: Representing Groups as Atoms
2 A M O DE L -T H E O RE T I C ANALY S I S After setting out the structure of the ontology, I will give enough syntactic rules, translation rules, and lexical interpretations to build a small fragment of English involving simple group terms, group nouns with of complements, simple plural terms, and conjunctions. 2.1
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Following Link (198 3) and others, I assume that the domain of discourse E is a set with a certain amount of internal structure. In particular, let E be a set with an associative, commutative, and idempotent join operator +. In other words, (E, +) is a join semilartice. Then the join operator determines a unique partial order � (Link's i-part relation). Specifically, � is that partial order such that a � b ('a is dominated by b') if and only if a + b = b. An element a E E is an atom just in case it dominates no other entity. that is, a is an atom just in case Vx E E [x f. a V x = a ].4 Non-atoms will be called proper sums. In general, atoms and sums are the semantic counterpart to singular and plural definite descriptions. That is, a singular term like John will denote an atom, and plural terms like the men or John and Bill will denote a proper sum. Furthermore, we shall see that the sum denoted byJohn and Bill dominates the atom denoted byJohn . These relationships established by the structure that the join operator induces on the domain of discourse will provide a means for describing the behavior of plurals and conjunctions. Definite descriptions, both singular and nonsingular, denote entities in the domain of discourse. Predicate phrases, then, including common nouns and intransitive verb phrases, denote functions from entities to truth values (either true or false). Such a function characterizes a set of entities, and I will treat a set and its characteristic function as completely equivalent. Since we are interested only in denotation, this paper does not discuss either generalized quantifiers or intensionality, although there is some discussion of intensional issues in sections 3, 4, and 6.1. A model for the fragment will be a tuple (E, +, [ · ] , f). The set E and the join operator + are as described above; [ · ] is the interpretation function mapping expressions to their denotations; and J, the membership function, maps E into E so thatfia + b) = fia) +fib) (i.e.J is an automorphism on E). The membership function exploits the fact that each proper sum cor responds in an obvious way to a collection of individuals, namely, the set of atoms dominated by that sum. This enables J to associate each group with its membership, or, more precisely, with the proper sum corresponding to the join of its members. Other treatments have membership functions, in particu-
C. Barker 75
lar Link (1984) and Landman (1989); however,Jis more closely aligned in spirit to the 'constitutes' function described in Link (198 3). The constitutes function associates an entity such as Jane with the portions of matter that make it up, such as Jane's hands. Similarly, the membership function associates a group with the collection of (discrete) objects that constitute its membership. Later sections will discuss fin more detail, especially sections 5 and 7. The interpretation function [ · ] will be constrained so that syntactically complex expressions are mapped onto their denotations according to the following schemata, where parentheses indicate functional application. Syntactic structure S - NP VP NP - Det CN CN - CN PP PP ofNP NP - NP and NP -+
Interpretation =[V P]([NP]) [S] [NP] =[ Det]([CN]) [ CN] -[PP]([ CN]) [PP] =[ oj]([NP]) [NP] -[and]([NP],[NP])
Furthermore, we will restrict our attention to models in which 15.
a. [and] = J..xly [x + y] b. [ oj] = ly.J.QJ..x [ Q (x)&fix) � y]
That is, the denotation of the conjunction and is a function that returns thejoin of the denotations of the conjuncts.5 The interpretation for of is more complicated, and I will defer a detailed discussion to section 5 . 1 . Briefly, an entity will be in the extension of a predicate such as [committee of the men ] just in case it is a committee and each of its members is a man. Since the sum of the members of a committe x is given by fix ), x will be a committee of men if[ committee] (x) is true and fix) � [ the men]. More generally, if y is the entity denoted by the complement of of, and P is the predicate denoted by the group noun, we require P(x) and fix) � y , as given in the definition. Finally, for the sake of explicitness, we must specify two technical details needed in any analysis involving plurals, although nothing crucial rests on the decisions made here as far as the main line of argumentation in this paper is concerned. First, our system must guarantee upward closure. Note that it follows from the fact that John is a man and Bill is a man thatJohn and Bill are men. Thus the properties shared by atoms automatically move up the lattice to their sums. We say that the predicates for which such entailments hold exhibit upward closure with respect to the join operator. For our purposes, we shall simply stipulate that plural predicates denote the closure of the denotations of their singular counterparts. Ifj E [ man] and b E [ man] (in (r6)), then it follows that j + b e [ men] by upward closure. Since Uohn and Bil� j + b, we predict -
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14. a. b. c. d. e.
76
Group Terms in English: Representing Groups as Atoms
0
the desired entailment. (See Link ( I 98 3) and Landman ( I 989, section 2. 3) for discussion.)
I 6.
