JOURNAL OF SEMANTICS AN INTERNATIONAL j OURNAL FOR THE INTERDISCIPLINARY STUDY OF THE SEMANTICS OF NATURAL LANGUAGE
MANAGING EDIT 0R: PETER BoscH (IBM Germany and University of Osnabriick) REVIEW EDITOR: TIBOR K1ss (IBM Germany} EDITORIAL BOARD: N. AsHER (University of Texas, Austin} R.BARTSCH (University of Amsterdam) J. VAN BENT HEM (University of Amsterdam) B.BoGURAEV (IBM Research, Yorktown Heights} D. S. BREE (University of Manchester) H. BREKLE (University of Regensburg) G. BROWN (University of Cambridge) 0. DAHL (University of Stockholm) S. C. GARROD (University of Glasgow) B. GEuRTS (University of Osnabriick) M.HERWEG (University of Hamburg) P. HOPPER (Carnegie Mellon University} L. R. HORN (Yale University} S.lsARD (University of Edinburgh) P. N. joHNSON-LAIRD ( Princeton University} H. K AMP (University ofSruttgan) E.LANG (University ofWuppenal)
S.LEVINSON ( MPI Nijmegen) S.L6BNER (University ofDiisseldor� SIR JOHN LvoNS (University of Cambridge) A.MANASTER-RAMER (Wayne Scare University} W. MARSLEN-WILSON ( MRC, Cambridge) J. McCAWLEY (University of Chicago) L.M.G.NooRDMAN (University of Tilburg} R.A.VAN DER SANDT (University of Nijmegen) T. SANFORD (University of Glasgow) R. ScHA (University of Amsterdam) H. ScHNELLE (University of Bochum) P.A.M.SEUREN (University of Nijrnegen) A.VON STECHOW (University of Tiibingen) M. STEEDMAN (University of Pennsylvania) W.WAHLSTER (DFKI Saarbriicken) B.WEBBER (University of Pennsylvania) H.ZEEVAT (University of Amsterdam)
EDITORIAL ADDRESS: Journal of Semantics, c/ o Dr P. Bosch, IBM Germany Scientific Centre, Vangerowm. 18, D.6900 Heidelberg, Germany. Phone: (49-6221- ) 59-4251 /4483 .Telefax: (49-6221) 59-3400. Email:
[email protected] New Subscribers co the Journal of Semantics should apply co the Journals Subscription Department, Oxford University Press, Walton Street, Oxford, OX2 6DP. For further information see the inside back cover. Volumes 1-6 are available from Swers and Zeidinger, PO Box 830, 2160 SZ Lisse, The Netherlands. ©Copyright Oxford University Press All rights reserved; no part of chis publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording. or otherwise without either the prior written permission of the Publishers, or a licence permitting restricted copying issued in the UK by the Copyright Licensing
Agency Ltd, 90 Tottenham Court Road, London W 1 P
Congress Street, Salem, Mass o 1970.
9HE,
or in the USA by the Copyright Clearance Center,
27
The Journal of Semantics is published quarterly by Oxford Universiry Press. Subscription is $117 per year. Second class paid at Newark, New Jersey. ISSN
0167-5133.
POSTMASTER: send address corrections to The Journal of Semantics, c/o Virgin Mailing and Disrriburion, Building 1 so, Newark International Airport, Newark, New Jersey
071 1 �. USA.
JOURNAL OF SEMANTICS Volume
10
Number 3
CONTENTS LAURA A MICHAELIS 'Continuity' with Three Scalar Models: the Polysemy of Adverbial Still
193
JAN VAN EIJCK The Dynamics of Description
239
)<��mwi4S<'mautics
10: 193-237
©Oxford Universiry Press
Il)<)J
'Continuity' within Three Scalar Models: The Polysemy of Adverbial Still
LAURA A. MICHAELIS University ofCalifornia, Berkeley Abstract
o INTRODUCTION' This inquiry will focus upon the semantic structure of theEnglish adverb still in particular upon the interrelations among its temporal and nontemporal senses. The nontemporal meanings to be investigated will be termed the adversative (or concessive) sense and the marginality sense. They are exemplified in (2-3), respectively. An example of the temporal usage is given in ( I ):
( I ) Uncle Harry is still pruning the shrubs. (2) We told Bill not to come, but he still showed up. (3) Death Valley is still in California. The meanings at issue can be described in broad terms as follows. The temporal sense refers to the extension of a state of affairs through to a given reference time (in ( I ), the present). The concessive sense, paraphraseable by
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
This study represents an elaboration and revision of Konig's (1977) account of the synchronic interrelations among three senses of the English adverbial still. These senses at issue are those in which still serves as a marker of a state's continuation to a temporal reference point, as a concessive particle, and as an indicator of marginal membership within a graded category. I argue here that the three semantically and grammatically distinct senses can be reconciled by the modem speaker: the lexeme still has an abstract meaning compatible with three types of scalar models. I n each of these models, still denotes the existence of effectively identical elements at rwo contiguous scalar loci. Still-bearing sentences code the existence ofan element at the more advanced of these loci, licensing the inference (via lexical presupposition or scalar entailment) that a like element can be found at (at least) one scalar point located closer to the origin of the scale. The three scalar models are ontologically distinct the scalar loci in question may be rime points, worlds, or simply rankings within a property scale. The elements ordered may be eventualities or entities. With respect to its role in discourse, still functions as a scalar operator in the sense of Kay (1990): it serves to relate rwo propositions within a scalar model. The sense nerwork described here, if it can be regarded as a plausible speaker generalization, provides evidence for the existence of an abstract conception of persistence, i.e. one nor restricted to the temporal domain. Persistence can be defined for scales and via scalar inference in ge�eral.
194
'Continuity' within Three Scalar Models: The Polysemy of Adverbial Still
nevertheless, indicates that a given event occurred despite the presence of conditions known to militate against it. Hence (2) portrays Bill's arrival as
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
having transpired in the face of efforts to prevent it. The marginality sense, perhaps first noted by Konig (1977) for German noch , is used to locate an entity at the margin of a graded category. Thus, in ( 3), Death Valley is presented as a marginal instance of California territory, where better exemplars of this (geographically defined) category are presumed to lie at points further removed from the eastern border of the state. This repertoire of meanings, and its etiology, has been of interest to semanticists concerned with the manner in which temporally based lexical schemata sanction nontemporal meaning extensions of various kinds. Konig & Traugott (1982) , for example, have investigated the development of the concessive use from the historically antecedent temporal use. They maintain, as will be noted below, that this development exemplifies the pragmatic strengthening of a quantity-based implicature associated with uses of temporal still (Traugott 1988). What is the relation between such historical develop ments and the links, if any, which connect these senses within the modem speaker's 'dictionary entry'? It has been presumed (e.g. by Traugott ( 1986)) that where a lexeme instantiates a synchronic polysemy network (in terms of Lakoff 1987), the structure of that network reflects the sequence of diachronic trajectories from which the modem array of senses arose. Thus, for example, the basic or central sense within a polysemy network is that sense from which extended meanings were derived historically. This situation occurs in, for example, Sweetser's (1990) analysis of polysemous sensory vocabulary, and in her analysis of modal verbs. Sweetser argues convincingly that the motivation for certain diachronic sense extensions is revealed through an examination of meaning connections forged by modern speakers. In particular, she proposes that extant metaphorical mappings, which link conceptual domains, also licensed meaning shifts in which certain lexical items acquired readings referring to the metaphorical 'target domain'. Thus, for example, an array of terms denoting vision come to refer to the domain of understanding (as Greek oida 'I know'< horao 'I see'). In such cases, the synchronic link between the senses of polysemous vision term (e.g. see) closely resembles the evolutionary path (metaphorical extension) by which the secondary sense arose. Further evidence for the relationship between meaning change and synchronically valid inference is provided by Horn ( 1984), who notes the role of quantity implicature in lexical change (e. g. in the formation of autohyponyms). Such studies demonstrate that one can profitably examine synchronic linguistic conceptual structure for clues about the mechanisms of meaning change. The present case study does not deny the validity of this approach. It does, however, question the tacit assumption that the interconnections among
Laura A. Michaelis
1 95
(i)n heterosemy, the semantic (as well as the formal) properties of the elements are too different to form a single conceptual category. Rather, the category has only a historical basis; what unites its members is their common ultimate source.
The theory of lexical meaning presumed by Lichtenberk is that of Lakoff ( 1987), in which polysemous lexical items constitute categories of (related) senses. The sense relations within such categories-e. g . metonymic links and image-schema transformations-are of a general nature: they represent widely applicable patterns of semantic extension. For example, prepositions coding paths can also, when coupled with a stative verb, code endpoints: the reading of around in Harry ran around the corner contrasts with that in Harry lives around the corner (Lakoff & Brugman 1986) . As noted by Jackendoff ( 1983: 13) , the existence of formal relations among apparently distinct readings of a polysemous word ... would make it easier for the language learner to acquire one reading, given another.
Patterns of sense extension are not, however, necessarily reducible to lexical redundancy rules: as Lehrer ( 1990) argues, the construal rules which create extended readings are only partially productive within semantic classes. For example, perception verbs like feel license both experiencer and stimulus subjects, whereas such verbs as see (versus look) are not characterized by this polysemy. We might presume that word senses linked via locally productive redundancy rules are most effectively stored and retrieved when they are assimilated to a lexical category, i.e. a conventionalized network of senses (cf Miller I 978). What can be the psychological status of a heterosemous lexical category, founded upon information of a sort available only to the historical linguist? Such a construct would not qualify as a linguistic generalization. If,
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
meanings of a polysemous lexical item recapitulate the evolutionary paths leading to those distinct senses. That is, one need not presume that an early meaning is a core sense, and that senses developing later in a lexeme's history are 'extended senses' . I will argue the following: the temporal sense of still cannot plausibly be regarded as a central sense, nor can, e. g. , the synchronic inference link between temporal and concessive still be equated with the path of historical development which yielded the latter. Historically, the sense extensions crystalized quantity-based implicatures associated with temporal still. These implicatures are present today, but, as will be seen, do not in themselves create a cohesive category of senses. This situation, in which the historical links relating a repertoire of senses to a single proto-etymon are not transparent to modern speakers, has been exami!J.ed by Lichtenberk ( 1991). According to Lichtenberk, instances of grammaticalization involving certain motion verbs in Oceanic can be regarded as examples of heterosemy , defined as follows (p. 480 ).
1 96
'Continuity' within Three Scalar Models: The Polysemy of Adverbial Still
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
however, we can assume that sense networks constitute useful generalizations, there is some reason to suppose that speakers will seek a plausible means of reconciling the disparate descendant readings of a given etymon. The impetus to reconcile such readings may be provided by the presence of suggestively similar use conditions. The synchronic meaning links forged for this purpose will bear no direct relation to any trajectory of semantic change. In the present case, I will argue, the modern speaker has reconciled the senses of still by extracting a set of accidental and yet salient semantic commonalities from these senses. The resultant generalization provides a schematic semantic structure under whose rubric all of the senses are grouped. The suggestion that there exist 'lexical categories' whose structure parallels that of'referential categories' (Lakoff 1987) is consistent with the dictum that the organization of linguistic knowledge is on a par with that of other sorts of knowledge (Goldberg 1992). The inferencing process involved in the development of the sense network at issue is analogous to that involved in the adduction of conditions upon category membership from ostensive definition. The distinct senses of still have common discourse pragmatic properties; each sense involves a particular form of expectation contravention. The shared use conditions provide the 'pointers' to an underlying semantic unity among the usages of still . The category rubric is devised as a means of capturing this semantic unity; it manifests scalar-semantic properties. As Konig observes ( 1977), uses of still involve 'man's ability to order . . . entities of various kinds [and) to rank them along a scale' (p. 173).Each of the senses, it will be claimed, partakes of and elaborates a general schema involving the maintenance of a given configuration across a sequence of scalar loci. The general schema has a modal component it evokes an 'expected outcome' in which the configuration in question is not so maintained, i.e. is not present at the scalar extreme serving as a reference point. The distinct senses will be said to owe their existence to the compatibility of the general schema with various scalar ontologies (temporal continuance among them). These ontologies accord with conceptual models of temporal extension, concession, and categorization. It has often been claimed that scalar organization-and scale-based inference-must be invoked in describing the semantics of certain grammatical markers. Most recently, studies by Fillmore, Kay & O'Connor (1988) and Kay ( 1990) have suggested that the adverbial elements let alone and even , respectively, should be analyzed as scalar operators.That is, these operators serve to relate pro positions within a scalar model (a set of background assumptions shared by speaker and addressee). The present study provides an additional set of observ ations about scalar operators. In particular, this study suggests that such an opera tor may have broad applicability across scalar domains, where such domains are defined by continuance through time, graded category membership, and the rel-
Laura A. Michaelis
197
r
PREV I OUS ANALYSES I.I
Temporal still
According to Hirtle (I977: 39), temporal still 'expresses continuance of [a) state'. While this definition certainly accords with our intuitions, most analysts have sought to provide a somewhat more precise definition of 'continuance'. Many have followed Horn (I970), in assigning to temporal still the function of relating two time phases, both of which are characterized by the presence of the same state of affairs. These phases have commonly been identified with presupposed and assertive components: according to Doherty (I973), Morrissey (I973). Konig (I977), Konig & Traugott (I982), and Abraham (I98o), still (a) asserts that some state of affairs exists or existed at a reference time and (b) presupposes that this same state of affairs obtained for some period prior to that reference time. In a tense-logic account of still's German analog, noch , Hoepelman & Rohrer (I98I) represent this presupposition of prior instantia tion by means· of overlapping phases: where j is a reference time, noch
atj is true iff j falls at the rightward boundary of an interval during which obtained. As shown in (4), this presupposition is preserved, as required, in polarity contexts. The entailment of (4a), that Bill was here for some period prior to the present moment, remains in a question (4b) and in a conditional protasis (4c): (4) a. Bill is still here. b. IsBill still here? c. IfBill is still here, we'll leave.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
ative likelihood of certain situation-outcome pairings. The general semantic structure of the operator constitutes the aforementioned semantic superstruc ture of still; these distinct domains of application yield its distinct senses. This study will be organized in the following fashion: the next section will provide a critical review of previous approaches to the semantics of temporal and concessive still-including that of Konig (I977), which we will take as our point of departure. This section will also establish some of the basic properties of the two senses. The third section will present an analysis of the three distinct senses. The fourth section will discuss issues related to the diachronic development of these senses. The final section will reconcile the senses, presenting the semantic superschema and relating it to Kay's (I989) class of contextual operators. This section will suggest that 'continuance' or 'persist ence' is best defined for our purposes as an abstract scalar conceptualization, i.e. one that does not necessarily involve temporal extension.
19X
'Continuity' wirhin Three Scalar Models: The Polysemy of Adverbial Still
(s) a. Bill (*still) caught the cat. b. Bill (*still) recognized Harry. c. Bill (*still) jogged. The class of perfective predicates subsumes both telic predicates (accomplish ments and achievements, as shown in (sa-b), respectively) and atelic predicates (activities, as shown in (sc)). Presumably, the unacceptability of (sa-b) can be explained within any of the aforementioned analyses simply by invoking a salient property of those predicates whichBennett & Partee ( I 978) have called nonsubinterval verbs . Such predicates (more commonly known as telic verbs ) code 'actions that involve a product, upshot, or outcome' (Mourelatos 198 r: 193); no subpart of that action counts as a valid instance of the whole event. Thus, for example, the inception of Bill's cat catching cannot be identified with the entire process. The instantaneous act of recognition simply has no extractable subcomponents.By contrast, a subpart of the action coded by the subinterval verb jog is clearly an instance of jogging. The telic-atelic distinction has-as pointed out by Dahl (r981), Mourelatos (op. cit.), and Vlach (1981)-a number of grammatical ramifications, and is subject to the following diagnostic: while, for example, the past progressive version of (sc) entails the preterite (sc), (sa-b), are not entailed by their respective progressive counterparts. If it is the case that, as claimed by Hom and others, temporal still requires that a given state of affairs persist from the presupposed phase to the assertoric phase, then the anomaly of (sa-b) can be said to arise from the nonsubinterval
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
(Note that the standard negation test is not used here: the peculiarity of examples in which negation has wide scope over still is perhaps due to the presence of a suppletive counterpart, anymore (c£ Morrissey 1973).) As noted by Traugott and Waterhouse (1969), the asserted and presupposed component states belong to a higher-order event whose aspectual class is imperfective. The still-bearing predicate then represents an imperfective process, in the sense ofLangacker (1987).A process, according toLangacker, is a 'relationship scanned sequentially during its evolution through conceived time' (p. 254). Imperfective processes-more commonly referred to as states-are those which do not involve a change over time-whose component relation states are effectively identical to one another. By contrast, perfective processes (nonstative predicates) portray a dynamic situation-one construed as episodic in character. A grammatical ramification of the perfective-imperfective distinction is, as noted byLangacker, that, at least in English, predicates of the former type do not occur in the simple present without a special interpretation (e.g. a habitual reading). As shown in (s), perfective predicates clash with the specifications imposed by temporal still (the reader is asked to ignore the acceptable concessive reading of still ):
Laura A. Michaelis
199
(6) A. How was Harry this month? B. He was still depressed. In the reply of (6), the asserroric phase represents a time span (a month), while the presupposed phase is probably another such interval. I will argue below that a 'moment' is best defined as the primitive or minimal unit of a temporally based scalar model (a time line), rather than as a pregiven measure of time (c£ discussion in Section 2.I of a similar point made in Herweg ( I 99 I b)). If still can be presumed to select from a time scale a point rather than a stretch of points
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
property: relic-verb scenarios do not possess the requisite identity among contiguous component states. In the case of accomplishments, each successive stage of the action is distinct; in the case of achievements, the coded event obtains within an interval-'at [an) isolated . . . instant . . . only' (Vlach I981: 277). The property of continuing throughout an interval then appears to be unique to subinterval verbs. This property is required by temporal still asserted and presupposed phases must represent identical situations. A problem is that, as noted, such subinterval verbs asjog also fail to co-occur with temporal still . This fact might cause us to sharpen up our definition of continuation. As far as temporal still is concerned, continuance of an activity of jogging (at least one coded by the nonprogressive) is not akin to continuance of the state of being here, etc. The distinction between the two types of subinterval verbs states and activities-has been noted by Herweg (I99Ib) and Taylor (I977), among others. According to this analysis, the subinterval property of activity verbs can be said to arise from a 'higher order' homogeneity, such that while individual components of the running scenario are distinct, a given span of running is effectively identical to a contiguous span. (The homogeneity of activity predicates often seems to arise from their cyclicity: in the case of running, the stride involves successive leaping motions characterized by an alternating 'trail leg'; the replication of this leaping motion gives the action an overall homogeneity.) By contrast, the homogeneity of state predicates can be identified at a finer level of granularity. All individual subcomponents of a state are identical to one another. There is no level at which such subcomponents are distinct: if one samples the state of'being here' at two distinct instants, those two samples will appear identical. The homogeneity of state predicates is thus appropriately defined with respect to moments other than intervals-the former being 'the fundamental units of time series', according to Bach (I 981: 66). This claim leads to the conclusion that temporal still serves to relate moments within the tenure of a state. While this conclusion appears correct, certain examples will require us to define what is meant by'moment' or'instant'. One such example is given in (6):
200
'Continuity' within Three Scalar Models: The Polysemy of Adverbial Still
within chat scale, then one can account for the fact that temporal still appears incompatible with durational phrases over which it has scope (7a). This explanation is parallel to that used to explain the incompatibility of punctual adverbs (like at 3 a.m. ) and durational adverbs, as in(7b): {7) a. Harry was still asleep (*for two hours). b. Harry was asleep (*for two hours) at 3 a.m.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
According to Herweg {1991a: 368), duracional adverbs likefor three hours 'Hx the minimum amount of time the situation occupies'; they hence entail downward with respect to the specified temporal boundary, but not upward. For example, if Harry was here for ten minutes, he was also here for nine minutes, etc. Thus, durational adverbs evoke a set of times at which a homogeneous predicate obtains. Given this feature of durational adverbs, we can explain the anomalous nature of (7b) in the following fashion: it is not coherent to assert simultaneously both that a state obtains at a single moment and that it obtains at a set of moments (irrespective of the reference time involved, which, as we will see, is the Hnal moment of the interval in the case of a durationally bounded state). It might, however, be difficult to base our account of (7a) on the afore mentioned account of (7b). Such examples as (7b) are problematic, for the following reason: punctual and durational adverbs invoke distinct reference times.While the punctual adverb maps to a reference time (3 a.m.) which is properly included within the state, the durational adverb invokes a reference time that is equated with the last moment of the coded interval (i.e. the cessation of the bounded state).The incoherence of (7b) might therefore arise from the fact that it is simply difficult to determine the appropriate time of evaluation for the sentence. (Use of the past perfect rather than past in (7b) would remove this indeterminacy-by identifying 3 a.m. with the last moment of the two-hour interval-and render the sentence acceptable.) Thus, one can conclude that the anomaly of (7b) does not stem from an inherent incom patibility between puncrual and durational adverbs, but merely from an indeterminacy as to the manner in which the 'viewpoints' invoked by the two adverb types are to be reconciled. Forrunately, there is another type of explanation for the incompatibility exhibited in (7a). Herweg (op. cit.) observes that states, unlike events, are not situational individuals; therefore, states cannot be counted.The interpretation of Harry hated cats three times requires that the count adverbial three times refer to occasions upon which the state obtained, rather than to hating 'events' per se (c£ also Mourelatos I98I). Herweg notes, however, that certain grammatical constructs provide an 'external criterion of individuation' (p.37I). The assignment of a duration to a state, for example, creates an individuated situation via the imposition of temporal boundaries upon that state.The state so
Laura A. Michaelis
201
(X) a. *Harry has still be unwilling to go. b. *Harry has still fed the cat.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
bounded 'loses' the subinterval property: no proper subpart of Harry's being asleep for two hours is a situation akin to the whole. The quantification of states is often said to be analogous to portion extraction of the spatial domain: a mass individuated via portion extraction becomes countable: two cups of margarine versus *two margarines . By the same token, according to Herweg, count adverbials in sentences like Harry was asleepfor two hours three times count 'atomic eventualites' rather than associated occasions. Given that quantized states are situational individuals, we can account for the clash in (7a) simply by likening this case to cases like (sa-b). In the latter cases, the failure of temporal still to co-occur with telic predicates was attributed to the nonsubinterval property of event predications. A proper part of being asleep for two hours is not an instance of being asleep for two hours; the internal heterogeneity of the quantized state does not allow for temporal extension (i.e. stasis over time). Such states therefore exclude temporal still. One problem with an explanation of this sort is the following: the anomaly of (sa-b) was said to stem from the fact that these events (like that coded by (sc)) lack the int�rnal homogeneity necessary to provide still with two phases of like kind: two component parts of an eventive episode are not identical. In the case of (7a), however, one can readily evoke a prior phase in which Harry was asleep. The asserted phase is simply a bounded instance of this same state; the durational adverb would in this case be augmentative: for another two hours . The identical presupposed phase is not a subpart of the quantized state itself, but a distinct earlier phase of that state. Under this interpretation too, however, (7a) is anomalous. This anomaly can again be attributed to the individuated construal supplied by the durational adverb. With Partee (1984), I assume that a state properly subsumes its reference time; i.e. reference time typically provides an internal perspective upon the state. Events, however, are subsumed by reference time; they afford only an external perspective. Quantized states, as events, lack a proper subpart at which the time of reference can be located. Such states then do not provide for the 'sampling' of a component moment by still . A distinct, although compatible, explanation is the following: in the case at hand, the presupposed phase is a state, while the asserted phase is an event (a quantized state); the two phases thus lack the identity required by still . They are not situations of the same type. An additional co-occurrence restriction, noted by both Hirtle (1977) and Hoepelman & Rohrer ( I 98 I ), is this: temporal still does not welcome the perfect aspect. This restriction will be motivated via reference to a presupposi tion connected to still-that of expected or possible cessation. The restriction is exemplified in (8):
202
'Conrinuiry' wirhin Three Scalar Models: The Polysemy of Adverbial
Still
R '----�w· ----------- R
----
-----+
W
Figure 1
In Figure I, the time line of speaker's execrations (W ) contains a reference· time analogous to that located on the time line of 'speaker reality' (W). A state of affairs (represented by the boldface segmented line) continues up to (and perhaps beyond) R in W. In W', this state of affairs has ceased at some point prior to R' (the counterpart of R in W' ). Thus, under the Hoepelman & Rohrer account, still has two presuppositions: (a) the presupposition of prior instantiation of the state in W and (b) the presupposition of cessation at R' in W '. The latter presupposition is reflected in the intuition that a sentence containing temporal still is uttered only when there is some possibility that the state of affairs in question might have ceased at R. 2 Such sentences as (9) are odd: '
(9) *Uncle Harry is still dead. This oddity is explained by the fact that the speaker cannot (ordinarily) countenance a world W' in which Harry is resurrected at some point following
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
If we presume that still has wide scope with respect to the perfect operator, examples like (8) appear to undermine the validity of accounts in which the perfect is viewed as an operator that maps an event predication into a state predication denoting a result of that event (Herweg I99 I a). The reference time at which this state obtains is established by the tense of the auxiliary head, the stative have (Klein I992). Evidence for the stative nature of perfect predications is provided by facts of the following sort: perfects (a) accept the temporal adverb now (i.e. are evaluated for the present moment) and (b) accept sentential adverbs like already, which otherwise scope only state propositions. If perfect-form sentences are state predications, however, why should they fail to accept temporal still? One line of explanation is suggested by Parsons ( I 990 ). According to Parsons, the result state entailed by sentences like (8b) is merely that of the event's having culminated at some point prior to now. A more specific result (e. g. the presence of a fed cat) is contextually inferred; the result entailed by the resultative perfect perse is indeterminate (cf Fenn I987). Parsons argues that this state of aftermath 'cannot cease holding at some later time' (p. 234). A view of this sort is assumed in the Hoepelman & Rohrer account of sentences like (Sb). They assume, as I do, chat temporal still evokes a 'world of speaker's expectations' in which the state coded by the still-marked predicate has ceased at the evoked reference time (R). This expected cessation contrasts with the state's actual continuance to R. A diagrammatic representation of this situation is given in Figure I, adapted from Hoepelman & Rohrer.
Laura A. Michaelis
203
(8) b.' Harry has still only FED the cat. In (8b '), the small caps indicate a point of prosodic prominence denoting a narrow or contrastive focus. This focus is imposed by the scalar operator only , which scopes the perfect-form proposition, Harry has fed the cat. Following McCawley (I987), we can view only as indicating that the proposition in which it appears denotes a less 'extreme' situation with respect to a scale along which situations of a given type are ranked. The situations in this case relate to kind nesses that Harry might bestow upon the cat. This model presupposes that feeding of the cat is a lesser kindness than, say, grooming or entertaining the cat. Only imposes an upper bound upon the proposition Harry has fed the cat , relative to the scalar model at issue; Harry has performed the kindness specified but no greater kindness. If only were absent, the proposition would be upward compatible vis-a-vis the scalar model; it would in fact be entailed by any proposition occupying a more advanced point in the model (Harry has walked the cat, etc.). By removing the upward compatibility of the proposition, only creates a predication which denotes a situation susceptible to change. That is, unlike (8b), (8b') does not denote a state that is eternally valid. The state which consists in aftermath of a cat-feeding event will never change. By contrast, the state consisting in the aftermath of a cat-feeding event simpliciter (i.e. one unaugmented by any further cat-benefaction event) will change at all and any points following the occurrence of a further act of kindness. The foregoing account of the incompatibility exhibited in (8b) has the advantage of generalizing to that exemplified in ( 10):
( 10) *Uncle Harry is having gone.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
his demise, as would be required by the schema in Figure I. Hoepelman & Rohrer argue that this schema also conflicts with the semantics of the resultative perfect. The resultative perfect denotes the occurrence of an event whose resultant state is eternally valid thereafter. With respect to the semantic contributions of still and the perfect operator, sentences like (8b) are self contradictory. Because it is a resultative perfect, sentence (8b) asserts that the aftermath of the past cat-feeding event obtains at present (R). Because it contains still , (8b) presupposes that this state of aftermath obtains at some point prior toR In addition, according to Figure I, the sentence presupposes that this state does not continue to R' in W'. However, the speaker who chooses to use the resultative perfect cannot be said to expect that the state of aftermath will have ceased at R. The presupposition of expected cessation at R conflicts with the assertion that the state of aftermath obtains at R This situation is complicated somewhat by the interaction of upper bounding scalar operators with the perfect and wide-scope still . As noted by a reviewer, such sentences as (8b ') are acceptable:
204
'Conrinuicy' within Three Scalar Models: The Polysemy of Adverbial Still
As shown in (Io) , the perfect does not progressivize. This fact does not appear
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
difficult to explain: auxiliary have is stative; since the progressive functions to derive a stative predication, stativization of an inherently stative predication is merely redundant (Langacker I 987; McCawley 197I; Vlach I98 I ). A number of authors have noted, however, that there are conditions under which states do progressivize. One commonly encounters progressive sentences like Harry is liking your sister more and more . Such examples are in fact used by Akmajian, Steele & W asow (I979) to refute the view that the prohibition against progress ivization of the perfect has a semantic basis. In order to maintain a semantically based account of the anomaly of (10), we must explain why progressives like (10) are unattested. As noted by Langacker (I99I), this requires that one identify the conditions under which stative verbs can progressivize. According to Langacker, statives amenable to progressivization are those which denote an unstable state of affairs-one which is subject to imminent or incremental change. (Under the heading of imminent change, we include transition to a state of 'failure to obtain', i.e. cessation.) If, as in our example, the degree of affection exhibited by Harry is increasing each day, then the situation is evolving toward a point of culmination. The progressive operator in some sense arrests the development of that situation toward its endpoint, capturing its 'in progress' state. The impossibility of sentences like (10) is said to arise from the fact that the state of aftermath can never change-it can neither culminate nor cease. It is thus inherently nondynamic. Since the progressive operator, like temporal still , presupposes that the 'input' situation is one susceptible to change, it is incompatible with the resultative perfect. Given this mode of explanation, we preserve the assumption that the perfect, like the progressive, is a stativizing operator. The aspectual class of the perfect is then identical to that of its auxiliary head. Another type of explanation sees the perfect not as a stativizing operator but as a completive marker upon event predications. This type of explanation is offered by Hirtle (I977). According to Hirtle, there exists an effective equivalent between still and the temporal adverb during. In essence, this claim reflects the intuition, mentioned above, that reference time provides an internal perspective upon a state. Hirtle provides the following account of sentences like (8b): 'one cannot reconcile the position of interiority expressed lexically by still with the position of posteriority expressed grammatically by the [perfect] aspect' (p. 38). With respect to its 'position of posteriority' vis-a-vis an event, the present perfect does not differ from the preterite; both present an event as having culminated at some time prior to speech time. In this respect, Hirtle's account of (8b) resembles that provided for the starred sentences in (s): temporal still does not accept perfective predicates, i.e. those which denote events that are fully instantiated upon reporting of their occurrence. The question now arises as to whether either. account of (8b)
Laura A Michaelis
:zos
extends to that perfect involving an imperfective complement-the continua tive (8a). The validity of Hirtle's account hinges upon the assumption that the continuative equatesR with the time of cessation of the coded state. As noted by Morrissey(I97 3), however, continuative perfects are in general ambiguous as to whether or not R provides a 'rightward boundary' upon that state. In such sentences as (I 1 ), continuation of the state past reference time is a virtual certainty:
( I I) Our Dalmatian has been deaf since birth. Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Hence, the continuative perfect does not evoke a posterior reference point in the sense that the state at issue ceases at or before R Instead, according to Chafe (I970: I72), sentences like(8a) and(II) evoke a construal in which 'everything is understood to obtain at the time of reference, as in a nonperfective [=non perfect] sentence, except that the beginning of the state .. . is pushed back to an earlier time'. In other words, the continuative asserts the existence of a span of time stretching from the inception of the state to(at least) R The left boundary of this span may be marked by a since adverbial(as in(II)), or the span itself may be denoted by a durational adverb (e.g.for the last three years). Like a durational, the continuative is downward entailing(with respect to the right boundary): if, in I992, Harry has been in therapy since I989, then he has also been in therapy since I991, I990, etc. Further, the continuative resembles a durational in that the state denoted by the complement verb is not upper bounded with respect to the right boundary: the state in question might continue beyond R Finally, the continuative, like a durational adverb, represents a grammatical means of individuating a state.According to Herweg (I99Ia: 3 7I), 'the occurrence of a phase of a state is an event'. Our explanation for the anomaly of (7a) is then applicable to (8a) as well. Bounded states, as events, lack the subinterval property, and thereby reject temporal still. As in the case of(7a), the anomaly of (Sa) persists even when an apparently identical prior phase is invoked.Sentences like the following are peculiar: ??Harry had been unwilling to go until yesterday; in fact, since then he has still been unwilling to go . Here again, the two phases are only superficially similar: as bounded states, each is a distinct episode. Historical evidence indicates that the incompatibility exhibited by (8a) was not always present: temporal still at one time served as a durational adverb akin to constantly or continually (Kemmer I990). In this capacity, still co-occurred with the continuative perfect, the former being in the scope of the latter. Kemmer provides the following citation from I704: '... his past reign, which still has been attended with one continu'd Series of Misfortunes'. The diachronic meaning shift in which, according to Kemmer, temporal still changes from a frequency adverb to a temporal reference point yields a concomitant prohibition upon its co-occurrence with the continuative perfect.
206
'Continuity' within Three Scalar Models: The Polysemy of Adverbial
Still
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
States quantized by the continuative have an episodic construal, and hence cannot properly subsume this reference point. For this reason, (Sa) is anomalous. A difficulty with this line of explanation arises when one recalls that the aspecrual character of the perfect, continuative or otherwise, is determined by that of the auxiliary head, not by that of the complement (the latter being a bounded state in the case of the continuative). As the auxiliary head here is a straightforward state; why should there not be the possibility of a scoping in which the stative predication represented by the perfect auxiliary falls within the scope of still? One answer to this question is suggested by Mittwoch's(1988) analysis of the continuative. In providing truth conditions for the continuative, Mittwoch (p. 218) specifies that the reference time must be the final moment of an interval in which the state denoted by the participial complement obtains. In this respect, the continuative perfect does provide a posterior reference point: reference time is equated with the cessation of one phase of the state, in much the same way that reference time is equated with the culmination (or endpoint) of an event. Here again, use of still is incompatible with the retrospective or external viewpoint invoked by the continuative perfect (and by event predications in general). Of course, as noted, the continuative perfect, like the resultative perfect, differs from a preterite-form event predication in that only the former is stative. Nevertheless, the state at issue is one which cannot be regarded as persisting from an earlier point. The state is the last moment of a phase; no earlier point within that phase is identical to this moment. The interaction of still and continuative is further constrained by the presupposition of possible cessation: the situation denoted by a continuative perfect is one in which a phase of a state has occurred. This phase cannot 'cease' to exist once it has culminated. Therefore, a speaker cannot be said to evoke a possible world in which the phase has ended. Of course, this explanation is identical to that given for the anomaly produced by the interaction of still with a resultative perfect (8b). The incompatibility of perfect and temporal still does not extend to negated perfects: such sentences as You still haven't answered my question are acceptable. Negated perfects are construable as continuative (i.e. universal): for all times within a present-inclusive range there is no event of question answering. These perfects are also construable as existential perfects bearing external negation (c£ Mitcwoch 1988): it is not the case that there was an event of question answering with a present-inclusive range of times. The equivalence between existential and continuative understandings disappears when a downward entailing bounding durational is added: He hasn't answered my question for twenty minutes can only be continuative. As such, this sentence will reject temporal still for the reasons given above. Negated perfects accept still on the externally negated existential reading only. Why should this be the case? Under (external)
Laura A. Michaelis
207
negation, the existential perfect simply denies the existence of some event within a specified range of times; the continuance asserted by still is not directly related to that event but is simply continuance of this deniability. The interaction of still and negated existential perfect is constrained by the presupposition of possible cessation. The state of there not having been an event of a given kind must be a state capable of ceasing. The state of there having been no answer to a given question would cease were that question to be answered. Nonnegated existential-perfect sentences like *Harry has still been there three times are, however, anomalous. Our explanation for this fact will closely resemble the explanation given for the oddity of (8b ). Numerals are downward entailing and, crucially, upward compatible (barring upper-bounding implicata). Therefore, any further accumulation of visits by Harry will not negate the truth of the proposition Harry has visited three times . This proposition will be entailed by, for example, Harry has visitedfifteen times . However, as noted with respect to the resultative and continuative perfect examples in (8), existential perfects containing an upper-bounding scalar adverb do accept still : Harry has still only visited three times . Here, the presence of only (like at most) removes the upward compatibility of the numeral expression. The numeral expression no longer denotes the ascending half line from three to infinity. Therefore, one can imagine the cessation of a state of there having been three visits; cessation of this state will occur when there is any additional visit. Hence, the possible-cessation presupposition of still is satisfied in such instances. Given that the foregoing account has made reference to a 'presupposition' of expected (or possible) cessation, we must ask the following question: is the oddity of (9) in fact due to presupposition failure? Konig (1977) suggests that sentences like (9) simply flout a quantity implicature, owing to their lack of information value. It is useless to assert the continuance of a state where the siruation could not be otherwise. In this respect, (9) does not differ from the corresponding sentence without still, when the latter sentence is not newsworthy. Quantity implicarures attach to assertions. For this reason, we would expect that nonassertive versions of (9) would be acceptable. This expectation is not confirmed. As shown in (12), (9) is not improved when it is cast as a yes-no question or conditional protasis: '
b. *If Uncle Harry is still dead, we'll be upset. Because it is present in nonassertoric contexts, we will regard the constraint of expected cessation as a presupposition of temporal still' rather than a quantity implicarure. I will argue that the paired-scales schema which represents this presupposition (Figure 1 ) also underlies the nontemporal senses of still .3
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
( 12) a. *Is Uncle Harry still dead?
208
'Continuity' within Three Scalar Models: The Polysemy of Adverbial Still 1.2
Concessive still
[t]he assertion that 'q continues' given another fact p gives rise to the generalized conversational implicature that this persistence is remarkable or unexpected and that therefore p and q do not normally go together.
Conventionalization of this implicature of expectation controversion is said to underlie the diachronic shift in which markers of temporal extension develop concessive meanings. The adversative implicature, although calculable, might nevertheless be regarded as conventional. It resembles a'short-circuited' conversational implicarure, in the sense of Morgan(1978). Since it is inferrable, the relationship between continuance and concession is synchronically transparent; persistence of a state despite adversity entails the continuance of that state. In such examples as (IJ), the two understandings are present simultaneously: (13) I studied all night, and I still don't understand it. Speakers would be hard pressed to resolve the ambiguity of ( I J) in favor of one or the other sense: the state of ignorance continues despite the intervention of an effort to end it.Temporal continuance is also involved in such adversative examples as (14): (14) Yes, Harry beats his dog.Still, he's a nice guy. In (14), a 'true conce�sive' (see Section 2.2 below), the validity of a claim is upheld despite the presence of an apparently reasonable counterargument. We might say here that the validity of the original assertion 'persists' despite an effort to impugn it. The lexeme still might then be said to subsume both an implicarure-free understanding and an understanding linked with Konig & Traugott's adversative implicature.This appears to be the analysis that Konig &
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Most analysts concerned with temporal still have also focused upon its nontemporal descendant, the concessive or adversative sense. In this usage, according to Quirk et al. (197�: 164), still expresses 'the unexpected, surprising narure of what is said in view of what was said before that'. For a number of these analysts (notably, Greenbaum 1969; Hirtle 1977, and Konig & Traugott 1982) the use of the word still to express both temporal and concessive meanings provides evidence for a 'strong relationship between "continuation" and "concessiveness"' (Konig & Traugott op. cit.: 178). There is general agreement upon the narure of this relationship: continuance of a given state of affairs is akin to persistence despite adversity whenever the context evokes a factor which would seem to militate against the continuance of this state of affairs.Thus, Hirtle (op.cit.: 42) remarks,'... [adversative] still characterizes the relationship as continuation in spite of an intervening element'. Konig & Traugott (op. cit.) maintain:
Laura A Michaelis 209
Traugott have in mind when they say, 'the original meaning . . . of . .. still account[s] for . . . the concessive use . . . of [this] particle . . .' (op. cit.: I 7o). A seemingly insurmountable difficulty for a polysemy analysis of this sort is, however, posed by sentences of the class exemplified in ( I 5- I 6}, for which we lack early citations:
( I s) Even though he studied all night, Larry still failed the test. ( I 6} Even if you gave him a raise, Harry would still quit.