[the men] J+b+t
�
Proper sums
J+b
b+t
Atoms [man]
Second, we must say something about the behavior of the determiner the in an ontology containing sums. Syntactically, the combines with a common noun phrase to form a noun phrase. Since common noun phrases denote predicates, i.e. sets of entities, and definite descriptions denote entities, the will be a context-dependent function which maps a set of entities onto an entity. More over, the (like all lexical determiners) is conservative: the always picks out some entity which satisfies the predicate in question, so that [ the man] will be some entity in the extension of man. Now assume that John and Bill and Tom are men, and consider the noun phrase the men. By upward closure, the predicate [ men] will contain Uohn and Bill] -j + b, [Bill and Tom] - b + t, Uohn and Tom] = j + t, and Uohn and Bill and Tom ] = j + b + t. But these (proper) sums are entities just like any other, so that all [ the] needs to do is pick one, say, j + b + t. Thus the men will denote a single entity, a sum corresponding to some contextually specified set of men. Entities appropriate on this view for the denotations of the man and the men have been indicated in the diagram in (I6).6 Now that we have specified the fragment, we can say what group nouns will denote. The main proposal of this paper is that we say nothing special about group nouns at all; that is, a singular group noun denotes a set ofatomic entities just like any other singular noun. The only special property of a group noun is that the membership function f maps elements in its denotation onto proper sums. We can now be more precise about what a group is in this model. Recall that a group was provisionally defined as an element in the extension of a group noun. A group, then, is any entity which f maps onto a proper sum. Thus a model for the fragment will have a structure as schematized in (I7). Since f maps the atom a on to the sum of b and c, a is a suitable representation for a group which has b and c for its members.
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[the man]
C. Barker 77
a
c
b
2.2
An example
-
I 8.
a.
b. c. d. e. £
g. h. i. j. k. 1.
[ Committee A] = 2 [ Committee B] = 3 [ Committee C] 5 Uohn] = j = 7 [Bill] = b I I [ Tom ] - t - I 3 [committee] = [group] = A.x [x E { 2, 3, 5} ] [ man] - A.x [x E { 7, I I, I 3}] [ woman] = A.x [x E { I 7, I 9, 2I}] [ meets on Tuesday] - A.x [x E {2}] [ meets on Wednesday] = A.x [x E {3 }1 [died] - A.x [x E {7, I I}] =
-
Furthermore, letjbe consistent with (I9).
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This subsection gives a model for a state of affairs which will provide interpretations for many of the examples in the remainder of the paper. For the sake of concreteness, let + be the least-common-multiple operator on integers, and let E be the closure under + of the primes greater than I . Thus E { 2, 3, 6, 5, Io, I 5, 3 0, 7, . . .}. There is nothing special involved in building E on the primes; it is simply a convenient choice for exposition in that atoms are easy to distinguish from proper sums (atoms are prime), and the � relation is transparent (a � b just in case b is a multiple of a). Also, given that predicates are represented by (characteristic functions o� sets, the fact that proper sums are simply integers helps prevent the typographical confusion resulting from sets of sets. As for the basic expressions in the various syntactic categories, assume that man , group, and committee (and their plural forms) are common nouns, that died, meets on Tuesday, and so on (and their plural forms) are verb phrases, and that John, Bill, Tom , Committee A, Committee B, and so on are noun phrases. Then let the denotation function [ · ] be consistent with (I 8 ).
78 Group Terms in English: Representing Groups as Atoms
I9. a. f{2) - 77 b. f{3) = 77 c. f{ 5 ) = 323
20. a. [ the group] b. [ the man] c. [ the groups] d. Uohn and Bill and Tom ] = [ the men] e. Uohn and Bill] f Uohn and Bill died. ] g. [ The committee died. ] h. [ the committee ofjohn and Bill] i. [ the committees ofmen] j. [ the committees ofmen and women]
= [ the committee] = 5 I3 = [ the committees] = 30 = j + b + t = I OO I = j + b 77 = true = false 3 6 30 =
=
The appropriateness of these representations will be discussed more fully in sections 4 and 5·
3 ALTERNATIVE P R O P O S A L S Link ( I 984) suggests that groups as individuals denote atoms, and the connec tion between a group and its members resides in a function mapping group atoms onto sums. These special atoms are called 'impure' atoms. The analysis given in section 2 adopts the same formal technique. However, the version in Link (1 984) differs in two substantive ways. As pointed out by Landman ( 1989), the version in Link (1984) does not allow for groups whose members are groups. This seems overly restrictive, since committees can form coalitions as easily as people can form committees. On my analysis, there is nothing to prevent the membership function J from mapping a group onto a sum that dominates
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Finally, assume that [ the] takes (the characteristic function o� a set of entities and returns that entity in that set which is arithmetically largest (a somewhat arbitrary bur plausible choice). For instance, since [ man] characterizes the set { 7, I I , I 3 }. [ the man] = I 3 = [ Tom]; and since [ men] is the closure of[ man] under the join operator, [ men] characterizes { 7, I I , I 3, 77, I 43, I OO I }. and [ the men] = I OO I = Uohn and Bill and Tom]. In addition, in order to allow bare plural terms such as men , we can add a zero determiner to the lexicon which behaves like the. In other words, I assume (for the purposes of this paper) that a bare plural noun phrase, when definite, denotes the same thing as the same plural count noun combined with the. It is easy to see that the fragment gives the following interpretations:
C. Barker 79
-
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individuals, groups, groups whose members are groups, and so on, or even mixtures of these types of members. More importantly, Link (1 984) provides impure atoms not only for groups, but also for plurals and conjunctions when they are understood as individuals. Thus Link (1 984) does not distinguish between group terms on the one hand and plurals and conjunctions on the other. I argue in section I that group nouns behave differently from plurals and conjunctions. The obvious alternative to the atomic approach is to take the denotation of a group term to be the collection of its members, and to calculate the group as individual on the basis of that collection. This is essentially the approach taken by Bennet (1975). I will not discuss Bennet's proposal in detail here; instead, I will present a more elaborate version based on set formation as developed in Landman (1989), on the assumption that my comments on the latter analysis will carry over by and large to the former. In order to understand the approach taken in Landman (1 989), assume the domain of discourse is a join semilattice containing atoms and proper sums as described in section 2.1. A group term denotes a sum, and the atoms dominated by that sum are taken to be the members of the group. If the committee denotes j + b, for instance, thenJohn and Bill are the two members of that committee. In addition, however, for each proper sum x there is a unique new entity t x which is added to the domain of discourse. The simple sum is used when we wish to have access to the members of the group; but when a group seems to be acting as an entity with properties independent of its membership, we can associate these properties with t x instead. More technically, let the join operator be set union. IfJohn, Bill, and Tom are the only men, and they are also the entire membership of Committee A, then [the men] - Uohn and Bill and Tom] - [ Committee A] = V• b, t}, (assuming Uohn] j and so on). Then t corresponds to an application of set formation which takes any proper sum and returns the singleton set containing only that sum. So in a context which demands an atomic reading of a group, in addition to the group as set denotation, we have [ Committee A] - t V• b , t} - {U, b, t}}. Let us call the entities in the range of t upsums. In general, then, definite descriptions are assumed to be systematically ambiguous between sums and upsums. Landman (1 989) argues that not only group terms, but plurals and conjunctions may denote upsums. For instance, upsums are crucially involved in providing an interpretation for the cards above 7 and the cards below 7 (which denotes the sum of the upsums of the conjuncts). Furthermore, since upsums are also in the domain of the join operator (by virtue of being entities in the domain of discourse), this means thatJohn and Bill and Tom is ambiguous between the three entities V• b, t}, V• {{b, t}}}, and {{U. b }}. t }. in addition to their respective upsums, depending on the syntactic con stituency and semantic need.
So Group Terms in English: Representing Groups as Atoms
4 RE S O LV I N G P O WE R This section explores situations in which a group has properties not shared by the sum of its members. In addition, we will see how the atomic analysis distinguishes among groups which accidentally have identical memberships. Recall that section I .2 argues that groups may fail to have a property which is true of the sum of its members, and let the pair in (2 I ) represent the examples that appear there? 2r. a. The men met on Tuesday. b. The committee met on Tuesday. If the committee in question meets only on Friday afternoons, then (2 Ia) can be true at i:he same time that (2 I b) is false. In the situation modelled in section 2.2, ifJohn and Bill are the only salient men, then [ the men] j + b. But the denotation of the committee is an atom, so that [ the committee] t= j + b, and (2I b) evaluates to false at the same time that (2 I a) evaluates to true, as desired. Thus the model can distinguish a group from the sum of its members. -
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My main objection to the use of upsu�s to represent groups is that it pre dicts that group terms are potentially indistinguishable from plurals and con junctions (in extensional contexts). lt is a mystery on this alternative why plurals and conjunctions should be intersubstitutable with each other but not with group terms, as illustrated in section I .2. More specifically, upsums do not provide sufficient resolving power. Given the membership of a group, there are exactly two entities in the domain of dis course capable of representing that group: the sum of the members, and their upsum. But it is certainly possible for more than two distinct groups accidentally to have the same membership. Landman (I989) discusses the resolution problem at some length; I will discuss the position advocated there more fully in section 4· Furthermore, if group terms denote proper sums, then by default a group should have any property shared by its members. I argue in section s that this is not so, that it is more natural to consider groups as atomic individuals. Thus I claim that interpreting groups as sets makes access to members too easy. Finally, it is not clear when a noun phrase will denote a sum and when it will denote an upsum. On my analysis, group nouns uniformly denote sets of atoms. There is one case in which I believe a definite description referring to a group may alternate between an atom and the sums of its members, namely British English; but in this case, agreement morphology clearly signals which inter pretation is appropriate (see section 7).