(I 7) Even ifBill pays me $200, I'm still not going to do it. According to Konig, still makes the following semantic contribution to( I 7): still induces an ordering in which various favors (including sums of money) are bestowed upon the speaker by Bill. The situation described in the first clause is the 'advanced case'. (p. 1 95).
Konig argues that sentences containing adversative still can be translated into a logical formula ·in which still is in construction with a clause and an
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
In (I S-I6}, still is coupled with verbs denoting events, foil and quit . There is no possibility of regarding the event in question as having persisted despite hostile factors. We understand in such sentences that the event in question (Larry's failing the test. Harry's quitting his job) happened or would have happened despite the presence of circumstances which one would expect to preclude that event. In such sentences, still does not evoke the continuance of a state over time. Although it is not clear what diachronic meaning-shift yielded that variety of concessive still compatible with event predications, this usage is clearly not related to the temporal usage in the manner suggested by Konig & Traugott. These examples provide evidence against the claim that the temporal and adversative sense are synchronically related in a manner which mirrors the development of the latter via conventionalization of the adversative implica ture. Given such evidence, we might either (a) presume that the adversative sense is synchronically unrelated to the temporal sense, or (b) propose that the senses are linked by another synchronically valid inference pattern, distinct from the adversative implicature. Alternative (b) will be investigated here.Admittedly, this choice reflects a theoretical bias: a presumption in favor of lexical polysemy over homonymy, i.e. that speakers will forge sense relations where such generalizations are plausible. Aside from this, however, it would seem that the presence of examples like (13), in which the senses coexist, would induce speakers to view adversative and temporal understandings as related. Speakers may relate the two senses on the basis of shared scalar-semantic properties. The scalar nature of adversative still , and of concessive semantics in general, is noted by Konig(I 977), with respect to examples like (I 7}:
2. 1 o
'Continuity' within Three Scalar Models: The Polysemy of Adverbial Still
abscracc. The abscract contains a conditional operator, as well as the conditional apodosis. The formul� is given in (18):
( I 8) (still, p (J.. x, (NOT (x - q)))) A rough paraphrase of ( r 8) is as follows: 'it is still the case that a given situation (here, p) does not entail another situation (q)'. In other words, the state of affairs p is one of several situations which fail to bring about situation q. A cranslation of( I 7) via (18) is the following: 'payment to me of $2oo by Bill still will not have the result of causing me to do the task in question'. The protasis is a scalar excreme; Konig notes (ibid.):
Although this analysis captures certain important insights about adversative still , the formula of(I 8) appears to diverge too widely from the syntax to which it is mapped. The formula incroduces a negative operator which does not necessarily have a surface realization. In ( I 9), the apodosis is positive:
( r9) They didn't offer him first aid, but he still survived. The formula in ( r 8) would require us to translate the assertion that the patient survived under adverse circumstances into a proposition of the following sort: the extreme case (lack of help) still failed to cause the eventuality of dying. A similar type of decomposition is necessary in (2o): (2o) They tried to help him, but he still died. Konig's logical representation would rework (2o) into a proposition of the following sort: the extreme case (rendering of aid) still failed to cause the eventuality of survival. That is, living is failure to die, while dying is failure to survive. The presence of such circularity in our logical cranslations of concessive assertions is an undesirable result. An additional problem with Konig's analysis is the following: it does not give us any insight into the meaning that still contributes to concessive conscructions. Konig notes that still is omissible in sentences like (I7); from this fact, he concludes that still might not provide the interpretative framework( 1 8) in concessive sentences. He does not consider the option that still reflects, rather than imposes, the concessive understanding. Further, Konig's analysis fails to account for the speaker's scrong intuition that such sentences as (17) and (I9-20) code an event that violates expectation. He notes with respect to ( r 7) chat the situation expressed by the protasis would otherwise be expected to have an opposite effect (the speaker's doing the requested task). He does not, however, explicate the manner in which
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
still induces an ordering between the situation described and other comparable situations. None of these situations can bring about the situation described in the consequent, even though the situation denoted by p is an advanced case which could be expected to have this effect.
Laura A. Michaelis
21 1
expectation contravention arises from concessive semantics-particularly, the scalar properties of this semantic structure. While his treatment of the concessive sense is problematic, Konig's analysis does succeed in delineating unifying semantic features of the senses. He states (p. I 87): our analysis . . . shows that there is a close relationship between [the] interpretations of noch ['still'] . . . and rhus accounts for the fact that they are associated with the same phonetic form. Noch [is] implicative under [all] interpretations. [All] interpretations involve the selection of certain entities, points in time, or entities of a different sort, as well as the introduction of an order relation for them.
2
2.1
THE S E N S E S Temporal extension
Temporal still can be regarded as a scopal operator (Kay I 990). Operators of this type express a relationship between two propositions; one of these propositions is represented by the assertion containing the operator. This assertion is termed the 'scope' of the operator. Hence, in (2 I) the scope is Grandma lives on the Lower East Side : (2 I ) Grandma still lives on the Lower East Side. Temporal still , as noted by Konig ( I 977), is thus implicative, in the sense of Karttunen ( I 97 I ). The scope carries a tense specification; the tense has narrow scope with respect to still (pace Konig I 977). The tense can be represented as a two-place relation: 'obtains at' (c£ Taylor I 977, in which the tense specifier is an additional argument of the main predicator of the proposition). The first argument of this relation is the scope. The second argument is an interval, which is identified with the reference time invoked by the tense operator. The reference time is the present in (2 I ). As mentioned, I will follow Partee ( I 984) in proposing that a state subsumes its reference time. As noted above, reference time provides an internal perspective upon the state. Events are characterized as having an opposite 'direction of inclusion': events are contained within the reference time. This reference time is necessarily interpreted as an interval, capable of accommodating the dynamic profile of the perfective episode. The rightward boundary of the reference interval is equated with the event's point
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Of course, the temporal sense does not merely involve the ordering of'points in time', but also the disposition of some state of affairs across these time points. Further, the nature of the ordered 'entities' remains to be explained; what are the scalar ontologies in question? It is the task of the present analysis to provide a clearer picture of the semantic commonalities observed by Konig.
212
'Continuity' within Three Scalar Models: The Polysemy of Adverbial Still
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
of culmination. Parsons ( 1 990) uses a two-place operator Cui (e, t ) to indicate that an event culminates at a point, this point being properly included within the reference interval. By distinguishing between events and states in this fashion, we account for the following intuition: an episode (event) is wholly instantiated within the reference interval; whereas a state obtains for an indefinite period. We can say that a state 'overflows' the bounds of the reference time, in so far as an interpreter is free to imagine a larger interval, which encompasses the time for which the state is asserted, and for which that same state also obtains. In arguing against this view, Herweg (1991a: 384) provides examples like the following, in which reference time apparently exhausts the tenure of the state: Yesterday, Harry was in London . Here, the reference time, yesterday, is readily construed as subsuming the state. (A reading in which yesterday is subsumed by the state is perhaps dispreferred via quantity: if the speaker knows that Harry lives in London, why should she assert his presence there with respect to one day?) An answer to Herweg's objection is the following. Reichenbach-sryle theories of tense assume that the reference time is the time of adverbial reference. Klein (1992) has shown that this is not necessarily the case; he notes, for example, that a temporal adverbial accompanying the past perfect can refer to either event or reference time. Whereas we must retain the claim that all tenses have a reference time (whether or not distinct from event time), we need not assume that all temporal adverbs denote the reference time. With respect to Herweg's counterexample, it is useful to follow Parsons ( 1 990) in distinguishing between reference time and rime-limiting adverbials. According-to Parsons, '[t)he same period of time that is constrained by the tense of the sentence may also be constrained by temporal modifiers' (p. 209). Parsons notes sentences like Yesterday, Brutus stabbed Caesar, in which the temporal adverb yesterday properly includes the temporal interval (i.e. the reference rime) in which the stabbing event culminated. In Parsons' example, tense and temporal modifier interact in the same way that they do in the more felicitous reading of Herweg's example. The temporal modifier subsumes the reference rime. There is nothing to prevent us from maintaining that the reference time itself is subsumed by the state. However, given the requirement that reference time represents a proper subpart of the interval denoted by the time-limiting adverbial, one cannot account for the alternate reading ofHerweg's example. In this reading, yesterday refers to the reference time; the reference time is again subsumed by the state of Harry's presence in London. The presence of this reading suggests that the reference time should be improperly included within the interval referred to by a temporal adverb. The possibility of coalescence between the two forms of time reference (tense and time adverb) does not detract from the claim that they are otherwise distinct; identity of the two is simply the limiting case of
Laura A. Michaelis
213
(22) Harry was still upset. Following Konig & Traugott, among others, we can represent the propositions mediated by still in (22) as in (23): (23) asserted: [(Harry be upset] obtains at' t] presupposed: [(Harry be upset] obtains at' t - I ] The question arises as to whether times associated with the presupposed and asserted phases mediated by still are best described as moments or as intervals. With respect to the asserted phase, the question can be framed in the following manner: is the reference time situated within the state a point or a span of time? Earlier, we concluded that temporal still has a punctual character: it functions to 'highlight' a component moment of an imperfective process (Langacker I 987). An apparent difficulty with this view arises when one considers sentences like (24): (24) This week, Clinton is still the frontrunner. The 'moment' at which the scoped proposition obtains is a week-long interval. One need not, however, regard (24) as a counterexample to the claim that temporal still selects a 'moment' within the tenure of a state. As noted in Section 1 . 1 , we need not view a moment as a temporal unit of any particular length. Intuitively, a moment is a minute or so, and it seems odd to refer to a week as a 'moment'. Equally intuitive, however, is the notion that every time line has a minimal unit of measure, and this unit may be small or large with respect to 'absolute' measures of time. Herweg ( 1 99I b: 982) makes a similar point, noting that it is futile to attempt to distinguish intervals from moments without considering the temporal units relevant to the cognizer:
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
inclusion. The distinction between reference time and time-constraining adverbials allows us to preserve the assumption that the reference time of a state is properly included within that state. Thus, the state referred to by the proposition within the scope of still subsumes its reference time in all cases. Still serves to relate the tensed state proposition within its scope to a presupposed proposition. The presupposed proposition is identical to the scoped proposition, except that the former represents the state of affairs as obtaining at some point prior to the reference time. As noted by Konig & Traugott ( 1 982), sentences like (2 I) bear a presupposition of 'prior instantia tion': (2 I ) presupposes that Grandma lived on the Lower East Side at some point prior to now. Note that the presupposed proposition need not bear a tense specification distinct from that of the asserted proposition. In (22), both asserted and presupposed propositions bear past tense; the presupposed interval is simply prior to the (implicitly specified) past reference time:
2. 1 +
'Continuity' within Three Scalar Models: The Polysemy of Adverbial Still
Since on the conceptual level we deal with mental representations of rime, we should rather say that viewing a period of rime as poinrlike means that irs internal structure is cognirively neglected as a matter of the granularity of perspective taken by the subject. Thus, we allow that one and the same temporal entity be represented as a poinrlike or complex rime depending on rhe situation.
... > [R/t ] Ti > [R/ti+IJ T.I+ I > [R/ti+2J Ti+2 > ... C
i
c
c
Figure 2
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
In the context of this analysis, 'situation' is to be construed as the particular time line invoked in the interpretation of the still -bearing sentence. A time line is a two-dimensional scalar model (Fillmore, Kay & O'Connor I 988; Kay I 990), in which some situation (a component state of a process} is coupled with a point at which it obtains. Sentence (24) presupposes a time-line model for a presidential campaign. Its 'primitive' is a week. The minimal unit of the time line evoked in (2 I } may be a year. Given this framework, we use the term 'moment' to code any minimal unit of a time scale. A moment is, as usual, opposed to an interval-a grouping of moments. Under this view, still 'selects' that portion of a state which obtains at a moment, rather than that which obtains at an interval. While time lines often code a course of development, the time line at issue here codes persistence of a given state of affairs. The sequence of component states arrayed across the time line are identical to one another. An overall perception of stasis is expressed by the evocation of two component moments of an imperfective process. It should be noted that this analysis explicates the semantics of temporal still at two levels. At one level, still is viewed as a scopal operator, which mediates between presupposed and asserted propositions. The two propositions code the same state of affairs. At another level, still is said to express persistence of a state of affairs across time; it highlights an 'advanced' instance of that state, which obtains at reference time. It is at this second level that the scalar nature of temporal still emerges most clearly; still operates upon a scalar model of persistence. The origin of this scale is equated with the inception of the state in question. A diagrammatic representation of the second type of explanation is provided by the scalar model given in Figure 2. At first glance, this representation does not seem to qualify as a scalar model in terms of Fillmore, Kay & O'Connor (I 988} and Kay ( I 990). In models presented by these authors, an 'argument space' is represented as a set of coordinates, such that the resulting structure is a lattice: an argument space is a set of diads, each member of which is culled from a distinct ordered set or scale. The two distinct scales are the two dimensions of the model: values along one
Laura A Michaelis
21s
__
Harry upset <-Harry upset ---� R'
__
Harry upset < Harry upset R
---�
W' W'
Figure 3
In Figure 3, as in Figure I , the paired time lines represent models of the speaker's expectation (W ') and of reality as conceived of by the speaker (W). As shown, both 'worlds' are defined by presence of Harry's upset state prior to reference time (R). We can view the tenseless propositions in Figure 3 as component states of the imperfective process schematized in Figure 2. As shown, a component state of the process obtains at R in W. There is no component of that state at reference time in W '. Thus, Figure 3 represents the digitization of Figure I : persistence is represented as the presence of two identical component states at contiguous scalar loci; cessation is represented by the lack of such a component state at the more advanced of these loci. The two levels of representation-propositional and scalar-are compatible, in so far as temporal still represents a scalar operator. Scalar operators, like even and only (Kay I 990; McCawley I 987), relate two propositions within a scalar model. In the case of even , according to Kay, the even -bearing assertion or text proposition (TP) unilaterally entails a contextually given proposition (CP). An example is given in (2 5): (25)
Did Harry come by? (CP) B: Yes. Even Fred showed up. (TP). A:
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
dimension are arrayed along the ordinate; values along another dimension are arrayed along the abscissa. In this analysis, scalar models, temporal and otherwise, will be 'collapsed', with one dimension (e.g. states of affairs) superimposed upon the other (e.g. times). One reason for doing this is simply that readers are more accustomed to horizontal representation of time lines, in which some succession of developmental stages is arrayed along a time scale composed of ascending values arrayed from left to right. The use of this linear format for nontemporal scalar models as well will afford a clearer view of what is meant by 'scalar continuity'. In Figure 2, the semantic contribution of temporal still is schematized by a boxed component state within the imperfectivity scenario described by Langacker ( I 987). This component corresponds to the reference time-the point at which, in Langacker's terms, the conceptualizer situates herself This representation does not show us the presuppositional properties of temporal still: the presuppositions of prior instantiation and of expected cessation at R These are more clearly portrayed in a representation of (22) given in Figure 3, analogous to Figure I :
216
'Continuity' wirhin Three Scalar Models: The Polysemy of Adverbial Still
(26) [[Harry is upset] obtains at' x] In (26), the variable ranges over time specifications. To summarize, then, temporal still evokes a two-dimensional scalar model, termed a time line. This time line matches some subpart of a state with the time point at which it obtains. In particular, temporal still requires a time line characterized by effective homogeneity of these subparts. This type of time line is identical to Langacker's imperfective process, in which a moment of conceived time is linked to a single relation-state (trajector-landmark pairing). Temporal still 'samples' from the imperfective process at reference time, licensing the inference that one or more components of this same process lie at points closer to the origin of the processual sequence in question. On the propositional level, temporal still relates two tensed propositions within a time-line model. The text proposition presupposes the context proposition (i.e. entails the CP in both assertive and nonassertive contexts). 2.2
Transspatial persistence
Concessive still , as its name implies, is found in various concessive ·constructions. The term 'concessive construction' is used here in a rather imprecise sense; it is not the case that each concessive type represents a unique form-meaning pairing. As Konig observes (1 986), diverse syntactic templates
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
The reply in (25) evokes a scalar model in which invitees are ordered with respect to the likelihood of their arrival. Fred is regarded as less likely to come than Harry. His presence at the event then unilaterally entails Harry's presence. The semantic material shared by CP and TP can be represented as a propositional function: [x showed up]. The TP contains a focus: that constituent that contrasts with some constituent within the CP, and which is represented by a variable in the propositional function. The focus in this case is Fred , which accordingly receives prosodic prominence (c£ Lambrecht (forthcoming) on the prosodic realization of narrow focus). One difficulty with assimilating temporal still to the class of scalar operators is the following: while still mediates between propositions within a scalar model, it does not appear to select a focus within its 'text proposition'. No linguistic element within this proposition receives focus accent. Nevertheless, there is a contrastive element in the semantic representation: the time specification of the text proposition, which contrasts with that of the presupposed proposition. The time specification of the assertion has a higher value than the time specification of the presupposed proposition; the former is further removed from the origin of the time line. Thus, the semantic material shared by the asserted and presupposed proposition in (23) can be represented as a propositional function of the following sort:
Laura A Michaelis 2 1 7
are drafted into service as concessives: conditionals, coordinate structures, and temporal clauses. The class of concessive constructs (although having such reliable formal concomitants as the factive subordinator although ) is more readily definable in semantic and pragmatic terms. Such a definition will be provided in what follows. First, it is necessary to draw a functional distinction between 'true concessives' and those concessives which might more accurately be referred to as 'adversative constructions'. As mentioned in Section 1 .2, concessives of the former type refer to the domain of argumentation. An example is given in the reply of (27): (27)
In (27), speaker A provides a potential counterargument to the claim that Berkeley is a desirable habitat. While conceding the validity of this argument, speaker B asserts that the claim so impugned can none the less be upheld. Hence, the reply in (27) includes both a concession to the conversational opponent and a reassertion of the impeached claim. The concession is coded by the expression even so , which is anaphoric to A's counterargument. The reassertion is coded by the main clause. The reply need not contain the concessive clause, in which case the concession is implicit in the reassertion. This type of concessive can be juxtaposed to those exemplified in (28-29): (28) Even though Harry apologized, Marge still left in a huf£ (29) Even if he loses twenty pounds, Harry will still fail the physical. In (28), a factive concessive, Marge's leaving is asserted to have occurred despite an effort to obviate the event. In (29), a concessive conditional, it is asserted that Harry's weight loss would not prevent his failing the physical. These concessives do not refer to the domain of argumentation. Since they do not function to concede the validity of the counterargument, they are not concessives in the strict sense. The antecedent and consequent code real-world situations, which are understood to be antithetical to one another. The sentences presuppose that the situation described by the protasis4 ordinarily entails the lack of that situation-coded by the apodosis. In terminology to be used here, the protasis establishes a world (whether actual or hypothetical) which is adverse to that situation or outcome coded by the apodosis. As mentioned in Section 1 .2, there are certain concessives in which still appears to have both temporal and adversative understandings. These are sentences in which the main predicator of the apodosis bears imperfective aspect. An example is given in (3o): (30) Mom has starved herself for a month, and she's still thirty pounds overweight.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
A There are a lot of strange people around here. B: Even so, I'd still rather live in Berkeley than anywhere else.
21 H
'Continuity' within Three Scalar Models: The Polysemy of Adverbial Still
(3 1) She hated the noise, but she still lived there for several months. (32) The political climate has improved, but times have still been difficult in Dubrovnik. In addition, as noted in Section I .2, concessive still accepts inherently perfective predicates, while temporal still does not. An example of the former situation is given in, for example, (28): still is here coupled with leave , an achievement verb. Th�se grammatical differences can be attributed to the distinct scalar ontologies evoked by concessive and temporal still . While temporal still codes the continuation of an imperfective process from one moment to the next, concessive still codes the persistence of an outcome (or state of affairs) from one set of circumstances to another. Sentence (29), for example, asserts that the outcome of Harry's failing the physical will obtain whether Harry is twenty pounds overweight (as he is now) or whether he sheds this weight (at some future point). Temporal still takes an internal perspective on a state: it 'samples' a component of this state at an advanced time point. By contrast, concessive still views the event or state in its entirety-as an episode or situation that obtains under specific (unfavorable) conditions. A state so viewed may represent a grammatically individuated situation, and hence that state may be described via the continuative perfect (32) or bounded by a durational adverb (3 I ). Adversative still, like temporal still, represents a scopal operator: it serves to relate the assertion within its scope to a presupposed proposition. Following Kay (I 990), we may refer to the former as the text proposition (TP), the latter as the context proposition (CP). The scope of still (the TP) is the entire concessive sentence, excluding the scopal operators even and still . In sentence (29), for example, the scope is (3 3):
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
In (3o), a state of affairs-Mom's obesity-is said to obtain despite an effort to prevent its continuance. As mentioned, earlier approaches to concessive still have focused exclusively on sentences like (3o), in which the concessive understanding of still is reducible to the temporal understanding plus a contextual implication that the state in question continues despite adversity. Such sentences are thus ambiguous in the manner described by Norvig (1988): temporal and adversative understanding of still are mutually compatible. The interpreter need not resolve this ambiguity in favor of one or the other reading.5 Such ambiguity also characterizes true concessives like (27): the assertability of an earlier claim endures despite an intervening counterargument. There is evidence, however, that the imperfective concessive still is not equivalent to the temporal usage coupled with the adversative implicature: it does not accept bounding durational adverbs, nor does it welcome the continuative perfect. As shown in (3 1-32), however, concessive still accepts both individuating operators:
Laura A. Michaelis
2 19
(3 3) If Harry loses twenty pounds (i.e. is slightly overweight), he'll fail the physical. In (3 3), Harry's failure is asserted with respect to a hypothetical space (Fauconnier 1 98 5) in which weight loss has occurred. The TP presupposes a CP of conditional form, in which Harry's failure is established with respect to another mental space. Let us assume that the CP of (33) is (34): (34) If Harry is obese, he'll fail the physical.
(3 s ) Under X circumstances, Harry will fail the physical. In (35), the variable ranges over worlds in which the outcome coded by the apodosis obtains. Thus, the focus of the TP is its protasis. The TP establishes a world that is less favorable (or, equivalently, 'more hostile') to Harry's failing the physical than is the world of the CP. As we will note below, the CP expresses a cause-and-effect scenario that is more consonant with general background assumptions than is that scenario evoked by the TP. The CP and TP are related within a two-dimensional scalar model that matches events with the circumstances under which they transpire. Within this model, worlds are arrayed with respect to the degree to which they favor the outcome in question; the least adverse (or most favorable) world is nearest the origin. This is the world of the CP. In the case of (29), this is the world in which Harry is grossly overweight. Failure of the physical is accordingly assured. The world of the TP is located at a more extreme point on this 'adversity scale'. This is the world in which Harry is only somewhat corpulent. The outcome at issue, Harry's failure of the physical, obtains in both of these worlds. A diagrammatic representation of this model (in which the two dimensions are 'collapsed') is given in Figure 4·
88 a
a- 1
Figure 4
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
In (34), the world of the CP happens to correspond to the speaker's reality space: Harry is in fact overweight. (This situation differs from that of factive concessives, to be discussed below.) The semantic material shared by CP and TP can be represented by the propositional function (3 5):
2.2.0 'Continuicy' within Three Scalar Models: The Polysemy of Adverbial Still
In Figure 4, the world of the CP is given the value a 1; it is less adverse to failure than the world of the TP (a). This model licenses an inference: if Harry's failure transpires under circumstances unfavorable to failure (lack of obesity), then it will also transpire under circumstances that are favorable to failure (obesity). That is, the TP unilaterally entails the CP. In May's terms, the TP is more informative than the CP. Kay's definition of informativeness allows us to account for the close association of even with still, and with concessive semantics in general: even typically introduces the protases of both factive and conditional concessives (hence the subordinators even if and even though ). According to Kay, even -
Thus for example, the sentence Even some thin people have high cholesterol can be taken as unilaterally entailing a less informative CP, Overweight people have high cholesterol . The semantic material shared by CP and TP here can be represented as an open proposition: 'x type of people have high cholesterol'. The focus of the TP, thin people, ranks higher on the relevant dimension of the model (say, persons ranked with respect to their immunity to disease) than does the equivalent argument of the CP, overweight people. Therefore, the proposition resulting from integration of focal argument and propositional function ranks higher than (i.e. unidirectionally entails) the CP within the relevant scalar model. In the concessive sentence (29), the relationship between CP and TP that is mediated by still is identical to that which is mediated by even in this sentence. The semantic material shared by CP and TP is in both cases can be represented by the propositional function (35). The focus of both operators is the protasis of the TP. As noted by Kay, the syntactic position of even commonly reflects its focus (c£ (2 5)). Thus, in concessives like (29), even is placed before the protasis. Note, however, that even and adversative still cannot be said to be synonymous. While even can be used wherever the requisite scalar entailment is present, adversative still must relate propositions relativizable co a scalar model of the sort represented in Figure 4· Within this model, still codes the continuity of an outcome across worlds; even simply flags the entailment relation that is licensed by this model. This model is not uniquely associated with still, but is linked to concessive semantics in general. Still is simply sympathetic to concessive semantics. For this reason, we find that, as Konig notes, still is redundant in hypotactic concessives of the sort exemplified in (28-29). In addition, it need not appear in paratactic concessives containing the connective but : (36) The interview went well, but he (still) didn't get hired.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
indicates that the sentence . . . in which it occurs expresses, in context, a proposition which is more informative {equivalently 'stronger') than some particular distinct proposition taken to be already present in the context (p. 66)
Laura A Michaelis
22 1
Syntactic templates like that exemplified in ( 36) are clearly devoted to the expression of concessive semantics. As Konig ( 1986) observes, however, biclausal templates of a less specialized function can also serve as concessives (coordinate structures, temporal-clause constructions, etc.). In such instances, the concessive understanding can arise from the presence of adverbial still alone. The concessive interpretation of coordinate structures like (37) can be attributed to the presence of still:
(37) Harry came and Marge still left.
adverbial elements-mirrors the semantics of concession, concessive assertions commonly appear within the scope of still . As noted, however, either can evoke the requisite semantic structure without the other. Our account of this semantic structure requires some refinement. We have established that concessives require the presence of identical outcomes in two worlds or mental spaces. In the case of concessive conditionals, the 'adverse world' is equated with Fauconnier's hypothetical space H. This mental space is established by conditionals whether or not they are characterizable as concessives. The world of the CP is akin to the world of speaker's reality (R). The requisite pairing of mental spaces is also evoked by sentences containing an instance of still that is interpretable as both temporal and concessive. In such sentences as (30), the world favoring obesity (in which Mom is not dieting) is established by the presupposition of prior instantiation. This world is the (past) time space described by Fauconnier ( 1985 ). In the case of factive concessives like (28), the adverse world of the TP is identified with R We might say that the factive concessive induces the conceptualizer to compare this world with an alternative reality, which is defined by the lack of those hostile conditions which define R In this case, then, the world of the CP is equated with a hypothetical mental space. In interpreting ( 28), we bring to bear our conception of a (more prototypical) alternate reality in which thefailure to proffer an apology leads to the outcome in question. This analysis leads us to speculate about the ontological statuS of the concessive CP. In general, the CP, as described by Kay, is construed as being 'in the context' at the rime at which the TP is uttered. As Kay points out, however, the CP need not represent a conversational contribution per se . In such cases, the CP often represents general background knowledge, which can be presumed to be accessible to the hearer and whose accessibility is exploited by the utterer of the concessive assertion. In the present case, the CP is represented
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
A concessive reading of (37) would also be licensed by the presence of nevertheless or yet in the second conjunct. These particles may be said to function in a manner similar to still , with the latter sharing some temporal uses (Konig & Traugott 1 982).6 Because adversative still-among other
222 'Continuity' within Three Scalar Models: The Polysemy of Adverbial Still
as an implicational statement. Sentence (28) might be uttered in a situation in which the addressee has explicitly committed herself to the following conditional proposition: (3 8) If Harry failed to apologize, Marge left in a huff The concessive (28) need not, however, rely upon the presence of a CP having precisely this form. The CP need not involve the particular participants, Marge and Harry. It need not have been asserted at all. Under such circumstances, the CP is a theoretical construct; it simply codifies the conversants' shared understanding of the conditions which favor the outcome at issue. This maximally general CP can be stated in the following fashion: This general conception of the CP provides some diffic ulty for accounts which use a Gricean mechanism to account for the association of concessives (and concessive still) with the violation of an expectation. One such account is Fauconnier (198 s). Fauconnier notes that conditional sentences are upper bounded via quantity implicature, such that sentences like (39) yield the following implicatum: (4o) Only if someone fails to apologize will the offended party storm away. This implicatum can be restated in scalar-semantic terms: the world coded by rhe protasis is the most hostile (or least favorable) in which the eventuality coded by the apodosis will obtain. The conditional (4o) will generate the inference (4 1 ): (4 1) If someone apologizes, then the offended party will be mollified. It is precisely this type of inference that, as Fauconnier points out, is contravened by concessives like (28). Thus, the concessive TP must by definition contravene an upper-bounding implicature associated with its CP. Given this fact, we have a ready explanation for the association of concessives with expectation contravention. This account, however, relies upon the assumption that the conditional CP is a conversational contribution. Upper bounding implicature arises from the assumption that in making a given assertion the speaker is being maximally informative. We cannot presume that an upper-boundng implicature attaches to a conditional sentence which has not been uttered in the relevant discourse. For this reason, we must assume that an inference like (4 1), which relates to an expected outcome, does not necessarily arise from upper-bounding implicature. We might assume instead that this sort of inference represents a presupposition of adversative still (and concessives in general). This presupposition is the concessive analog of the presupposition of
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
(39) If someone fails to apologize, the offended party will storm away.
Laura A Michaelis
223
expected cessation (discussed with respect to the temporal sense). It can be described as follows: the outcome denoted by the apodosis of the TP will not typically obtain in the world of the TP. With respect to (29), represented in Figure 4, this presupposition is the following: if Harry is not grossly overweight (i.e. if he loses the twenty pounds), he will not fail the physical. This presupposition is represented in Figure s. a modified version of Figure 4·
® s
w· a'
® ® s
s
a-1
w
a Figure 5
In Figure s, the upper adversity scale (W ') represents the general expectation that the world of the CP (in which Harry is obese) represents an adversity threshold: no world more adverse to the failure outcome will support that outcome. As shown, a lighter Harry does not fail the physical in the world of the TP (a ') within W '. In W, by contrast, failure does occur in a world which disfavors it (a). While there is a persistence of outcomes across worlds a - I and a in W, there is no such persistence in W '. The contrast in threshold values on the two adversity scales W ' and W is responsible for the flavor of expectation contravention associated with both concessive assertions and adversative still. 2.3
Marginality within scalar regions
Konig ( 1977: I 84) observes that , sentences like (3) and {42-43) 'do not establish a relation between various points in time . . . but between various entities comparable' to one another: (42.) Compact cars are still fairly safe; subcompacts start to get dangerous. (43) Disturbing the peace is still an infraction; malicious mischief is a misdemeanor. According to Konig's analysis, such sentences presuppose that the subject denotation of the still-bearing sentence represents a 'borderline case' of the
B
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
a- 1 '
224
'Continuity' within Three Scalar Models: The Polysemy of Adverbial Still
0
midsize
safe
compact
subcompact
x-1
X
x+l
s
s
D
vehicle integrity Figure 6
In Figure 6, the scalar loci at which entities are placed are represented by numerical values (x - 1 , etc.). The subscript beneath these values indicates the region within which the ranked entities fall. Thus, both midsize cars and compacts are in the safe region (S), while subcompacts fall within the dangerous region (D). Marginality still selects an entity at the periphery of the safety region: the class of compact cars. It presupposes that there are entities ranked closer to the origin of the scale; these entities are better exemplars of vehicle integrity. Like the other senses, marginality still can be regarded as a scalar operator. The asserted and presupposed propositions related by still in (42) are given in (43): (43) asserted: Compacts are safe. presupposed: Midsize cars are safe, etc. That is, (42) presupposes that there is at least one other class of vehicles that can be described as safe. As in the case of adversative still , the asserted
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
category defined by the descriptor. Thus, for example (42) presupposes that compact cars are located at the periphery of the graded category of safe vehicles. At the same time, (42) asserts that compacts none the less fall within the 'safe region' of a scale upon which cars are ranked with respect to the accident protection afforded their occupants. Sentences like (42-43) again evoke a two-dimensional scalar model, analogous to the time line and adversity scale discussed with respect to the temporal and concessive senses of still . This scale ranks entities in accordance with the degree to which they manifest a given property; an entity manifesting the property to a high degree will be placed at an advanced point, i.e. at some distance from the origin. The scale also contains a threshold, such that those entities above this threshold and those at or below the threshold are partitioned into distinct 'regions'. In Konig's terms, the scale is 'divided up by two (or more) predications' (p. 1 84). In the case of (42), cars are ranked with respect to their increasing lack of structural integrity. This scale is partitioned into 'safe' and 'dangerous' regions. Entities arrayed between the origin and transition point lie within the 'safe region' of that scale.The entity described in (42-43) is 'located' at or very near the transition point for the scale.A diagrammatic representation of the scale evoked by (42) is given in Figure 6.
Laura A. Michaelis
225
proposition unilaterally entails the presupposed proposition within the scalar model. Within the model represented in Figure 6, the proposition that compacts are safe unilaterally entails that midsize cars are safe. The semantic material shared by the asserted and presupposed propositions (43) can be represented as a propositional function (44): (44) x is safe
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
This propositional function differs from those which have been adduced in the analyses of temporal and adversative still . In (44), the variable occupies an argument place, rather than an adjunct position (c£ (26) and (3 5)). This difference can be attributed to the distinct properties of the scalar models evoked by temporal and adversative still , on the one hand, and marginality still , on the other. In the former case, homogeneous situations are matched with corresponding scalar loci-points in time or worlds. The succession of moments or of worlds represents an autonomous ordered sequence. (Thus, for example, the passage of time exists independently of the situation which obtains at any given moment.) In the latter case, entities (rather than situations) are ranked with respect to one another. These entities derive their homogeneity from a shared property. The property scale involved (auto safety, etc.) does not exist independently of the entities ranked within it (although we may assign a numerical value to a given position in this ranking). In all cases, however, the focus of the asserted proposition creates a proposition which ranks higher than a presupposed proposition within the scalar model at issue. In the case · of the temporal and adversative senses, 'advancement' within the scalar model occurs via replacement of a less advanced scalar locus (time point or world) by a more advanced locus within the appropriate propositional function. That is, in these cases the divergence between presupposed and asserted propositions arises from the fact that these propositions (a) bear distinct time specifications or (b) establish distinct mental spaces. In the case of the marginality sense, the divergence between asserted and presupposed propositions arises simply via substitution of one entity for a higher-ranked entity within the same scalar region. Such substitution allows the requisite 'advancement' along the relevant scale, while preserving the overall homogeneity provided by the entities' shared membership in a given scalar region. Thus, the nature of the propositional function is determined by the scalar ontology evoked by an assertion involving still. The homogeneous contiguous elements can be situations or entities. Accordingly, the invariant portion of the open proposition may be either a full clause (an adjunct is supplied by the focus) or a predicate (an argument is supplied by the focus). That is, addition of the focus may either (a) derive a proposition from a proposition or (b) a proposition from a predicate. Konig captures this distinction by assigning the marginality
ll(J
'Conrinuiry' within Three Scalar Models: The Polysemy of Adverbial Still
(45) Good. Harry is still here. (temporal) (46) I apologized, and still she left in a huf£ (concessive) (47) *Still, Death Valley is in California. (marginality)
·
Although still always mediates between full propositions semantically, it has syntactic sentential scope only when the requisite identity between scalar elements is an identity between states of affairs, rather than an identity between entities. Only in the former case are the compared scalar elements directly mapped to propositions. In the latter case, the compared elements are mapped to arguments, and the continuation asserted by still is not akin to the continued instantiation of a proposition. It should be noted that the argument variable in open propositions like (44) need not fill the subject position. Strictly speaking, therefore, the invariant portion is not a predicate. Konig discusses such examples as (48): (48) I can still beat PAUL. Peter is too good for me. Sentence (48) presupposes a proposition with which it which shares some semantic material. This shared material can be represented as the propositional function (49): (49) I can beat x Sentence (49) evokes a property scale upon which players are ranked according to their skills. This scale is divided into two regions: those players whom the speaker can beat, and those whom she cannot. Sentence (48) asserts that Paul is a borderline case with respect to the former region; it presupposes that there are players whom the speaker can more readily defeat. As it stands, this analysis has not accounted for a prominent use-condition upon assertions involving marginality still : assertions like (3) and (42 43) are most felicitously uttered when there is reason to doubt that the descriptor in question is applicable to the entity under discussion. Sentence (43), for example, -
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
sense the categorial index (o, I , (o, 1)): the proposition is derived via addition of a name to a propositional function. Note that Konig does not regard still as a scopal operator: his account does not invoke a relation between asserted and presupposed propositions. Hence, the categorial index amalgamates the focus of the asserted proposition and the propositional function which that focal element completes. Categorial indices for the other two senses derive a proposition from a complex or simple proposition. (Thus, the concessive sense has the category index (o, (o, o)), while the temporal sense has the index (o, o).) This distinction has a grammatical ramification. As noted by Konig, marginality still does not function as a sentence adverb. It cannot be placed in pre- or post-clausal position. In this respect, its syntax differs from that of temporal and concessive still. These differences are shown in (45-47):
Laura A. Michaelis
227
is most appropriately directed toward an addressee who has expressed the belief that disturbing the peace is a misdemeanor, i.e. is more serious than an infraction. This sentence would not typically be used to enumerate various offenses and legal sanctions to an apparently uncommitted listener. Marginality still , like the other senses, expresses expectation contravention. This property can be represented as a presupposition, again using parallel scales. A representation of this presupposition is given in Figure 7, for sentence (42).