C. Barker 8 1
The failure of entailment in (21) clearly poses a problem for analyses which identify a group with the set of its members. On the upsum analysis, however, the entailment correctly fails to go through if we assume that the group term denotes an upsum. Then [ the men] = (i, b} .f [ the committee] = t (i, b} {(i, b }}. Thus it is entirely possible that [ the committee] has properties different from [ the men ]. However, if terms can freely be interpreted as upsums, then there should always be a construal of(r9) in which the entailment holds (in both directions), independent of the facts of the situation. But this prediction is not borne out. Even if the upsum analysis can describe the failure of entailment in (2 1 ), it fails to distinguish among groups with identical memberships. =
The value of the denotations of (22a) and (22b) are entirely independent, even assuming that Committee A and Committee B have the same members. This presents no difficulty on the atomic account, since Committee A and Com mittee B denote distinct individuals. In the model given in section 2, (22a) is true and (22b) is false. The fact that both committees happen to have the same membership is the result of the membership function J accidentally mapping them onto the same sum. On a set analysis, a group is entirely determined by its members, so two groups with the same members must be extensionally equivalent. Given upsums, a group can denote the set of its members or the upsum of its members, so we could potentially discriminate among at most two committees with identical memberships by means of sums and upsums alone. But we can have a Committee D, Committee E, and so on, any number ofcommittees with identical membership, so upsums are not sufficient to model the relationship between a group and its members. One possibility is that Committee A and Committee B have different intensions, since there is some possible world in which their memberships differ. But this will only help if predicates normally taken to be extensional, such as meet, are sensitive to intensions just in case their arguments are group terms, a rather uncomfortable solution. Furthermore, notice that all of the examples seen so far involve terms in subject position, and subject position is normally taken to be transparent to intensionality (see e.g. Montague 1970). Therefore I will reject intensionality as a solution to the group resolution puzzle. Landman (r989) also rejects intensionality, and proposes that committees with identical memberships differ in intention (note the t). He suggests providing a level of intentional objects called 'pegs' built on top of the domain of discourse, so that distinct terms can denote distinct pegs at the same time their extensions in the domain of discourse coincide. Apparently intentional
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22. a. Committee A meets on Tuesdays. b. Committee B meets on Tuesdays.
82 Group Terms in English: Representing Groups as Atoms
predicates such as meet, then, are functions on pegs, rather than entities in the domain of discourse.8 Augmented with intentionality, the upsum analysis clearly can provide the necessary resolving power. But the atomic analysis achieves exactly the right resolving power without any additional assumptions. Furthermore, Landman (1989) argues that intentions are available to plurals and conjunctions as well as to group terms, once again assimilating group terms with plurals and conjunctions. To the extent that the resolution puzzle does correlate with the other behavior of group nouns distinguishing them from plurals and conjunctions, the atomic analysis gives a more satisfying explana tion.
A C CE S S T O MEMBE R S
There is an intuitive connection between a group and its members, and this correspondence is lost if a group is simply an atomic individual. Thus the atomic analysis unadorned suggests that this intuitive connection resides in our conception of the world independent oflinguistic structure. However, there arc at least two constructions for which truth conditions clearly depend on recovering the membership of a group. The first is the of phrases mentioned above: a committee of women has only women for members. In order to provide cif phrases with an interpretation, we must make the members of a group available to the semantics. Section 5.1 shows how the membership func tionf can provide an interpretation for of phrases. The second case involves the interaction of agreement marking with truth conditions involving subject group terms in British English, as described in section 7· In addition to these two constructions, Landman (1 989) proposes that there are systematic entailment relations between sentences with denotations involving a group and sentences with denotations involving the members of that group. Such examples seem to motivate allowing a group to denote the sum of its members, as in the upsum model, so that the semantics can guarantee that the desired entailment relations go through. For instance, if a group meets at a particular location, it follows that the members of that group were present at that location. This seems more like non-linguistic reasoning about the real world than a constraint imposed by the semantics on possible interpretation functions. However, section 5.2 shows how to guarantee such entailments on an atomic analysis if necessary. Furthermore, I show that the upsum model does not give the correct predictions when groups denote upsums rather than sums; once the upsum analysis is adj usted, the rwo proposals seem equivalent in complexity. Therefore locational predicates do not argue in favor of an upsum analysis over an atomic one.
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5
C. Barker 8 3
s.r
of phrases
The denotation given for of in (I s b) is repeated here:
23. [ oj] - J.y J.Qh[Q (x)&j{x) � y] Since this interpretation is the most complex element in the fragment given in section 2, it will be helpful to work through a concrete example in some detail. We want the predicate committee ofmen to have in its extension only groups whose members are men. The diagram in (24) summarizes the parts of the model specified in section 2.2 which are relevant to calculating the denotation of this phrase. The predicate committee accepts the atoms 2, 3, and S · Only two Part of
( E.r ) :
323
2
3
committees
5
7
II
men
13
�
17
19
women
21
•
.
•
of these committees are committees of men: the two that the membership function maps into the sublattice of men, namely, 2 and 3 · Both the committee 2 and the committee 3 have the same members, namely, 7 and I I (representing John and Bill) , whose sum is 77· The comrllittee 3, however, has a pair of women for its membership. The interpretation of of picks out the correct groups by comparing their image under f to the denotation of the restricting noun phrase men . Recall that this fragment treats the zero determiner as if it were the, so that men as a definite description coincides with the men . Since [ men] is the closure of[ man] under the join operator, [ men] - { 7, I I , I 3, 77, 9I, I43, r oo I }. Since [ the] picks out the arithmetically largest sum, [ men ] = I oor. The interpretation of committee ofmen , then, accepts any atom which is a com mittee and whose image underfis dominated by r oor.
25. [committee ofmen ]
[ofmen]([ committee]) �of]([ men])]([ committee]) [[J.yJ. QlX [ Q(x)&f(x) � y]] ([ men ])] ([ committee]) [J.Qh[ Q (x)&j{x) � [ men ]]]([ committee]) Ax� committee ](x)&j{x) � [ men]] Ax� committee ](x)&j{x) � IOOI ] h[[J.y [y E {2, 3, S}]] (x)&.f{x) � IOOI ] h[x E { 2, 3, s}&f(x) � roo i ]
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24.
84 Group Terms in English: Representing Groups as Atoms
In order to calculate the set characterized by this predicate, we need only test entities in the extension of[ committee], since all others will be excluded by the requirement that the candidate entity be either 2, 3, or S ·
2 E {2. 3, S}&.f\2) � I OO I true&77 � I ooi - true b. [h[x {2, 3, S }&.f\x) � I OO I ]] (3 ) 3 E {2, 3, 5}&./\3 ) � I OO I true&77 � wo I = true S E {2, 3, 5}&./\ S) � I OO I C. [h [x E {2, 3, S }&.f\x) � I OO I ]] ( S) = true& 32 3 � I oo I = true&false = false Therefore [committee ofmen] = { 2, 3 }. as desired, so that [ the committee ofmen] = 3· In other words, the result is that committee ofmen denotes all and only those 26.
a.
[h[x {2 3 , S}&.f\x) � 1001]] (2) E
.
E
=
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committees whose members are exclusively men. Now consider [committees of men], in which the group noun is plural. The entities to be checked against the [ men] sublattice are now potentially proper sums. This leads to the requirement stated in section 2.I that f be an auto morphism, which ensures that the membership of a sum depends only on the membership of the parts of that sum. In particular, the membership of the join of two groups is thejoin ofthe memberships of the groups. For instance, ifJohn and Bill are the members of Committee A, and Mary and Sandy are the members of Committee C, then the members of the entity [ Committee A and Committee C] = .!\[Committee A] + [ Committee C]) = .!\[ Committee A ]) + .!\[ Committee C]) - j + b + m + s. Given this assumption, the fragment gives the reasonable prediction that [committees ofmen] = { 2, 3, 6}, and [ the committees ofmen ] = 6. Along the same lines we also have [the committees ofmen and women ] 3 0 . On this account, a committee of men and women is any committee whose image underfis dominated by the sum of[ men] and [ women]. The account automati cally excludes many implausible readings. In particular, it is not necessary that any committee member be both a man and a woman; it is not necessary that each committee be uniformly composed of men or uniformly composed of women; it is not necessary that any particular committee have at least one male member and also at least one female member; and so on. Thus the account automatically gives a reasonable representation of group noun of when it has a conjoined complement. As a last comment on the predictions made by the analysis of group noun of, consider what would happen if we attempt to evaluate [group ofthe committee]. There is a grammatical reading where of occurs in its possessive or attributive use; but this phrase cannot be used to pick out groups ofpeople whose members are all taken from the membership of the most salient committee. Since groups always contain at least two members, the image of any group underf will be a
C. Barker
Ss
proper sum. But the denotation of the committee is an atom, by hypothesis. Since an atom can never dominate a proper sum, the extension of group of the com mittee would be empty in every model. The atomic analysis, then, gives an explanation for why singular group terms are ungrammatical as complements to group-noun of On the upsum analysis, however, a group term can denote a proper sum just like a nonsingular term, so there is no semantic reason why they cannot serve as the complement to group noun of 5 .2
Locational predicates
27. a. Committee A stayed in Boston yesterday. b. John and Bill stayed in Boston yesterday. It seems reasonably graceful to say that in any situation in which (27a) is true, (27b) is necessarily also true. We can express the generalization illustrated in (27) by referring toJ, once we have some way of talking about the location of an entity. Assume that every entity x has a value under a function nuch that r(x ) is interpreted as the location of x. We need only stipulate thatJ constrains T as in (28). 28 .
r
(ftx)) - r(x)
This will guarantee that if the committee is in Boston, then its members are also in Boston. We should also stipulate that that Tis a homomorphism from the domain of discourse into the hierarchy of locations which preserves the sense of the join operator. That is, ifBill andJohn are in Boston, then Bill is in Boston, and so on. In the other direction, if Bill is in Boston and John is in New York, then the location of the sum representing the pair of John and Bill is not a discrete location in the normal sense; but there is not room here for a detailed develop ment of a theory of location. (See e.g. Lasersohn I 98 8 for a detailed proposal.) On the upsum analysis, the desired entailment goes through automatically only on the sum reading, that is, only when [ the committee] = [ the men]. Notice that this extensional identity predicts that the entailment relation should be symmetrical, so that (27b) entails (27a). As argued in section 2.2, this prediction is too strong, since John and Bill may happen to be in Boston for reasons having nothing to do with the operation of the committee. In any case, the upsum analysis predicts that the locational entailment will be guaranteed only when a group term and a plural term have identical denota tions, that is, only when they both denote sums or both denote upsums. But
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Landman (1 989) notes that certain predicates, including locational predicates, are sensitive to the membership of a group. More specifically, if a locational predicate is true of a group, it will also hold the members of the group.