0
subcompact midsize compact -----+--�---+ W'
safe
X
D
x+1 D
midsize compact subcompact -------r--�--4---� w
safe
x-1 s
X
s
vehicle integrity
x+1 D
Figure 7
In Figure 7, the model W ' within the speaker's expectations places the class of compact cars beyond the threshold for safety, and within the 'danger region'. The model W contrasts with W ': the class of compact cars lies within the safety region. Here, as in the earlier case, persistence of a property (as against a situation) across two contiguous scalar loci contrasts with an expected transition at the more advanced of these loci. Particular scalar regions, like the scales themselves, do not exist independ ently of the entities ordered within them. The point of transition to a conti guous scalar region will be identified with the point at which one situates the highest-ranking entity (vis-a-vis the scale as a whole) that can be characterized as possessing the property defining that region. Locating this entity within the scalar region entails that all lower-ranking entities will also be located within that scalar region. The 'dangerous' regions within W and W ' have distinct sets of members; this difference arises from the fact that compacts qualify as dangerous vehicles in W ', but not in W. ·
4 D IACHRON IC I SSUES One of the major claims of this study is that the network of senses associated with the lexeme still can be examined without r�ference to the diachronic sense extensions through which those senses arose. it is none the less useful to examine the limitations of a diachronic account based solely upon pragmatic strengthening (Traugott 1 988). We noted earlier that, according to Konig &
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
0
x-1 s
228 'Conrinuity' within Three Scalar Models: The Polysemy of Adverbial Still
(42) Compacts are still pretty safe; subcompacts start to get dangerous. In the second clause of (42), the inchoative start toget is not used to assert that subcompacts as a class are becoming increasingly dangerous these days. Instead, the inchoative is used to assert that subcompacts as a class can be located at the point of origin of a scalar region containing dangerous vehicles. This scalar region is properly included within the vehicle-integrity scale shown in Figure 7· Sentences like (42) presuppose that more dangerous vehicles (less structurally
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Traugott ( 1 982), a quantity implicature-or rather its conventionalization-was responsible for the development of the adversative sense. The speaker asserts both continuance of a state of affairs and the existence of factors which might militate against this continuance. Quantity-based considerations dictate that the conjunction of these two assertions have some informational value. In such contexts, continuance comes to implicate continuance despite adversity. It was argued earlier, however, that this 'adversative implicatum' cannot be said to attach concessive assertions involving perfective predicates. Thus, the develop ment of a concessive sense compatible with perfective predicates cannot be attributed to this implicature. Instead, semantic broadening may be responsible: the concept of existence despite adversity comes to subsume the existence (under unfavorable circumstances) of two types of eventualities-states and events. In the latter case, still evokes occurrence rather than persistence despite hostile circumstances. This broadening cannot, however, account for the emergence of the marginality sense, which does not evoke the domain of eventualities. This sense can be said to conventionalize a quantity implicature as the presupposition of expected transition: the speaker's assertion that an entity bears some scalar property is informative only in so far as the entity's location within the relevant scalar region, as against a contiguous region, is subject to debate. The equivocal nature of the entity's membership within a subregion of a property scale arises from its being situated at or near a transition point within that scale. That is, the presupposition of expected cessation is readily translated into the presupposition of an expected transition from one scalar 'region' to another. The transition at issue is not situated within the temporal domain. The scale is here a graded category within which entities are ranked (and relegated to subclasses) according to the degree to which they manifest a given property. A certain degree of that property, rather than a time point, represents the threshold at which the transition occurs. There is evidence, that a semantic extension of the type represented by the marginality sense can arise from a temporal understanding. An example of such a meaning shift is provided by nontemporal scalar uses of inchoatives. Sentence (42), repeated here for convenience, contains an example of such an extension:
Laura A. Michaelis 229
sound subcompacts) are located at points beyond the transmon point, i.e. further removed from the origin of the vehicle-integrity scale. Note that this use of the inchoative is not an instance of abstract motion, as defined by Langacker ( I 987). Langacker has noted examples like (so), in which a motion verb is predicated of a static entity: (so) Frontage Road runs along Interstate 8o.
(42 ) *Harry starts to get forgetful. (so ') *Look! Harry runs past the house. '
Aspectually, both abstract-motion predicates and nontemporal inchoatives qualify as states. Another nontemporal inchoative is the marginality usage of already , noted by Konig with respect to German schon . As I argued, in Michaelis ( 1 992), temporal already represents a pragmatically ambiguous marker of temporal priority. It asserts the existence of a state prior to a reference interval containing a state of a like type. One usage of already codes anteriority of a state with respect to an expected point of eventuation, as in (s I): (s I ) Only s o'clock and it's already dark out. In chis usage, already resembles temporal still: the time line in W is paralleled in W ' by a time line of speaker's expectations. Each adverb requires that the proposition within its scope obtain at the reference time specified by the tense; each presupposes the lack of the state in question at reference time in W '. In the case of already , however, lack of the state in question is also presupposed for all times prior to reference time in W and W '. Further, in W ', the state obtains at some more distant point in the course of development at issue. A representation of(S I ) is given in Figure 8 (again following Hoepelrnan & Rohrer 1 98 1 ).
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Here, according to Langacker, a motion predicate is called for, owing to the fact that the conceptualizer is in essence 'tracing' a static configuration. In so doing, she notes the manner in which the configuration present at one spatial point differs from that located at a previous point. In the case of(42), however, motion does not define the conceptual domain which gave rise to the atemporal meaning extension. In this case, the semantic extension consists in (a) 'replacing' time points with rankings (degrees) along a property scale and (b) defining a transition over like entities located at contiguous scalar loci rather than over sub-episodes of a state at contiguous 'moments'. It should be noted, however, that abstract-motion predicates and non temporal inchoatives share a particular aspecrual property: in these usages, a perfective predicate can occur in the simple present without a special · interpretation (e.g. habitual). Ordinarily, these predicates cannot be used in the simple present to report events ongoing at speech time.
2 30 'Continuity' within Three Scalar Models: The Polysemy of Adverbial Still It's light < It's light < It's dark R'
It's light < It's dark < It's dark R Figure S
(52) Compacts are already safe. Here, as in (42), a scale of vehicle integrity is invoked. In this case, however, the orientation or direction7 of the scale is different the most dangerous cars are nearest the origin. As in (42), what is asserted is that compact cars are safe. Here, however, the 'safe region' does not include the origin of the scale. What is presupposed is that cars safer than compacts (e.g. midsize cars) are located at points further removed from the origin within the region at issue. Already here also presupposes a world of speaker/hearer expectations in which compacts·do not qualify as safe, but larger cars do. The model, given in Figure 9, is analogous to the temporal model shown in Figure 8. 0
dangerous 0
dangerous
subcompact
compact
midsize
x-1 D
X
D
x+ 1 s
subcompact
compact
midsize
x-1
X
x+1 s
D
s
vehicle integrity
W'
w
Figure 9
Marginality still (Figure 7) asserts that the property of being a safe vehicle obtains at a more extreme point in the integrity ranking for vehicles than expected; the origin of the scale is equated with the safest vehicle. By contrast, marginality already asserts that the safety property obtains at a less extreme point than expected; the onset of the scale is the point of least structural soundness. In both cases, the temporal and nontemporal scalar models are structurally isomorphic. In the case of already , as in the case of inchoatives in general, the nontemporal reading represents an analogical mapping of a temporal model onto a model of graded categorization.
·
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
In this usage of already, what is at issue is not merely a sequence of phases of a given state, but a transition from one state to another. The transition that has occurred at reference time in W is premature with respect to a canonical course of development, represented as the time line within W '. In its nontemporal usage, already is the counterpart of marginality still . An example of the temporal usage is given in (52):
Laura A. Michaelis
23 1
It was claimed above, however, that the development of marginality still was not so direct this sense was said to 'inherit' its semantic structure from an a temporal schema which subsumed both temporal and concessive uses. Perhaps this claim cannot be maintained in light of examples involving nontemporal uses of inchoatives. If we do allow that marginality still developed directly from temporal still, this does not impeach the argument that pragmatic strengthen ing alone does not account for the development of a concessive use of compatible with perfective predicates or of me marginality sense. Further, whatever path of diachronic development yielded marginality still, it would seem that only a superstructure involving abstract continuation can create a coherent conceptual grouping of senses synchronically. C O NC L U S I O N
A representation of the semantic commonalities which unite the three senses of still is given in Figure 1 0. The common traits schematized in Figure 1 0 can be enumerated as follows. A scale in W contains two identical elements, S. These elements are located at two contiguous scalar loci. The more advanced of these loci is 'highlighted' by the predication. This highlighting is indicated by the boldface brackets. The assertion that S obtains at the more advanced scalar locus licenses the inference (whether by lexical presupposition or scalar entailment) that S also obtains at (at least) one scalar point located closer to the origin of the scale. The scale in W is paralleled by an analogous scale in W ', the world of speaker/hearer expectations. On this scale, the scalar element (S '), obtains at the less advanced point; the more advanced point Xj' is characterized by the lack of S (or by the presence of another element-entity or outcome). The scalar loci in question may be time points, worlds, or simply rankings within a property scale. The elements ordered may be states of affairs (outcomes or situations) or entities. Thus, the schema given in Figure 10 is an abstraction over scalar ontologies. The distinct scalar ontologies yield the distinct senses. Thus, still is a polysemous lexical item. Grammatical evidence for the existence of distinct senses is provided by co-occurrence restrictions and syntactic restrictions: for example, temporal still does not accept durational adverbs, and marginality still cannot be placed in pre- or post-clausal position. The distinct semantic s tructures are none' the less isomorphic. As shown in Figure 1 o, the shared semantic properties can be represented in a straightforward fashion. It does not stretch credulity to suggest that Figure 10 represents a semantic generalization grasped by the speaker. As mentioned, a speaker will arrive at this generalization only once she has access to the full array of senses. A full grasp of the senses includes a knowledge of the conditions under which they are appropriately used in discourse. All assertions involving still represent
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
s
232
'Continuity' wichin Three Scalar Models: The Polysemy of Adverbial Still
0----[�i� IJ [�J--o--[�i-.J [ �J---
W'
w
Figure 10
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
assertions of sameness despite expectation of change. This shared pragmatic content might induce one to reconcile senses with respect to their semantic content. The formation of this semantic generalization then resembles the process by which type information is extracted from tokens Gackendoff I98 3). Use-conditions shared by the senses are analogous to the set of ostensive definitions from which the speaker extrapolates conditions upon category membership. The general semantic structure diagrammed in Figure 10 is then a rubric under which the distinct senses are grouped. This grouping is a 'natural category of senses' (Lakoff I987: passim ). As mentioned, a polysemy network of this sort does not represent a radial category of the kind described by Lakof£ It does not contain a 'core sense'. Instead, the distinct senses cohere by virtue of their common link to an abstract semantic superstructure. This type of analysis avoids the need to posit a polysemy structure which recapitulates the series of diachronic meaning extensions that give rise to the distinct senses. Although such polysemy structures exist, it was argued that, in the present case, the diachronic trajectory connecting temporal to concessive still cannot represent a synchronic 'sense link'. The historically primary temporal sense is not the central sense. The senses are related not by their resemblance to a core sense, but by their resemblance to the semantic superstructure. The semantic super structure is computed only once the full array of sense is available. A polysemy network of this type is then by definition discontinuous with the historical developments which yielded the individual senses. In addition to augmenting the repertoire of sense networks available within a theory of lexical polysemy, this study has also provided further evidence that use conditions and 'meaning proper' must be examined in tandem. Still is a scalar operator possessed of 'direct pragmatic interpretation' (Kay 1990: 6 3). 1t thus belongs to the family of linguistic constructs which Kay has elsewhere termed contextual operators: 'lexical items or grammatical constructions whose semantic value consists, at least in part, of instructions to find in . . . the context a certain kind of information structure' (I 989: I 8 I ). The information structure evoked by still is a scalar model, 'a set of propositions which are part of the shared background of speaker and hearer at the rime of the utterance' (Kay I 990: loc. cit.). As argued here, still evokes various types of scalar models: a rime line, an 'adversity scale', and graded categorization. These models are
Laura A. Michaelis 2 3 3
LAURA A. MICHAELIS University of California Department ofLinguistics Berkeley, CA 94 720 USA
Received: 1 2-8-92 Revised version received: 22-I -93
N O TES I For their help i n developing the present analysis, I would like ro thank John Dinsmore, Gilles Fauconnier, Charles Fillmore, George Lakoff, Knud Lam brecht, and Eve Sweetser. Especially valuable assistance was provided by Paul Kay and Jean-Pierre Koenig. I would also like ro thank three anonymous reviewers for their insighrful criticisms and sugges tions. Still, I am responsible for all errors. 2 Doherry ( I 973) has attempted ro repre Sl"llf rhe sernanrics of still in terms of rhree ·
phases. In phase I , prior ro reference rime, a stare obtains; in phase 2, located ar reference rime, rhar same stare obtains. In phase three, following reference rime, the stare does nor obtain. As noted by Konig (I 977), however, examples like (a) impugn rhe validiry of this analysis: (a) Our house is still standing! The speaker of (a) certainly does nor presuppose rhar the house in question will nor be sranding ar some point following
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
represented by distinct schemata. As noted, the discourse function o f still is more amenable to a propositional representation. In discourse, still functions to relate propositions within a scalar model. A proposition pertaining to a less advanced scalar locus in the model is regarded as part of the discourse context, whether or not this proposition has been asserted as such. The 'text proposition' containing still entails this context proposition. In all of its senses, still presupposes a world of speaker/hearer expectations, in which that situation coded by the TP does not obtain at the scalar point in question. In positing this semantic presupposition, we codify the intuition that assertions involving still violate expectation. Thus, contextual meaning-and discourse function-are portrayed as part of'literal meaning'. An additional consequence of this study is the following: the existence of the lexica] network, and its organizing rubric, provides evidence for the ability of speakers to evoke an abstract conceptualization of'continuance' or 'persistence', a notion which is prototypically defined with respect to the temporal domain. Continuance can be viewed at a level of abstraction at which its scalar-semantic properties emerge. This abstraction consists in the 'digitization' of a continuum, such that persistence is equivalent to the presence of effectively identical elements at two contiguous scalar loci. An assertion of persistence is equivalent to the assertion that one such element is present at the more advanced of these loci. This abstract scalar conceptualization provides the basis for an analogy within event srructure: the notion of continuation is applicable both to the endurance of a situation through time and to the 'persistence' of an outcome across worlds.
234 'Conrinuicy' within Three Scalar Models: The Polysemy of Adverbial Still
4
(a) Although he's sixcy, he is still vigorous. (b) ?Although he's only twency, he is still feeble.
(b) As everybody expected, Uncle Harry was still pruning the shrubs. Thus the term expected cessation , while a convenient shorthand for the modal component of the Hoepelman & Rohrer time-line model, is misleading. The reader is asked to interpret this term as referring to a presumption of possible cessation at R Given this understanding of the term, one retains the abilicy to explain the anomaly of such sentences as Harry is still deail : under ordinary circum stances, one is loath to invoke a possible world wherein the state of death obtains for some period and then ceases to obtain at a later period. A synthesis of the implicature and pre supposition analyses is possible. Traugott ( 1 98 8) has noted cases of 'pragmatic strengthening', in which conversational implicatures associated with certain lexi cal items become conventionalized. It is possible that, in the present case, the (quanricy-based) implicature of expected cessation associated with temporal still became a conventional concomitant of both the temporal and nontemporal uses. As noted in Section 4, however, our definition of the temporally based notion cessation must be broadened to cover cases in which the scale in question does not
represent a rime line. This broad defini tion will be entailed by the atemporal scalar definition of conrinuicy suggested here. The term 'protasis' is used here in an extended sense: it refers not only to the antecedent of a conditional, but also to the subordinate clause of a factive conces sive. This terminology extension is justi fied by the fact that the two subordinate clauses function in a similar fashion with respect to concessives: both code the 'adverse world' within which some even tuality obtains. C. Fillmore (p.c.) has noted that such sentences as (b) (as against (a)) are peculiar:
Sentence (a) accesses both temporal and adversative understandings of still. In sentence (b), the temporal understanding is not available. Its peculiarity stems from the fact that the coupling of still and an imperfective misleadingly evokes the temporal interpretation. E. Sweetser (p.c.) has pointed out that (b) is acceptable under an epistemic interpretation (Sweet ser 1990): 'I conclude that he is feeble, despite the existence of otherwise valid counterevidence (indicating his youth).' An additional example of the epistemic reading of concessive still is given in (c): (c) Timber wolves eat a lot of meat, but they're still omnivorous.
6
Sentence (c) can be paraphrased in the following fashion: 'Despite evidence to the contrary, the conclusion that Timber wolves are omnivorous continues to have validicy.' The enduring validity of a conclusion in epistemic concessives is directly analogous to the enduring assert abilicy of a claim in argumentative (or 'rrue') concessives like (27). Although it has nor been discussed, I assume that the concessive use ofyet , as in
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
her utterance. We can say, however, that this speaker presupposes that the house might not have been standing at R This is the 'modal component' in the meaning of temporal still that is captured by the twin rime lines in Hoepelman & Rohrer's analysis. By including reference to a parallel possible world in which the state in question ceases at R, this model represents the presupposition of expected cessation. The term expected cessation is used with considerable hesitation. The speaker need not expect cessation of the state of affairs in question, but merely view such cessa tion as a fair possibility. A reviewer notes that such sentences as (b) are possible:
Laura A. Michaelis 2 3 5 (a), is another example of rranssparial persistence: (a) I raced down there, yet I missed the rrain.
(a) Death Valley is already in California. I thank C. Fillmore for making this observation.
R E F E RE N CE S Abraham, Werner (I98o), 'The synchronic and diachronic semantics of German temporal noch and schon , with aspects of English still , yet , and already ', Studies in Language, 4, 3-24. Akmajian, Adrian, Susan M. Steele & Thomas Wasow ( I 979), 'The category AUX in universal grammar', Linguistic Inq uiry , 10, 1-64. Bach, Emmon (I 98 I), 'On rime, tense and aspect: an essay in English metaphysics', in P. Cole (ed.), Radical Pragmatics , Academic Press, New York, 6 3-8 I . Bennen, Michael & Barbara Partee ( I 978), 'Toward the logic of tense and aspect in English', Indiana University Linguistics Club, Bloomington. Chafe, Wallace ( I 970), Meaning and the Structure ofEnglish , University of Chicago Press, Chicago. Dahl, Osten ( I 98 I ), 'On the definition of the telic-atelic (bounded-nonbounded) dis tinction', in P. Tedeschi & A. Zaenen (eds), Syntax and Semantics , vol. I 4: Tense and Aspect , Academic Press, New York, 79-90. Doherty, Monika ( I 973), ' "Noch" and "schon" and their presuppositions', in F. Kil'ft:r & N. Ruwet (eds), Generative
Grammar in Europe , Reidel, Dordrecht, I 5 4-77Fauconnier, Gilles ( I 98 5 ), Mental Spaces: Aspects of Meaning Construction in Natural Language, MIT Press, Cambridge. Fenn, Peter ( I 987), A Semantic and Pragmatic Examination of the English Peifect , Gunter Narr Verlag, Tubingen. Fillmore, Charles J., Paul Kay and M. C. O'Connor (I 988), 'Regularity and idio maricity in grammatical constructions: the case of let alone', Language, 64, 50 I -38. Goldberg, Adele (I 992), 'Argument structure constructions', doctoral dissertation, Uni versity of California, Berkeley. Greenbaum, Sidney (I 969), Studies in English Adverbial Usage, University of Miami Press, Miami. Herweg, Michael ( I 99 I a), 'A critical exami nation of rwo classical approaches to aspect', journal ofSemantics , 8, 36 3-402. Herweg, Michael ( I 99 I b), 'Perfective and imperfective aspect and the theory of events and states', Linguistics, 29, I O I I - 5 1 . Hirtle, W . H . ( I 977), 'Already , still , and yet ', Archivum Linguisticum , 8, 28-45. Hoepelman, J. & C. Rohrer (I 98 I ), 'Remarks on noch and sclzon in German', in P. Tedes chi & A. Zaenen (eds), SyntaxandSemantics ,
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
As Konig and Traugonargue( I 982), yet and still are distinct in the following respect: yet presupposes that the state of affairs in question will end at a point fol lowing reference rime. Thus, He's not here yet presupposes that this (negative) state will terminate later; the a nalogous sent ence with still bears no such presupposi tion. Both adverbs are, however, markers
of temporal persistence, and as such exhibit analogous temporal-concessive polysemy. 7 This scalar directionality can be literal. Sentence (3) is an appropriate response to the easrward bound motorist who assumes that Death Valley is in Nevada. However, only sentence (a) is appropriate ifthat same individual is traveling wesrward:
236 'Continuity' within Three Scalar Models: The Polysemy of Adverbial Still
Dangerous Things: What Catexories Reveal about the Mind , University of Chicago Press, Chicago. Lakoff, George & Claudia Brugman ( I 986), 'Argument forms in lexical semantics', in K. Nikiforidou et a/. (eds), Proceedings ofthe Twelfth Annual Meeting of the Berkeley Linguistics Society, Berkeley Linguistics Society, Berkeley, CA, 442-54. Lambrecht, Knud (forthcoming), Information Structure and Sentence Form , Cambridge University Press, Cambridge. Langacker, Ronald W. (I 987), Foundations of Cognitive Grammar, vol. I , Stanford Uni versity Press, Stanford. Langacker, Ronald W. (I991), Foundations of Cognitive Grammar, vol. 2, Stanford Uni versity Press, Stanford. Lehrer, Adrienne ( I 990), 'Polysemy, con ventionality and the structure of the lexicon', Cognitive Linguistics, I, 207-46. Lichtenberk, Frantisek ( 1 991), 'Semantic change and heterosemy in grammaticali zation', Language, 67, 474- 5 09. McCawley, James D. {I97 I), 'Tense and time reference in English', in CharlesJ. Fillmore & D. Terence Langendoen (eds), Studies in Linguistic Semantics, Holt, New York, 96I I 3· McCawley, James D. (r 987), 'The focus and scope of only', unpublished MS, University of Chicago. Michaelis, Laura A. ( I 992), 'Aspect and the semantics-pragmatics interface: the case of already , Lingua , 87, 3 2 I -39· Miller, George (I 978), 'Semantic relations among words', in M. Halle et a/. (eds), Linguistic Theory and Psychological Reality. MIT Press, Cambridge, MA, 6o- I I 8. Mittwoch, Anita ( I 988), 'Aspects of English aspect: on the interaction of perfect, progressive and durational phrases', Ling uistics and Philosophy, I I , 203-54. Morgan, Jerry ( I 978), 'Two types of conven tion in indirect speech acts', in Peter Cole (ed.), Syntax and Semantics , vol. 9: Prag matics , Academic Press, New York, 26 I ·8o. Morrissey, Michael ( 1 973), 'The English
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
vol. I 4: Tense and Aspect , Academic Press, New York, 103-26. Horn, Laurence R. ( I 970), 'Ain't it hard (anymore)', in M. A Campbell et a/. (eds), Papersfrom the Sixth Regional Meeting ofthe Chicago Linguistics Society, Chicago Lingui stics Society, Chicago. Horn, Laurence R. (I 984), 'Toward a new taxonomy for pragmatic inference: Q-based and R-based implicature', in D. Schiffrin (ed.), CURT '84: Meaning, Form and Use in Context , Georgetown University Press, Washington, DC, I I -42. Jackendoff, Ray (I 983), Semantics and Cog nition , MIT Press, Cambridge, MA. Kamunen, Lauri ( I 97 I ), 'Implicative verbs', LAnguage , 47, 340- 5 8. Kay, Paul ( I 989), 'Contextual operators: respectively, respective and vice versa ', in K. Hall et a/. (eds), Proceedings of the Fifteenth Annual Meeting of the Berkeley Linguistics Society , Berkeley Linguistics Society. Berkeley, CA, I 8 I -92. Kay, Paul ( I 990), 'Even ', Linguistics and Philo sophy, IJ, 59-I I r . Kemmer, Suzanne ( I990), 'Still', paper presented at the Fourth Annual UC Berkeley-UC San Diego Cognitive Ling uistics Workshop. Klein, Wolfgang (I 992), 'The present-perfect puzzle', Language ' 68, 5 2 5 - 5 2. Konig, Ekkehard (I 977), 'Temporal and nontemporal uses of noch and sclzon in German', Linguistics and Philosophy , I, I 7398. Konig, Ekkehard ( I 986), 'Conditionals, con cessive conditionals, and concessives: areas of contrast, overlap, and neutralization', in E. Traugott (ed.), On Conditionals, Cam bridge University Press, Cambridge, 22946. Konig, Ekkehard & Elizabeth Traugott (I982), 'Divergence and apparent con vergence in the development of yet and still', in M. McCaulay et a/ . (eds), Proceed ings of the Eighth Annual Meeting of the Berkeley Linguistics Society , Berkeley Lin guistics Society, Berkeley, CA, I 70-9. Lakoff, George ( I 987), Women, Fire and
Laura A Michaelis 237
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
perfective and �still/anymore" ', journal of Traugott, Elizabeth (1 986), 'From polysemy to internal semantic reconstruction', in K. Linguistics, 9, 6 5-9· Mourelatos, Alexander ( 1 9 8 1 ), 'Events, pro Nikiforidou et a/. (eds), Proceedings of the cess and states', in P. Tedeschi & A Zaenen Twelfih Annual Meeting of the Berkeley (eds), Syntax and Semantics , vol. 1 4: Tense Linguistics Society , Berkeley Linguistics and Aspect , Academic Press, New York, Society, Berkeley, 5 39-50. 1 9 1 -2 1 2. Traugott, Elizabeth (1 988), 'Pragmatic Norvig, Peter ( 1 988), 'Interpretation under strengthening and grammaticalizarion', in ambiguity', in A.Jaisser et a/. (eds), Proceed A Jaisser et a/. (eds), Proceedings of the ings of the Fourteenth Annual Meeting of the Fourteenth Annual Meeting of the Berkeley Berkeley Linguistics Society , Berkeley Ling Linguistics Society , Berkeley Linguistics uistics Society, Berkeley, 1 8o-2o 1 . Society, Berkeley, 406- 1 6. Parsons, Terence ( 1 990) , Events in the Semantics Traugott, Elizabeth & John Waterhouse (1 969), ' �Already" and �Yet": a suppletive ofEnglish , MIT Press, Cambridge, MA. set of aspect markers?', journal of Linguis Partee, Barbara (1984), 'Nominal and tem tics , 5. 287-304. poral anaphora', Linguistics and Philosophy, ,, 243-86. Vlach, Frank ( 1981 ), 'The semantics of the Quirk, Randolph et a/. ( 1972), A Grammar of progressive', in P. Tedeschi & A. Zaenen Contemporary English , Longman, London. (eds), Syntax and Semantics , vol. 1 4: Tense Sweetser, Eve (1 990), From Etymology to Prag and Aspect , Academic Press, New York, 27 J-()2. matics , Cambridge University Press, Cam bridge. Taylor, Barry (1 977), 'Tense and continuity', Linguistics and Philosophy , I, 1 99-220.
)<•umal ofSemantia
10: 239-267
©Oxford University Press 1993
The Dynamics of Description
JAN VAN EIJCK Centrefor Mathematics and Co mputer Science, {CWI), Amsterdam
Abstract
1
INTRO D UCTION
This paper presents a logical analysis of indefinite and definite descriptions in terms of dynamic logic, argues that such an account is superior to an account in terms of static logic, but finally shows how the dynamic semantics of descrip tions can again be related to a static semantics with the use of assertion logic. We start with a standard dynamic semantics and show that it gives a superior account of the process of picking an arbitrary individual satisfying a property (using an indefinite description) and referring back to it (using a pronoun with that indefinite as an antecedent), and of the process of picking the individual which in the current context is the unique thing satisfying a property (using a definite description), and referring back to it (using a pronoun with that
c
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
In a static approach co che semantics of natural language, the use of definite and indefinite descriptions encounters certain difficulties. This paper shows chat these problems can co a large extent be overcome by switching co a dynamic perspective, and demonstrates how description operators acquire a new l ustre and attractiveness in a dynamic sec-up. The scarring point of chis paper is dynamic predicate logic. The paper first extends the semantics of dynamic predicate logic (Groenendijk & Scokhof I 99 I) with a clause for definite 1 assignment. The constructs for indefinite and definite assignment (TJ and t ) allow a very straightforward analysis of indefinite and definite descriptions in natural language. lc is shown how che standard semantics for t assignment (van Eij ck & de Vries I 992) leads co a Russellian treatment of definite descriptions. A Hoare/Pracc-scyle calculus of assertions for dynamic predicate logic is presented, and it is demonstrated how che axiom schemata of che calculus allow for the calculation of success conditions (static truth conditions) or, equivalently, for the calculation offailure conditions (static falsity conditions) of dynamic predicate logic programs. Next, the dynamic semantics is enriched with error states, intended to monitor failure of uniqueness presuppositions for definite descriptions. The semantic clause for t assignment can now cake the presuppositions of the use of definite descriptions into account, which gets us a Scrawsonian treatment of definites. It is indicated how a Hoare/Pratt-scyle calculus for the error state semantics can be set up. The paper ends with a demonstration of the use of this calculus for finding success conditions, failure conditions, and error conditions (conditions for presupposition failure). It is also shown that the axiom system may serve as a calculus of presupposition projection.
2.40 The Dynamics of Description
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
definite as an antecedent).The analysis of this system with the tool of assertion logic shows that the standard dynamic semantics of definites is in fact aRussell style treatment of definites. We then present a modification of the dynamic semantics that allows for the possibility of error abortion, in order to handle uniqueness presuppositions. This new semantics is also analysed with assertion logic. The account we now get enables us to calculate the projection of uniqueness presuppositions of descriptions embedded in larger contexts.Thus, the assertion logic serves as a calculus for presupposition projection (Langen doen & Savin I 97 I). To ease the intellectual digestion of what follows, here is a bit of information on the sequential composition of this paper. Section I is the section you are now reading. The section you are now reading, by the way, is an example of a definite description with a uniqueness condition depending on the current context. Section 2 discusses some proposals made by logicians for the logic of descriptions.Section 3 argues that a dynamic account of meaning makes descriptions easier to handle, for two reasons. In the first place, in a dynamic set-up the interpretation of an indefinite description can be viewed as an act of picking an arbitrary individual, i.e. as an indeterministic action. In the second place, the perspective on meanings as relations between inputs and outputs provides a natural treatment of context change: the current input state serves as a context which changes dynamically as the discourse processing goes on. Section 4 informally introduces dynamic predicate logic (DPL), extended with a clause for definite assignment.Section 5 gives the formal definition of the standard DPL semantics. In Section 6 the dynamic meaning of definition for DPL is linked to a static meaning definition by means of an assertion language allowing statements about the behaviour of DPL programs.Assertion reasoning about DPL can be axiomatized, as is shown in Section 7, where a calculus is introduced and its use demonstrated with some simple examples. It turns out that the extension of DPL with definite assignment programs results in a Russell-style logic of definite descriptions. In Section 8 the possibility of handling presupposition failure in terms of dynamic clauses for error abortion is informally introduced. Section 9 gives the formal definition. Section 10 proposes an axiom system for this new semantics, and Section I I demonstrates the use of this new calculus. Section I 2 gives a brief summary and a conclusion. The treatment of definite descriptions in (Russell I905) is logically very elegant, but it does not do justice to the use of descriptions in natural language. My aim in this paper is ro proyjde a treatment of definite descriptions that rakes the presuppositional behaviour of definite descriptions into account, while at the same rime retaining the formal elegance of the Russell proposal.The formal tools for this enterprise are dynamic predicate logic with a matching assertion language. I implore the reader not to be intimidated by the tools that are used.
Jan van Eijck
24 1
All Ill· or she needs to know about them for the analysis of descriptions in namral language is explained in the pages that follow.
2
D E S C R I PT I O N S I N S T A T I C L O G I C
(I) 3x
'Vx"i/y ((
(2) 3x
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
For a logical account o f the meaning of definite descriptions, let us first look at an account of the use of definite descriptions in mathematical logic. There are several such accounts, but for now we focus on one example. Consider the way in which Hilbert & Bernays use che definite descriptor. In Hilbert & Bernays (I 939), a definite descriptor LX :
.!.p.
The Dynamics of Description
member of the universe in case there are no cp s. In case there are cp s, ex : cp (x) denotes an arbitrary cp, in case there are no cp s, ex : cp (x) denotes an arbitrary non-cp. Hilbert & Bernays are not concerned with the semantics of e-terms. The e -terms are introduced as proof theoretic devices, and it is proved that a deduction of an e-free formula from a set of e-free hypotheses that uses e terms can always be replaced by an e -free deduction. This means that it is unnecessary to define truth conditions for arbitrary formulae with epsilon terms. Such e-terms are introduced by axioms of the form (3), where cp (v) denotes the result of substituting v for t in cp, and
3 T HE D Y N A M I C S O F P I C K I N G A N ARB I T R A RY cp In static logic, the command 'Pick an arbitrary cp' is awkward, because there may not be such a cp . The introduction of e terms to remedy this defect does not really help, because the semantics of e terms is unintuitive. A semantic account (Leisenring 1969) involves a choice function
that picks out a member of the universe for every definable subset of the universe (where a subset of the universe is definable if there is a formula cp of the language with one variable free which is true of precisely the objects in that subset). Given a particular choice function , and assuming that assigns to the set I dl vft l=x :-d cp), that is, to the set of objects d for which cp is true in vft if d gets assigned to the variable x . In case there are no cp s, the term ex : cp (x) will refer to the individual that is the value under cJ> of the empty set. Suppose we apply this to natural language, and translated an indefinite noun phrase such as a man as an epsilon term. Suppose we use the noun phrase twice. The second use of a man will then refer to the same individual as the first. This is hardly ever what we want. In some cases this bug can be fixed by using a translation ey : (man y 1\ y #- (ex : man x)), a description that refers to a different individual than ex : man x, but this ploy can never be a systematic remedy. What we want, instead, is to employ different choice functions as we go along. and to let the interpretation process fail in case no appropriate choice of cp is
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
(3) cp (t) -+ cp(ev : cp(v)!t).
J
an van
Eijck
243
possible because there are no cp s. It turns out that dynamic logic for natural language in the spirit ofBarwise ( I 987) and Groenendijk & Stokhof(I 99 I) gives roughly the results we want, on condition that one disregards the presupposi tions of the use of descriptions. Consider mini discourse (4), where the hearer is asked to take rwo different individuals in mind. (4) A man walked in . He sat down . Another man walked in .
Note that we are not trying to give an account of the strategies a language user might employ to arrive at reading ( s ); the pragmatic coreference and non coreference rules that may be involved are outside the scope of the present investigation. What intuitively happens when one processes discourse (4), in the manner indicated by the indexing in ( s ), can be described as the following set of instructions. First focus on an arbitrary man. Then assume that the choice of man was lucky, and that that very man walked in. Then assume that the choice was still luckier: the man in focus sat down as well! Next keep this choice of man in mind, and again pick a reference to an arbitrary man, but in such a way that the new man is different from the first. Finally assume that the second man is also a man that walked in. This account sounds like a piece of imperative programming, which suggests that the meaning of the discourse can be given in terms of a translation into a programming language. Here is such a translation (tense is ignored), in essentially the language of dynamic predicate logic of Groenendijk & Stokhof (I 99 I ), but with a bit of extra emphasis on its imperative programming nature.
(6) 1]V 1 : man v 1 ; walk-in v 1 ; sit-down v 1 ; 1]V2 : ( v2 f= v 1 ; man v2); walk-in v2• Note that the dynamic effects that we focus on here involve the linking of pronouns to their antecedents. A quite different kind ofdynamics is involved in the state changes suggested by tense and aspect of verb phrases (such as the change from a state of standing upright to a state of sitting). These tense/aspect phenomena are of a very different dynamic nature, and they deserve to be srudied in their own right, but they are outside our scope in this paper.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Since we intend the reading where he is anaphorically linked to the earlier indefinite and another is anaphorically constrained (to borrow a term from Barwise (I 987)) by that same indefinite, we may use indices to indicate the intention. I follow Barwise (I 987) in using superscript indices for antecedents and subscripts for anaphors. The following indexing indicates the reading of text (4) that we intend. ( s ) A man 1 walked in . He1 sat down . Another 1 man 2 walked in .
2.H The
Dynamics of Description
4 D Y N A M I C P RE D I C A TE L O G I C : SYNTAX A N D I N F O RM A L S E M A N T I C S
This section is meant as a brief introduction to dynamic predicate logic (DPL) in its undisguised form as an imperative programming language. We have already encountered atomic tests, sequential program composition, and indefinite assignment; in the syntax description below we add implication, negation, and definite assignment (the latter construct is not considered in Groenendijk & Stokhof ( I 99 I)). In natural language, one does not engage in explicit bookkeeping with
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
The programming language employed in (6) has two kinds of basic statements: assignments and tests. Sequences of statements are formed with the sequencing operator ;. The assignments are non-deterministic, which means that semantically the program is not a function from states to states, but a relation between states (or equivalently, a function from states to sets of states). Non-determinism here means that there are different ways in which the assignment command can be carried out. Test statements narrow down the set of output states. A test relates an input state that satisfies it to itself, and an input state that does not satisfy it to nothing at all. In the first case we say that the test program succeeds; in the second case that it fails. What makes a dynamic approach to natural language semantics particularly attractive is that it provides us with a means of handling context dynamically. By picturing meaning as a relation between input states and output states, we perceive the processing of meaning as an activity of changing contexts. The meaning of the definite description the chapter you are now reading depends on who is you and when is now , and this information is part of the current context. The same dependence on current context holds for even simpler definite descriptions like his wift or her husband . Their interpretation depends on contextual information about the reference of the possessive. As the formal analysis below will show, in a dynamic approach to natural language processing, such information is provided by the current input state. We fix the meaning for this assign-and-test mini-language by giving it a dynamic semantics. For good measure, later on we will also provide a set of Hoare/Pratt-style axiom schemata for this representation language. The advantage of this addition is that the axioms provide a link to notions of static semantics. This allows us to take snapshots of truth conditions at various stages in the discourse processing, so to speak. In other words, the Hoare/Pratt-style calculus will allow us to consider projections from dynamic logic to static logic, in the sense of van Benthem ( I 99 I).
J
an van
Eijck 245
If R is an n -place relation symbol and t 1, , t" are terms, then Rt 1 t" is a DPL program. 2. If t1, t2 are terms, then t1 - t2 is a DPL program. J. If n1 and n2 are DPL programs then (n1; n2) is a DPL program. 4· If n1 and n2 are DPL programs then (n1 � n2) is a DPL program. 5· If n is a program, then ...., Jr is a DPL program. 6. If n is a DPL program and v is a variable, then rJV : n is a DPL program. 7· If n is a DPL program and v is a variable, then tv : n is a DPL program. 1.
•
•
•
•
•
•
I will follow the usual predicate logical convention of omitting outermost parentheses for readability. Also, it will become evident from the semantic clause for sequential composition that the ; operator is associative. Therefore, I will often take the liberty of writing n 1 ; n 2; n 3 instead of (n 1 ; n 2 ); n 3 or n 1 ; (n 2; n3 ). Also, t1 "i' t2 will be used to abbreviate ...., t1 - t2 (c£ example (6)). Note that 17 and t are program building operators (in fact, dynamic quantifiers) rather than term building operators, as in the logic of Hilbert & Bemays. The remainder of this section is devoted to an informal account of the dynamic semantics of atomic test predicates, implication and negation of DPL programs, and TJ and t assignment. The next section will give the formal dynamic semantics. Semantically, what we are interested in is states , functions from the set of DPL variables to individuals in a model. Semantically, DPL programs act as state transformers: a DPL program maps input states to sets of output states. A program maps an input state to the set of aU possible outputs the program can produce for that input. A program which is a test will on input A either produce output sec {A } (in case the test succeeds) or output set 0 (in case the test fails). For example, the instruction man x tests whether the value of x in the input state satisfies the predicate man . If it does, the output will be the same as
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
regard to the 'slots' used for keeping track of individuals mentioned iri discourse. One just keeps them in mind, and does not confuse them, that is all. One could ensure that in DPL the slots do not get confused by stipulating that new assignments to variables which are already 'active' are forbidden (see van Eijck & de Vries (1 992)), but it turns out that such scrupulousness is unnecessary. The set of programs of DPL has as its terms a set C u V, where C is a set of individual constants and V a set of individual variables. Individual constants are needed in the translation of proper names. Individual variables will be used in translation of indefinite and definite descriptions and in the translation of anaphoric pronouns. Given a set of terms and a set of relation symbols, the set ofDPL programs is the smallest set such that the following points hold.
246 The Dynamics of Description
=
·
To get the semantics (roughly) right, one has to assume that (7) is true if and only if every output state for the antecedent will be an appropriate input state for the consequent (see Barwise ( I 987) or Groenendijk & Stokhof ( I 99 1 )). Negation should allow one to treat examples like the following, where the negation has scope over an indefinite. (8) The manager 1 does not use a PC2• This example can be translated into DPL as follows:
(9)
w1
: (manager v 1 ); -.(rw2 :pc v2; use(v1, v 2)).