86 Group Terms in English: Representing Groups as Atoms
meet has locational entailments even when it distinguishes between a group and its members. 29. a. The men first met this year. b. The committee first met this year. c. The men were all in the same place this year. As argued in section
6 A D D I T I O N AL AR G U ME N T S T H AT G R O U P S A R E AT O M S 6. 1
Names ofgroups as rigid designators
Traditionally, names are rigid designators. That is, a name denotes the same entity at every intensional index. This means that if two names ever denote the
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2.2, (29b) does not entail (29a), since (29b) will be true at the same time that (29a) will be false in a situation in which the men were first introduced to each other years before the committee was formed. Nevertheless, (29b) does entail (29c), since the members of a committee must all gather in the same place in order for a meeting to take place. This means that the upsum analysis unadorned does not predict the full range oflocational entailments. Therefore we must stipulate for the upsum analysis that r(x) = r(t x) in parallel with (28). Thus (28) is not an artefact of the atomic analysis, but must be stated in any semantics which attempts to model entailments involving loca tion. Landman (1 989) appeals to examples similar to (27) as a partial motivation for providing group terms and plurals with (the optional oD identical denota tions. Once a requirement similar to (28) is in place, however, the desired entailments go through without assuming that the group term is ever co extensive with a plural. Thus locational predicates do not provide an argument in favor of the upsum analysis over the atomic analysis. Landman (1989) gives other examples of entailments. For instance, we can conclude from the fact that The Talking Heads is a pop group that David (a member of the Talking Heads) is a pop star. Although I do not have space to develop arguments parallel to the one above given for location predicates here, my position on these other sorts of entailments is that they too are facts about the way the real world works which should not be included in a description of semantic regularity. If an analysis on which they go through is desired anyway, then the entailments will continue to go through even in contexts in which an upsum is needed. A separate stipulation will be needed for each sort of entail ment, so that the upsum analysis will offer no advantage over the atomic analysis.
C.
Barker 87
6.1
Similarity to measure nouns
Group nouns bear a strong similarity to measure nouns. 30. a. b. 3 I . a. b. 32· a. b.
two committees of Hungarians two cups of flour a flock of geese a bowl of rice a forest of elm trees an acre of elm trees
Intuitively, measure nouns provide a means of referring to a portion of matter as a unit. Similarly, group nouns are nothing more than the counterpart of measure nouns in the count domain. That is, group nouns also provide a means of referring to a collection of countable objects as a unit. A potential objection to this comparison might come from the tendency of measure nouns to specify the exact quantity of the portion of matter they describe: a cup of water is a fixed amount, but a committee can have any
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same entity, they cannot be distinguished (by means of truth conditions) even in intensional contexts (ignoring propositional attitudes). Thus if Richard and Dick are two names for the same person, you are seeking Richard just in case you are seeking Dick. Clearly names of groups should be rigid designators just like any other names. Say that Committee A and the House Ways and Means Committee are two names for the same committee; then you are seeking the approval of Committee A just in case you are seeking the approval of the House Ways and Means Committee. Assuming that names of groups are rigid designators is a problem for the set analysis. If a group term denotes the sum or the upsum of its members, then the extension of a group-denoting expression must change with every variation in the membership of the group. Rigid designators could no longer denote the same individual at every index, and it would become more difficult to guaran tee that two names for the same group were intensionally equivalent. But if groups correspond to atomic entities, no such problem arises. For instance, we can have [ Committee A] = [ The House Ways and Means Committee] = c for some atom c at every world-time index, in the normal fashion of rigid designators. The membership of the committee can still vary over time or across possible worlds, since the membership function f is free to give a different value for c at each index. Thus the atomic analysis but not the set analysis automatically extends to the standard treatment of names as rigid designators.
88 Group Terms in English: Representing Groups as Atoms
number of members (although it should have more than two). But this alleged conttast between group nouns and measure nouns fails in both directions. There are measure nouns which are vague in the same way as group nouns, for instance piece or portion , and there are group nouns which specify the precise cardinality of their membership, such as platoon , pair, or cabinet. Given this parallelism, it makes sense that the denotation of group terms should resemble the denotation of measure nouns. And since there is no reason to suppose that measure terms denote anything other than an atomic entity, at least as far as their behavior in the count domain is concerned, the most natural assumption is that group nouns also denote atoms. See Krifka (1987) for an analysis of measure nouns on which measure terms denote atoms.
A GREE M E N T
Additional support for the hypothesis that group nouns denote atomic entities comes from their agreement properties. A large part of the plausibility of distinguishing between atoms and proper sums in the ontology is the close correspondence between noun phrases which are syntactically singular and those which denote atoms. For instance, the man is singular and denotes an atom, and the men is plural and denotes a sum. Given this observation, an analysis on which a group term denotes the same entity as a nonsingular term predicts that group terms should be syntactically plural; however, this is generally not the case. On the other hand, if group terms denote atomic entities as proposed here, they are correctly expected to behave like singular terms. I continue to use the terms 'singular' and 'plural' exclusively to refer to morphosyntactic properties of phrases. They correspond roughly in the semantics to 'atomic' and 'proper sum'. Group nouns in the plural morpheme always trigger plural verb agreement: 33·
a. The committees have left. b. *The committees has left.
But group nouns in the plural behave just like other plural terms, and we can ignore them henceforth. More relevantly, singular group nouns are always capable of triggering singular agreement marking on the verb. 34·
The committee has left.
This much is unsurprising (on the atomic analysis). However, in some dialects, the singular of some group nouns is systematically capable of triggering plural agreement, although singular agreement continues to be grammatical:
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7
C. Barker 89
35· a. The committee is old. b. The committee are old.