To get the semantics right (again, roughly), a negated program should act as a test: -.:n should accept (without change) all variable states which cannot serve as
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
i:he input; this indicates success of the test. If it does not there will be no output, indicating failure of the test. Tests have only one possible output: they are deterministic instructions. Programs which may produce non-singleton sets are non-deterministic; for some inputs there is more than one possible output state. Examples of non deterministic programs are 17 assignment programs; the program 1JV : :n has, on input A , the set of all states which may differ from A in the fact that they have another x value, namely some value that satisfies :n. There are as many ways of carrying out the instruction 1JV : man v as there are different men available in the model under consideration. I will use skip as an abbreviation for -.7'/Vo : v0 # v0 (where v0 is a variable of the language), and fail as an abbreviation for -.skip. This abbreviation is intended to ensure that the program skip is a test which always succeeds, in other words, it is a command to do nothing. For every input state A , skip will produce output set {A}. The program fail expresses a test which always fails; it is a command to exit without output. For every input state A , fail will produce output set 0. Atomic predicates like t1 t2 or Rt1, • • • t. are meant to express tests which may fail. The test is in fact an ifthen else statement: if Rt1, • • • t. is true for the current input state then do nothing, else fail. Again in terms of output behaviour: If Rt1, • • • t. evaluates to true in state A , the predicate will have output set {A}, otherwise the output set will be 0. Programs of the form (:n 1 � :n 2) are intended to treat the interplay of natural language implication and descriptions. Note that in the following examples indices . are used to indicate anaphoric links. An indexing gives an anaphoric disambiguation of an example sentence or piece of text. The srudy of the possible constraints on such indexings is important, but outside the scope of this paper. (7) Ifa man 1 admires the kingl, he1 cheers him2•
J
an van
Eijck
24 7
input for :n , and reject all others. In fact, it turns out that if we adopt fail as a primitive, -.;n is definable in terms of � and fail, as :n � fail. In the semantic clauses below we will do it the other way around: we take � and -. as primitives, and let the semantic clause for fail follow from the abbreviation convennon. Definite descriptions can be used as anaphors, while at the same time acting as antecedents. Discourse ( 1 0) provides an example. ( I o) A customer 1 entered. The womanf sat down. She2 smiled .
(I 1)
: customer v1; enter v1; w2 : (v2 v 1; woman v2); sit-down v2; smile v2• 1JV1
�
The t assignment in ( 1 I ) is dependent on the 1J assignment to variable v 1 . With respect to a particular assignment for v1, the description is unique. Note that the t assignment to v2 d�es indirectly act as a test on the previous 1J assignment to v1: this test will weed out 1J assignments that are inappropriate in the light of the subsequent discourse. Definite descriptions can also be dependent on each other. Consider the string of characters in ( 1 2).
( 1 2) a A
-be
Suppose just for an instant that ( 1 2) is a state of affairs one is talking about. The state of affairs involves characters and hat symbols (hats for short). With respect to ( 1 2), it does make sense to talk about the character with the hat , although ( 1 2) neither has a unique character nor a unique hat. We can, for instance, truthfully assert ( I 3) about ( 1 2).
( 1 3) The character with the hat is a capital. The translation into DPL is rather straightforward if we bear in mind that the preposition with has to translate as a two-place relation symbol, and also that the definite is not treated as a term but as an assignment instruction telling us to find the unique thing v2 that is a hat related to v1, given an assignment of a character to v 1•
( 1 4) tv1 : (clzaracter v1; tv2 : (hat v2; witlz (v1, v2))); capital v1• lnruitively, the first t assignment 'tries out' individual characters C until it finds the unique C with the property that a hat H can be found that is unique for C. Note that in a situation where some characters have several hats but there is one character with only one hat, the instruction would pick out this one
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
The indices indicate that the woman has a customer as its antecedent, while at the same time acting itself as antecedent for she in the next sentence (and constrain ing the gender of the pronoun). A DPL translation of ( I o) is given in ( I I ) .
248 The Dynamics of Description
character. Thus, the phrases the character with the hat and the character with a hat will give rise to non-equivalent representations. As one of the referees pointed out to me, it might be argued that the distinction made by the representation language is a bit too fine here. The semantic picture sketched above is still in need of one extra touch. So far I have said nothing about presuppositions of the use of descriptions. In fact, I will refrain from doing so for the moment, and first work out a semantics that treats descriptions in the Russellian·(cwo-valued) way.
P R O P E R STATE SE M A NT I C S F O R D P L
In this section I will spell out the formal details o f the standard semantics for dynamic predicate logic with t assignment. I refer to the standard semantics as proper state semantics to emphasize that the definition is couched in terms of proper states only. Given a model vft - (M, I), M a universe of individuals, and I an interpretation function for the individual constants C = {c0, c 1 , ) and the first order relation symbols of the language, a proper state for vft is a function in Mv. I will refer to the set of proper states for vft as S .ff . A proper state A for vft = (M, I) determines a valuation V .ff .A for the terms of the language as follows: if t E V then· V .ff .A ( t) - A ( t ), if t E C, then V .u .A (t ) - I(c ). If A is a proper state for vft , x a variable, and d an element of the universe of vft , then A [x := d ] is the proper state for vft which is just like A except for the possible difference that x is mapped to d . I define a function [ · ] .ff : S .ff .9' S ; by recursion. A , B are used as metavariables over (proper) states. [ :n] _p(A ) gives the set of output states that :n may produce for input state A . Note that in the clauses for atomic relations and identities we rely on the common predicate logical notion of satisfaction of a formula in a model, given an assignment: vft F=A cp . This relation is defined in the standard way (see the clauses for atomic tests). •
-+
I.
li (A ) [Ri t , . . . lnu
2_
[t 1
4·
[(n1
_
=
,A (t t ), . . ., V { {A } ifoth(Verwtse. . 0
.ff
.,({
,A (tn )) E I(R ),
{
V V 1 2] .u (A ) _ {A) if ; � (t 1) = ; ,A (t2), 0 otherwtse.
�
n2)] ; (A ) -
I
{A) if for all B E [:n 1 ] ; (A ) it holds that [ n2] ; (B) -1' 0, 0 otherwise.
•
•
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
5
J S·
7·
{
[-.n] . (A ) _ {A) if[nL� (A ) If
an van
Eijck 249
0,
0 orherwtsc.
[ .nJ.� (A [v := d ] ) for the unique d E M for which [n] .«(A [v := d] ) ¥ 0 [ w : n] .�� (A ) if d exists, otherwise. 0
Fact: n1 dynamically entails n 2 iff (if and only iQ skip dynamically entails .7lt => n z . The statement 1'/V : .7l p erforms a non-deterministic action, for it sanctions any assignment to v of an individual satisfying n . Th e statement acts as a test at the same time: in case there are no individuals satisfying .7l the set of output states for any given input state will be empty. In fact, the meaning of YJV : .7l is equivalent to YJV : skip; .7l, or in more standard notation, v := ?; .7l . It follows imm ediately from this explanation plus the dynamic meaning of sequential composition that YJV : (n 1 ); n 2 is equivalent with YJV : (n 1 ; n 2 ). The interpretati on conditions for L assignment make clear how the unique ness condition is h andled dynamically. The statement tV : .7l consists of a test fol lowed by a deterministic action in case the test succeeds: first it is checked whether there is a unique n; if so, this individual is assigned to v and .7l is perfor med; oth erwise the program fails (in other words, the set of output states is empty). It is not difficult to see that this results in the Russell treatment for defi nite descripti ons. Also, we see that th e two programs LV : (n1 ); n 2 and LV : (n1 ; n 2 ) are not equivalent. The program w : (n 1 ; n 2 ) succeeds if th ere is a unique object d sati sfying n 1 ; n 2 , while the requirement for tV : (n1 ); n 2 is stronger: there has to be a unique indivi dual d satisfying n 1 , and d must also satisfy n 2• Th e clause for dynamic implication should take care of th e proper treatment of th e definite description his wife in example (I s ).
(I s ) Ifjohn is married, his wife will be cross with him .
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Note that it follows from th e abbreviation conventions and the definition of [ · l u that [skip] .��(A ) = {A ) and that [fail] .�� (A ) = 0. Truth is defined in terms of input- output behaviour: .7l is true relative to model vft if th ere are proper states A , B for vft such that B E [ .7l ] .u (A ). Two programs n 1 , n 2 are equivalent if for every model vft and every state A for vft , [ n1 ] .�� (A ) = [n2] .« (A ). Dynamic entailment is defined as follows: n1 dynamically entails n 2 if for every model vft and for all proper states A , B for vft : if B E [ n 1 ] Jf (A ) th en there is a proper state C with C E [n2] .�� (B ).
250
The Dynamics of Description
( 1 6) Ijjohni is married then [hisi wife} will be cross with himi . A suitable DPL translation for the example now runs as follows: ( 1 7) (marriedj ) � ( IX : wife-of (x ,j ); cross-with (x ,j )). Now either the program for john is married will not complete successfully, and then the program for the consequent his wife will be cross with him will not be executed at all, or it will indeed give precisely one output (this is because the antecedent program is a test). But then the fact that there is an output guarantees that there will be a unique referent for t assignment in the con sequent, so the program for his wife will be cross with him will only fail if the per son who is in fact John's wife is not cross with John. 6 M A K I N G A S S E RT I O N S A B O U T D P L P R O G R A M S Because our intuitions about static meaning seem to be much better developed than our intuitions about dynamic meaning, we can, for a large class of natural language sentences, check whether the · intuitive meaning of a sentence S corresponds to the meaning of its DPL translation :rc in the following precise sense. Does the intuitive meaning of S precisely describe the set of states for which :rc succeeds? In terms of so-called assertion logic for imperative programs we can describe the set of states for which :rc succeeds by means of the so-called weakest (existential) precondition of :rc with respect to some statement which is always true. One way of expressing weakest preconditions of DPL programs is by supplementing the proper state semantics of DPL with an axiom system in the style of Hoare (see Apt ( 1 98 1 ) for an overview of this approach, and Hoare
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
To get this translated into DPL, under the intended reading that the possessive pronoun his is anaphorically linked to john , we have to decide what to do with proper names. The trouble is that proper names do not observe the same anaphoric constraints as definite or indefinite descriptions. It seems to me that the anaphoric behaviour of proper names can be accounted for by assuming that they are assimilated to descriptions, but this will only work if descriptions are treated as carrying uniqueness presupposi tions. Since we are now exploring a Russellian treatment of definites, this road is not yet open to us, however. Therefore I will sidestep the issue for now, and just treat anaphoric links to names by translating the anaphor as the constant which also translates its name antecedent. An indexing for example ( 1 s ) using constants as indices for antecedent and anaphors, as in (1 6), paves the way for this.
Jan van Eijck 25 1
I. 2.
3· 4· 5·
If R is an n -place relation, and t1, tn are terms, then Rt1 If t1, t2 are terms, then t1 = t2 E QDL . If cp , tjJ E QDL , then ( cp 1\ tjJ ), -.cp E QDL . If v e V and cp e QDL , then 3vcp E QDL . If n e DPL and cp e QDL , then ( rr )cp e QDL . •
•
•
•
•
•
tn E QDL .
We need to distinguish the programs of QDL from the static QDL relations. We use boldface for the test program R t 1 tn and italics for the formula Rt 1 •
•
•
. . . ln .
We will continue to use the abbreviation conventions with respect to DPL programs in the QDL format. As is customary, we abbreviate -. (-.cp 1\ -. tjJ ) as ( cp V tjJ), -. ( cp 1\ -. tjJ) as ( cp - tjJ ), ( cp - tjJ ) 1\ ( tjJ - cp ) as cp - tjJ , -.(rr)-.cp as [rr] cp and -.3v-. cp as 'rJvcp . Also, we omit the outermost parentheses for readability. Finally, we add the conventions for QDL formulae that T is an abbreviation of'rJv0(v0 - v0) and .L an abbreviation of -. T. Note that there is a distinction between skip, the DPL command to do nothing, and T , the QDL formula which, as we will see, is always true. Similarly, there is a distinction between fail, the DPL command to fail, and .L , the QDL formula which, as we will see, i s always false. We can now define the notion of satiifaction of a QDL formula by a state A for a model ..,{( - (M, I). I.
..,{( I=A R t . . . ln if (V .A (t l), . . ., V ,u .A { tn)) E l(R ) l
,g
(this is the standard Tarski satisfaction definition). 2 . ..,{( I=A t 1 = t2 ifV.ff .A ( t 1 ) = V,u .A ( t2) (again the standard Tarski satisfaction definition). 3· ..,{( I=A -.cp if it is not the case that A I=A cp . 4· ..,{( I=A cp 1\ t/J i f ..,{( I=A cp and ..,{( I=A t/J · S · ..,{( I=A 3vcp iffor some d e M, A I=A iv:-dJ cp . 6. ..,{( I=A ( rr )cp if there is some B E [ n ] ,u {A ) with ..,{(
1=8
cp .
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
(1 969) for the original proposal). Such a calculus is presented and proved sound and complete with respect to the proper state semantics in DPL in van Eijck & de Vries (1 992). Here, I want to present a slightly different kind of assertion language, in the style of Pratt's system of dynamic logic (Pratt 1 976). If we want to be able to use the full range of logical connections between static assertions from predicate logic and programs from DPL we need a powerful assertion language. I will define a version of quantified dynamic logic, inspired by Pratt's dynamic logic (Pratt 1976; Goldblatt 1 987; Kozen & Tiuryn 1 990), that gives us the expressive power we need. The assertion language QDL will have the same relation symbols, the same individual constants and the same variables as the DPL language we want to make assertions about. In fact, the DPL programs will occur as dynamic operators in the QDL statements. Here is the definition of the assertion language.
2 5 2 The Dynamics of Description
7 A C A L C U L U S F O R P R O PE R STATE SEMAN T I C S This section gives a proof system for dynamic interpretation with proper state semantics. We build this proof system on top of an axiomatization for predicate logic, so assume AP to be a set of axioms for predicate logic. See e.g. Enderton (1 972) for one possible choice, plus discussion and motivation. . The atomic predicates ofDPL act as tests. The following test axiom schemata account for their behaviour. Atomic Test Schemata A I (Rt l . . . tn ) cp - (Rtl, . . . tn 1\ cp ). A 2 ( t 1 = t 2)
•
•
•
•
•
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
It follows from this definition and the notational conventions that 4 I=A [ 1T)
Ja n van Eijck 2 5 3
Note that the following dual versions are derivable using the notational conventions and standard propositional reasoning. T I (R tl ln -+ q; ). tn] q; - (Rtl T 2 (t 1 - t2] q; - ( t 1 = t2 - q; ). •
•
•
•
•
•
Schemata for Complex Programs A 3 (rr 1; rr2)q; - (rr 1)(rr2)q;.
What this schema says is that the following are equivalent. o
As can be seen from the DPL clause for ; these two statements are indeed equivalent, so the schema is sound. Again, the abbreviation conventions and propositional reasoning enable us to derive a dual version. T 3 (rr 1; rr2] q; - (rr J](rr2] q; .
Here is the schema for program negation: What this says is that the following are equivalent: o o
For input state A , program �n gives at least one output state satisfying q;. For input state A, statement q; holds and prqgram n fails.
The DPL clause for negation makes clear that these two are indeed equivalent, so the schema is sound. Here is the dual formulation that can be derived from it. Here is the schema for dynamic implication. A 5 (rr 1 � rr2) q; - (q; 1\ (rr1](rr2)T).
What this says is that the following are equivalent: o
o
On input state A , performing program n 1 � n 2 will succeed, with at least one output state satisfying q; . O n input state A , q; holds and furthermore it holds that for all outputs of n1 in A , n 2 will succeed.
By checking the DPL clause for � one sees that these are indeed equivalent. This shows that the schema is sound. Again, we can derive a dual formulation. T 5 (rr 1 � rr2] q; - ( (rr 1 ] (rr2)T -+ q; ).
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
o
For input state A the program n 1 ; n 2 succeeds and produces at least one output satisfying q; . For input state A the program n1 succeeds and produces at least one output B for which n 2 succeeds and produces at least one output satisfying q; .
254
The Dynamics of Description
The schema for rJ assignment. A 6 ( fJV : n-)cp - 3 v( n')
This says that the following are equivalent: •
•
For input A , program 'YJV : n succeeds and has at least one output satisfYing
T 6 (17v : rr]
Before we give the schema for t assignment, it is convenient to introduce one further abbreviation. We will use 3!x
This says that the following are equivalent. •
•
For input state A , program tv : n succeeds and gives at least one output state for which
And indeed, these statements are equivalent, as the DPL clause for t assignment shows. This proves the soundness of the schema. A dual formulation of it T 7 [t v : rr)
.....
't v [ rr )
Note that the schemata for rJ and t assignments and their duals can be used to contextually eliminate the rJ and t operators. To look at the schema for t assignment and its dual a bit closer, consider the following easy example. Assume for a moment that n is the atomic test program Kx, for testirLg whether x is a king. Suppose we are in a model with a unique king, i.e. a model in which 3!xKx holds for every state. Assume also that in our model everyone of royal blood is related to Queen Guenever. Finally assume that we are in a state A where y is mapped to Queen Guenever. Then
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
The DPL clause for rJ assignment shows that this is indeed the case, so the schema is sound. Here is its dual formulation.
J
an van
Eijck
255
the t schemata allow us to conclude that the statements (tx :Kx)Rxy and [tx : Kx l R.\y hold in A . Rules of inference . For purposes of reasoning with the system we also need a set of derivation rules. These are the following. R 1 (Modus Ponens) Concludefrom 1- cp ljJ and 1- cp to 1- ljJ . R 2 (Universal Generalization ) Concludefrom 1- cp to 1- V vcp . R 3 (Necessitation ) For every program :rr , concludefrom 1- cp to 1- [ 1T] cp . ......
( r 8) The King ofFrance is bald . Example ( 1 8 ) can be translated into DPL as t.'< : Kx; Ex . Here is a derivation of the weakest precondition for success of this program, i.e. a derivation of its static truth conditions. (tx :Kx; Bx)T - (tx : Kx)(Bx)T - 3!x(Kx) T 1\ 3x(Kx )(Bx) T - 3!xK'< 1\ 3x (K'< 1\ (Bx)T) 3!xKx 1\ 3x(Kx 1\ Ex). ++
Here is a derivation of the static falsity conditions of the Russell example. [tx :Kx; Bx] .l.. - [tx :Kx][Bx] .l.. - 3!x(Kx)T .... Vx[Kx] [Bx] .l.. - 3!xK'< .... Vx(K'< .... [Bx] .1.) - 3!xKx ...... Vx(K'< ..... (Ex ..... .l.. )) - 3!xKx .... Vx (Kx .... -.Ex).
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
The first two o f these are borrowed from predicate logic, the third one is rhe so called necessitation rule, which is standard in axiomatizations of modal and dynamic logics (see e.g. Goldblatt ( 1987)). The notion of theoremhood in the calculus is also standard: Formula cp is a theorem of the calculus, notation 1- cp , if cp firs one of the axiom schemata or cp follows from theorems in the calculus by an application of one of the inference rules. It is not difficult to see that the rules ofinference preserve validity. Combining this observation with our knowledge that the program axioms A 1-7 are sound and that the axioms ofpredicate logic AP are sound, we arrive at the soundness of the QDL calculus: if I- cp then I= cp. In fact, ,.,e have already given a number of theorems of the calculus, namely the dual formulations of the axiom schemata. The axiomatization ofDPL in QDL that we have given is not only sound but also complete, although we will not prove that fact here. See van Eijck (to appear) for a proof It may be enlightening to work our some examples of derivations of static meanings using the calculus. I will concentrate on very simple sentences.
256 The Dynamics of Description
This outcome is of course not surprising, for 3!x.Kx - Vx(Kx - -.Bx) is the negation of3!x.Kx I\ 3x(Kx I\ Bx), the weakest precondition for success of the program. Now consider example ( r9).
(I 9) The King ofFrance is not bald. Following Russell, I will suppose that there are two readings, with different scopes for the negation operator. It is left to the reader to verify in the calculus that the weakest precondition for success of the program I.X :Kx; -.Bx is given by: 3!x.Kx I\ 3x(Kx I\ Bx) The weakest precondition for success for the other reading is given by the following derivation. -.
.
This is indeed the result one would expect. Finally, let us look at an example where the definite is part of the consequent of an implication, with the antecedent setting up the requirements for uniqueness of reference. (zo) Ifa woman is married, her husband will look after her. Here is a DPL translation that shows the intended anaphoric links.