36. a. The group of people are sitting on the lawn. b. # The group of statues are sitting on the lawn. Also, note that plural agreement is possible with proper group nouns: 37· a. Chrysler are pulling out of South Mrica. b. Parliament are pulling out of South Mrica. This makes it clear that the rule for British English operates only when the denotations of definite descriptions are available, rather than at the level of, say, common noun phrase denotations. We can now describe the British dialect as given in (3 8). 38. Group term agreement in British English: Syntax Semantics NP[plural] - NP[singular] [NP[plural]] - f([NP(singular] ]) We must also stipulate that invoking this rule forces the referent of the noun phrase to be interpreted as sentient.
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British dialects typically allow both (3sa) and (3 sb) as grammati�al. Other dialects reject the plural agreement in (35b). There is considerable variation among speakers; at the very least, there is a dialect in which plural agreement as in (3sb) is always ungrammatical. I will refer to the most finicky dialect as the standard American dialect, and I will ignore the variation between the two extremes of the American and the British dialect. / Note that the atomic analysis describes the American dialect witho�t further modification. Since group terms denote atoms, it is unsurprising that they trigger only singular agreement. Thus we need only provide an explanation for the British dialect. Fortu nately for the atomic analysis, the difference in agreement between (35a) and (35b) corresponds to a difference in meaning. In the British dialect, singular agreement as in (3 sa) is appropriate only when it is the age of the committee as a group which is of interest; it can be true even if the individual members are all young. Plural agreement as in (3 s b) is appropriate only when it is the age of the members of the committee which is important, and (3 sb) can be true even when the committee itself was chartered recently. Before we attempt to formulate a rule characterizing the dialect split, there are several other semantic constraints on the availability of plural agreement which should be noted. Specifically, plural agreement with singular group terms is possible in British English only when the members of the group are human, or at least sentient.
90 Group Terms in English: Representing Groups as Atoms
The rule in ( 3 8) says that a group term can denote either an atom or the sum of its members, as disambiguated by the marking on the verb. This inter pretation rule brings the British dialect in line with the generalization that singular verb phrases take noun phrases which denote atoms, and plural verb phrases take those which denote sums. This account predicts the difference in truth conditions as described for ( 3 sa) and ( 3 s b), and, assuming that [ the members ofthe committee] = fi[ the conlmittee ]), it predicts that the following two sentences are synonymous:
39· a. The committee are old.
b. The members of the committee are old.
40. a. b. 4 1 . a. b.
The Talking Heads are giving a concert in Belgium. ?The Talking Heads is giving a concert in Belgium. ?The Clash are giving a concert in Belgium. The Clash is giving a concert in Belgium.
However, when the proper group noun is morphologically singular, as in (41), singular agreement is preferred, and in no case is the agreement in free variation as it is in the British dialect. I take (40) to be a fact about the morphology of proper names, rather than a reliable probe on the denotation of a group term. More problematic are the cases where the sum interpretation is inescapable despite singular agreement. For some speakers of the American dialect, the committee is old is ambiguous between the atomic reading and the sum reading. In fact, there are even some cases in which every American speaker seems to have a sum reading despite singular agreement. 42. a. John and Bill have risen to their feet. b. The committee has risen to its feet. If group terms are atoms independent of their membership, then the truth of (42b) should be independent of the truth of(42a). However, ifJohn and Bill are the only members of the committee, then (42a) entails (42b). It is as if the properties common to the members of the committee are extended to the group entity as if by courtesy. In general this does not happen, as argued in section 1 .2; and the effect is enhanced by non-linguistic reasoning about the real world. For instance, committees do not have feet, but committee members do, so the use offtet in (42b) makes a group-distributive reading more salient. But no matter how these last two problems are resolved, the British.
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In sum, the atomic group hypothesis supplemented with a membership func tion J provides a simple account of the dialect split. Even in the American dialect there are certain situations in which plural agreement is more acceptable. For instance, plural agreement is preferred when the subject is a name with plural morphology, as in (40).
C. Barker 91
CONCLUSION I have proposed that group terms, like all terms containing a singular noun, denote atomic entities, and that the membership of a group is available only through the mediation of a function f This scheme provides exactly the resolving power needed for discriminating among groups, at the same time that rigid designators operate exactly as expected. Furthermore, the membership functionJ mapping group atoms onto their memberships provides limited but effective access to members when it is needed, most notably for group-noun of phrases and for describing group term agreement in the British dialect.
Acknowledgements would like to acknowledge with gratitude the comments and advice of Peter N. Lasersohn, William A. Ladusaw, and two anonymous reviewers. This paper would doubtless have been much improved if Roger S. Schwarzschild's ( 1991) University of Massachusetts dissertation, On the Meaning ofDefinite Plural Noun Phrases, had been available to me in rime to take account of it. I
CHRIS BARKER
Centerfor Cognitive Science 208 Ohio Stadium East 1961 Tuttle Park Place Columbus OH4321 0 USA
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American dialect split supports the claim that group terms denote atoms rather than sums. There are two argumenrs in this direction. First, all dialects permit singular agreement where any dialect has singular agreement, but only some dialecrs permit plural agreement. This asymmetry makes sense if the inter pretation of a group as an atomic entity is basic and irs incarnation as the sum of irs members is more remote. Second, even in those dialecrs which permit the extraordinary plural marking on the verb, singular marking is always grammat ical, but the special plural is available in a more restricted set of cases. Once again, we would expect the atomic interpretation to have a wider availability if it is the basic denotation of the group noun. Thus the evidence from number agreement supports the atomic hypothesis, and argues against the set formation perspective.
92 Group Terms in English: Representing Groups as Atoms
NOTES 1.
traditional treatment given in Montague (I970) as well as che plurals-theory oriented proposal in Link (198 3). Nothing crucial hinges on this decision, bur it will be convenient for a sentence such as the man died to have a chance at being true in a model in which the predicate [man] con tains more than one entity. Assume that Bill and John are men, so chat the exten sion of man contains rwo entities. Given such a siruation, in the fragment in Mon tague (I 970), the man denotes a generalized quantifier which is true of no predicate, so the man died is always false; in che fragment in Link (198 3), mere is a uniqueness requirement, so that the man fails to denote. The version of the given here is more along the lines of che type shifting analysis proposed in Partee and Rooth (I 98 3), where thejob of the is to take a pre dicate and package it as a noun phrase denotation. 7· For clarity in the discussions which follow I will let an example with a plural term stand for similar examples involving con junctions. In each case I will assume that it is clear how che analysis presented in section 2 predicts that plurals and con junctions pattern together with respect to truth value whenever they denote the same sum. 8. We can roughly approximate pegs by allowing spontaneous upsums of upsums. A group term such as the committee could be ambiguous berween U· b), (U, b)), {{V. b })), . . . Then we could have [ Committee
A]
-
[U, b)), [ Committee B]
-
{{U, b))),
and so on. The technical machinery involved in a fully explicit intentional system is rather elaborate; see Landman (I989, part 3) for details.
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There is a parallel test involving che parti tive which usually gives the same resuh. A partitive phrase is just like the of phrases above except chat the complement noun phrase is definite, e.g. a group ofthe students versus a group ofstudents. However, the bare plural test is preferable, since noun phrases in the partitive do not always contain group nouns. For instance, we have aJew of the men and •aJew ofthe man , even though few is not a group noun: it is not regular with respect to che plural, it is not a count noun, and there is no contrast with a bare plural of complement •aJew ofmen, •aJew ofman (c£ afew men, •ajew man). 2. Landman (1 989) shows chat mere are many seemingly innocent predicates which are not extensional enough for our purposes. For instance, the hangmen may be on strike without che judges being on strike, even if che hangmen happen to be the judges in a particular situation. Thus the predicate be on strike can distinguish between the rwo plural terms the judges and the hangmen even when chey have che same extension. However, if the hangmen die, then it follows that the judges die, and vice versa, so I will take die to be a purely extensional predicate. 3· It should be noted that plural group terms (e.g. the committees, the groups of women) behave like ocher plural terms in all respects, including che ability to trigger plural agreement marking. 4· This definition of atom reflects che non crucial assumption chat the domain of dis course lattice does not contain a zero element. 5· Of course, this interpretation only covers one restricted use of and; see e.g. Hoeksema (I983, I 988). 6. This treatment of the diverges from the
C. Barker 93
REFERE N CE S plurals and mass terms, a lattice theoretical approach', in R Bauerle et al. (eds), Meaning, Use, and Interpretation of Language, Walter de Gruyter, Berlin, 3022 3. Link, G. (I984), 'Plural', to appear in D. Wunderlich & A von Stechow (eds),
Handbook ofSemantics.
Montague, R (I 970) 'The proper treatment of quantification in English', in J. Hintikka,J. Moravcsik & P. Suppes (eds),
Approaches to Natural Language: Proceedings of the 1 9 70 Stanford Workshop on Grammar and Semantics, Reidel, Dordrecht, 22 I -42. Also in R Thomason (ed.), (I974) Formal Philosophy: Selected Papers of Richard Montague, Yaie Univ. Press, New Haven,
247-70. Partee, B. & M. Rooth (198 3), 'Generalized Conjunction and Type Ambiguity', in R Bauerle et a/. (eds), Meaning, Use, and Interpretation oJLanguage, Walter de Gruy ter, Berlin, 36 I -8 3 ·
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Bennet, M. (I975), Some Extensions of a Montague Fragment ofEnglish, Indiana Uni versity Linguistics Club, Bloomington, Indiana. Hoeksema, J. (I983), 'Plurality and conjunc tion', in Alice G. B. ter Meulen (ed.), Studies in Mode/theoretic Semantics, Vol. I in the Groningen-Amsterdam Studies in Seman tics, Foris Publications, Dordrecht, 6 3-83. Hoeksema,]. (I988), 'The semantics of non boolean "and"', journal ofSemantics, 6: I940. Krifka, M. (I 987). 'Nominal reference and temporal constitution: towards a seman tics of quantity', Forschungsstelle fur natiirlich-sprachliche Systeme, Universi tat Tiibingen. Landman, F. (I989). 'Groups', Linguistics and Philosophy, 12, part l: 5 59-605 in no. 5. part II: 723-44 in no. 6. Lasersohn, P. (I 988), 'A semantics for groups and events', dissertation, Ohio State Uni versity. Link, G. (I983). 'The logical analysis of