(2 1 ) ( 17x : Wx ; Mx) � ( ty : Hyx; Lyx). Note that we have translated the definite noun phrase her husband with the use of a definite assignment, expressing that we want to refer to the unique individual y satisfying the relation Hyx , where x is the variable that was used for the antecedent of the possessive pronoun. ((77x : Wx; Mx) � (ty : Hyx; Lyx)) T - ( qx : Wx; Mx](ty : Hyx; Lyx)T - [qx : Wx] [Mx](ty : Hyx)(Lyx) T - Vx [Wx] [Mx](ty : Hyx)(Lyx)T - Vx(Wx - (Mx - (ty : Hyx)(Lyx)T)) ... Vx(Wx - (Mx - (3!y (Hyx) T I\ 3y (HyxXLyx)T))) ... Vx( Wx - (Mx - (3!yHyx I\ 3y (Hyx I\ Lyx)))). Deriving the conditions for which program (2 1 ) fails we find the negation of this formula. These results are again what one would expect under the present regtme.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
(-.(,x : Kx ; Bx)) T - [tx : Kx] [Bx] ..i - 3!x(Kx) T - Vx[Kx; Bx] l. - 3!x(Kx) T - Vx [Kx] [Bx] l. - 3!xKx - Vx(Kx - [Bx] .l) - 3!xKx - Vx(Kx - (Bx - l. )) - 3!xKx - Vx(Kx - -.Bx).
J
an van
Eijck
257
The examples show that in the proper state semantics of DPL, the uniqueness presuppositions of the definites are swallowed up by the truth conditions, so to speak. No distinction is made between falsity and failure of presupposition. In the next section I will propose a means for introducing this distinction in the DPL framework.
8 E R R O R STATE S E M A NT I C S : I N F O RMAL D I S C U S S I O N
(22) a a b � b c. (2 3) The character with the hat is not a capital. On a Russellian analysis (Russell 1 905), example (23) is false with respect to (22) if the description is taken to have scope over the negation operator, as in DPL translation (24). (24)
w1 : (character v1; LV2 : (hat v2;
with ( v1; v2))); -.capital v 1 •
We intend to follow the account of Frege (1 891), Frege (1 892), Hilbert & Bemays (1 939), and Strawson (1950) rather than Russell's analysis, so this is not quite what we want. We intend to preserve the distinction between falsity and failure of presupposition. In the Frege view, which is shared by Hilbert & Bemays and by Strawson, (24), rather than being false, suffers from presupposi tion failure. Our method of working out this distinction will be as follows. I assume that DPL programs can proceed in one of three ways when acting on a given input state: they report success by producing at least one proper output state, they report failure by not producing an output state at all, 3· they report error by producing a special error state as only output. 1.
2.
The first case indicates truth of the information contained in the program in the context of the current input state. The second case indicates falsity of the information contained in the program in the context of the current input state. The third case, finally, corresponds to failure of presupposition in the context of the current input state. In formulating dynamic meaning, one must specify the (mutually exclusive) conditions for the three cases. Interestingly, in many cases uniqueness presuppositions for definite descriptions are carried along in the discourse. Consider example (2o) again, with its translation repeated here for convenience as (25).
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Nothing we have said so far makes clear how the dynamic treatment of definite descriptions is meant to deal with their uniqueness presuppositions. Consider situation (22) and assertion (23) about this situation (c£ also Haddock (1 987)).
; 5 X The Dynamics of Description
(2 5) ( �x : Wx ; Mx) � (tv : Hyx; Lyx).
(26)
A capital with a hat precedes another capital.
It is not clear to me whether this is intuitively acceptable, but possibly my inruitions are blurred by the fact that I find it hard to forget about other situations which do not contain characters with hats. I take it, however, that example (27) makes clear that in general a presuppositional treatment of indefinites a Ia Hilbert & Bernays cannot be correct for natural language analysis. (27) There is a capital with a hat . The most reasonable assumption seems to be that (27) is simply false with respect to (22). I will therefore not treat indefinites as presupposition-loaded.
9
E R R O R S TA TE SEMANT I C S : F O R M A L DE F I N I T I O N S
Assume a model .£{ = (M, I) as before. I use S .�� for the set of proper states for .£{ , i.e. for i:he set of functions Mv. In the same way as before, a proper state A for .£{ (M, I) determines a valuation V ..«.A for the terms of the language. The symbol £ will be used co designate a special error state. If S ..« is the set of proper states for .£{ =' (M, I), then S ..« u (e) is the set of states for .£{ . There is no connection between th� error state £ and the epsilon terms from Section 2. We define a function [ ] ..«: (S ..« u ( £}) ..... .9' (S ..« u ( £}) by recursion. The meaning conditions are rather involved because of the need to specify error abortion behaviour. The reader should keep in mind that the only case where error arises is the case where a t assignment aborts because no unique referent =
·
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
The presupposition of the consequent of(25), namely that ty : Hyx has a unique referent relative to an assignment of a married woman to x , is nicely taken care of by the antecedent of the implication. Strictly speaking, one also has to assume a meaning postulate expressing that married women have one and only one husband. But given that, an account that handles presuppositions should ensure that the presupposition of the consequent program will be cancelled in the larger context of the dynamic implication. This is one of the projection properties for presuppositions that the presupposition literature in the style of Karctunen (1 974) intends co describe. Given the distinction between program failure and program error abortion, one can also easily implement the view, found in Hilbert & Bernays ( 1 939), that indefinites are also loaded with a presupposition. This view entails that (26) has no truth value relative to situation (22), because the situation does not contain a capital with a hat.
J
an van
Eijck
259
can be found in the context of the current input state. The mention of error states in the conditions of the other program constructs is meant to take care of error propaganon. The first semantic clause specifies what happens when the input of a program is the error state. The other clauses define recursively how programs act on proper input states. A is used as a metavariable over proper states, and B as a metavariable over states.
l
l
{e) if[ .n ] ..« (A ) = {e),
6. [ --..n] ..« (A ) = (A} if[.n ] ..« (A ) = 0, 0 otherwise.
7· [ 1Jx : .n] .rr (A ) = v{[ .n] ..« (A [x := d]) l d E MJ. 8. [ tx : .n] ..« (A ) =
[ .n ]..«(A [x :- d]) for the unique d E M ' with [ .n ].rr (A [x :- d]) !t (e) if d exists, otherwise. {eJ
Again, success of a program is defined in terms of input-output behaviour: .n succeeds relative to model 4 for (proper) input state A if there is a proper state B with B E [ .n] -« (A ) . Because of the possibility of presupposition failure it makes sense to define the following three sets for any program .n and model 4. I , .K � (A E S .K I [.n] ..« (A ) n s .K � 0). " o,,-« d�f {A E S ..« I [.n] ..« (A ) = 0) . df e *,,..« � (A E S -« I [.n] ..« (A ) = {e) } .
e
•
Note that it follows immediately from these definitions that we have the following:
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
S·
(e) if there is a state B E [ .n1lu(A ) with [ .n2l u(B ) = {e), [.n 1 � .n2] ..« (A ) - (A) if for all B E [.n1]..«(A) it holds that [�] ..«(B) !t {e), 0 otherwise.
260 a e 0
The Dynamics of Description
S .ff - (o,,.ff u *,,.ff ). o,,.ff = S "' - ( I "·"' u *"·"' ). *,,.ff = S .ff - ( I ,,.;r u o,,4). I " "' ·
=
Dynamic Error Entailment n1 error-entails n2 if for all models .4 and all proper states A and all states B for .4 : B E [ n1] 4 (A ) implies [ n2] 4 (B ) g; (c}. Dynamic Proper Entailment Jl 1 properly entails n2 if for all models .4 , all proper states A and all proper states B for .4 : B E [ n1 ] 4 (A ) implies [n2].�� (B ) g; {c}.
The first of these notions is intimately tied up with the relation of dynamic implication. From the definition of error entailment we immediately get . Fact: Jl1 error-entails n2 iff skip error-entails n1 � n2• Still, the definition of dynamic proper entailment may give us something which is closer to the consequence relation of natural language, because it takes presuppositions into account, in the following sense. To ascertain that n1 properly entails n2, the fact that f may be among the outputs for n1 does not matter; the only thing that matters is that program n2 succeeds for all proper outputs of n 1 • Thus, the program n2 is processed on the assumption that the presuppositions of n 1 are fulfllled, and we can say that dynamic proper entailment preserves presupposition. In the rest of this paper, the choice between these two dynamic entailment relations will not concern us, however. The interpretation conditions for t assignment make clear how the uniqueness presuppositions are now handled dynamically. The statement tx : n consists of a test followed by a deterministic action in case the test succeeds, followed again by the program n. First it is checked whether there is a unique JT ; if so, this individual is assigned to x and n is executed in the result state; otherwise, the only possible output state is the error state. In other words, if the uniqueness presupposition is not met, the program will not fail, as it did under
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Two programs n, n ' can be called truth equivalent in case for all models .4 it holds that I n. .P = I :rr' ,.ll , falsity equivalent in case for all models .4 it holds that o,,.ff = o:rr .,.ll , and error equivalent in case for all models .4 it holds that •:rr ,.ll = *:rr ', .t1 · Because of the possibility of error, truth equivalent programs need not be falsity equivalent, for there may be a proper state for which one of the programs gives error and the other falsity. Likewise, falsity equivalent programs need not be truth equivalent, for there may be a proper state for which one of the programs gives error and the other truth. In defining dynamic entailment we now have to take error states into account. The following two notions of dynamic entailment can be dis tinguished.
Jan van Eijck 261
10
A CAL C U L U S F O R E R R O R S T ATE S E M A NT I C S
Because of the presence of the error state t , the semantics for DPL that was presented in the previous section is even more awkward to deal with directly than the proper state semantics presented earlier. An obvious next move is the development of an extended axiom system that is sound and complete for this interpretation. In this section I will outline how this can be done. The general idea is to use a version of QDL that sacrifices the dualiry berween ( rr) and [ rr]. In the new satisfaction definition for QDL we change the clauses for the program operators as follows (assume that A is a proper state): o o
.4 I=A ( rr )cp if there is some B E [ .n] (A ) with B ;6 t and .4 .4 I=A [rr ] cp if for all B E [ .n] (A ) i t holds that B ;6 t and .4 .u
.u
1=8 1=8
cp . cp .
To see that dualiry berween the operators does nor hold anymore, notice that according to the first of these new clauses (and the usual clause for negation) we have: .4 I=A ( rr )-.cp iff for all B e [ .n] .u (A ) either B = f or .4 1=8 cp . This is not equivalent to the new clause for [ rr] cp , although it is entailed by it. Note that [rr] T now expresses that all output states are proper, i.e. [ rr] T characterizes the input states for which .n does not produce t among its outputs. As we will see, [ rr] T has become a very useful statement. The new axiom system has explicit axioms for the rwo program modalities. It looks as follows: -.
·
Ae l Ae z Ae 3
(Rt t tn)cp - (Rt t · · · tn l\ cp ). [Rtt tn] cp - (Rt t · · · tn -+ cp ). (t t = tz)cp - ( t t = lz l\ cp ). •
·
•
·
•
•
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
the regime of proper state semantics, but instead it will abort with error. It is not ditllcult ro see that this implements the Frege, Hilbert & Bernays, Strawson Vtl.'W of the behaviour of definite descriptions. Also, we see that the rwo programs LX : (.n 1 ); .n2 and LX : (.iTt ; .n2) again are not equivalent. More precisely, they are neither truth equivalent nor falsiry equivalent. The program LX : (.n t ; .n2) succeeds if there is a unique object d satisfying .n t ; .n2, while the requirement for LX : (.nt); .n2 is stronger: there has to be a unique individual d satisfying .n1, and d must also satisfy .n2• The programs are not truth equivalent because LX : (.nt; .n2) may succeed while LX : (.nt); .n2 aborts with error. This happens in case there is a unique object satisfying n 1 ; .n2, but more than one d satisfies .iTt · They are not falsiry equivalent because LX : (.n t ; .n2) may abort while IX :(.nt); .n2 fails. This happens i n case there is n o unique object satisfying .nt ; .n2, but there is a unique object satisfying .nt , and this object does not satisfy .n2 •
262 The Dynamics of Descripcion Ae Ae
4 5
Ae 6 Ae 7 Ae 8 Ae 9 Ae Ae Ae
1o II 12
[ t1 t2j cp ..... (t l t2 -+ cp ). (1rl ; 1T 2) cp (1r t )(1r2) cp. [ 1r t; 1T 2j cp [ 1r t] [ 1T 2j cp . (-. 1r) cp ... ( cp 1\ [ 1r] l.). [-. 1r) cp ((1r) T V ( cp 1\ [1r) 1.)). (1r t � 1T2)cp ( cp 1\ [ 1r ,] (1r2) l.). [ 1r t � 1r 2] cp - ( [1r t ] ((1r2) T V [1r 2) l.) 1\ (-.cp -+ (1r t )[1r2) 1. )). ( 1] V : 1r )cp - :Jv (1r )cp . ['l v : 1r ]cp ... 'v' v [ 1r] cp . �
�
++
++
...
++
To check that this schema is sound for the error state semantics, note that it states that the following are equivalent. •
e
In proper input state A the program w : n gives at least one proper output B , and B satisfies cp. In proper input state A there is precisely one individual d in the domain of the model with the property that n succeeds (has a proper output) on input A [v := d ] , and moreover there is an individual d' in the domain of the model with the property that n succeeds on input A [v : d'] , with one of the proper outputs satisfying cp. �
B y looking up the conditions for success of the error state semantic clause for assignment one can see that these are indeed equivalent. The schema is sound. Here is the second t assignment schema, with a minimal but crucial change with respect to the formulation ofT 7 in Section 7· t
This second t axiom schema expresses that the following are equivalent. e�
o
For proper input state A , the program L V : n does only have proper outputs, and all outputs satisfy cp. For proper input state A, there is precisely one d in the domain of the model for which n has a proper output on input A [v := d] , and for all d' for which n has proper outputs on A [v := d'] , all outputs of n on A [v : d'] are proper and satisfy cp . �
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
We will not check the soundness o f these axiom schemata here; we merely proclaim that they are sound for the error state semantics of DPL. The real difference between this calculus and the one for the proper state semantics is in the schemata for t assignment, for it is here that the 'error wedge' is driven between success and failure of programs. The existential t schema has not changed.
Jan
van
Eijck 263
Some reflection shows that these rwo are indeed equivalent. The axiom schema is sound. If we happen to know that program :rr never aborts with error, we can simplify the equivalence. The QDL formula to express that :rr does not give error, whatever the value of v, is given by Vv [rr] T . It turns out that the follow ing theorem becomes derivable in the error calculus. T"
1
V v [rr] T .... ([' v : rr] cp - (3!v (rr) T 1\ Vv [rr] cp)).
It is left to the reader to check that this schema is also sound. It follows from the last schema that in case :rr does not contain t assignments, we can safely employ the equivalence (28).
It is instructive to see what goes wrong when we adopt (28) to reason about a program :rr which itself contains a t assignment. Suppose we want to calculate the conditions under which the program t.x : (ty : Rxy ) executes without producing an error. We would get the following conditions for ['x : ('Y : Rxy)] T.
('x : (,:Rxy)] T - 3!x(,y : Rxy) T 1\ Vx (,y : Rxy] T - 3!x('Y : Rxy) T 1\ Vx (3!y((Rxy] T 1\ Vy (Rxy] T). - 3!x3!yRxy /\ Vx3!yRxy. This is clearly wrong, for it is certainly not required that every x has a unique y for which Rxy holds in order for the program t.x : (ty : Rxy ) to execute without error. If we perform the calculation using axiom schema Ae 1 4 instead of equivalence (28) we get the correct result:
['x : ('Y : Rxy)] T - 3!x('Y : Rxy) T 1\ Vx (('Y : Rxy) T - ['Y : Rxy]T) - 3!x3!yRxy 1\ Vx (3!yRxy .... ['Y : Rxy] T)). - 3!x3!yRxy 1\ Vx (3!yRxy .... (3!yRxy 1\ T )) - 3!x3!yRxy . That's more like it. Rules of Inference. Same as before, only we have to replace R 3 by the following more cautious rule: Cautious Necessitation. For every program :rr , conclude from f- cp to f- ...., ( 1T)...., cp .
We proclaim here without proof that the system consisting of the axiom schemata AP and Ae 1-14, and the inference rules Modus Ponens, Universal Generalization, and Cautious Necessitation, is sound and complete for the error state semantics of DPL. The reader may wish to investigate the sound ness of the axiom schemata that we did not check and of the inference rules
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
(28) [,v : rr] cp - (3!v(rr) T 1\ Vv [ 1r]cp).
264
The
Dynamics of Description
for her- or himself, and/or may wish to consult van Eij ck {I 992) for the details of the soundness and completeness proofs. In the next section we will show that the minimal change in the schemata for t assignment, together with the sacrifice of the duality between the two program operators of QDL, gives us precisely the leeway that we need to distinguish failure without error from presupposition failure.
II
C AL C U LA T I N G S U C CE S S , F A I L U R E , A N D E RR O R
-.
['x : Kx ; Bx] .L - ['x :Kx] (Bx].l - 3!x(Kx) T 1\ Vx (.Kx] (Bx] .l - 3!xKx 1\ Vx(Kx ..... (Bx].l - 3!xKx 1\ Vx(Kx ..... -.Bx). To get the presupposition of the example, we take the disjunction of the success and failure conditions. This gives formula (29).
(29) (3!xKx 1\ 3x(Kx 1\ Bx)) V (3!xKx 1\ Vx(Kx
.....
-.Bx)).
It is a simple exercise in predicate logical reasoning to see that this is equivalent to (3o). (3o) 3 !xKx .
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
We will now demonstrate how the new calculus is used to calculate success by reducing QDL formulae of the form (1r)T, how it is used to calculate failure without error by reducing QDL formulae of the form [ 1T ].L, and, finally, how it is used to calculate error (presupposition failure) by conjoining the negation of the conditions for success and the negation ofthe conditions for failure without error. In other words, presupposition failure of a program n is expressed in QDL as ( n-) T 1\ -.["] .l. Conversely, the presupposition of a program n is given in QDL by ( 1r) T V (1r] .l. The presupposition of a program characterizes the model/state pairs where the program does not abort with error. The crux of the matter is that in the new calculus calculating the success conditions of a program is not in general the same as calculating the negation of the failure conditions for that program. In considering an initial example, note that nothing changes in the calculation of the success conditions for the Russell example The King ofFrance is bald . We still get a reduction to the predicate logical formula 3!xKx 1\ 3x(Kx 1\ Bx). But now the derivation of the failure conditions of the example shows that the failure conditions are different from the negation of the success conditions. As there are no embedded t assignments, we can use principle (28).
Jan van Eijck 265
(32) 3x ( Wx I\ Mx I\ -.3!yHyx ). But this is the negation of the 'meaning postulate' for being a married woman, namely that this entails having one and only one husband. If we impose this meaning postulate, then our calculation shows that the program for (2o) will never abort with error. This demonstrates the use of the error state calculus as a tool for calculating the projection properties of uniqueness presuppositions. Hopefully the examples have made clear how the calculus for error state semantics works. Of course, failure of uniqueness presuppositions of definite descriptions is only the simplest kind of presupposition failure. See e.g. van der Sandt (I98 8) for lots of examples, and Kracht (to appear) for a logical perspective on the phenomenon. In another paper (van Eijck I 992), I argue that the dynamic approach to presupposition failure by means of an error state semantics for a dynamic representation language, and the method of calculating conditions for success, failure, and error by means of assertions about the effects of programs, have a much wider range of application than this. I2 CON CLUSI O N In this paper I have explored rwo varieties of dynamic semantics, proper state semantics and error state semantics, while focusing on the constructs of rJ and t
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Finally, we demonstrate that, in the error state semantics for DPL, example (2o) never aborts with error. The derivation of the success condition goes through as in the case of the proper state calculus. Here are the failure conditions. In the first step, we use the fact that married women have one and only one husband to simplify the calculation. ((17x : Wx; Mx) � (ty : Hyx; Lyx)] .i - (11x : Wx; Mx)(ty : Hyx; Lyx] .i - ('lx : Wx)(Mx)(ty : Hyx] (Lyx] .i - 3x( Wx)(Mx)[ty : Hyx] [Lyx].i - 3x ( Wx I\ Mx I\ [ty : Hyx] [Lyx] .i) - 3x ( Wx I\ Mx I\ 3!y (Hyx) T I\ 'Vy (Hyx](Lyx].i ). - 3x ( Wx I\ Mx I\ 3!yHyx I\ 'Vy (Hyx - -.Lyx )). What this says is: there exists a married woman who has one and only one hus band, but no one who is her husband looks after her. The error conditions are given by the conjunction of the negations of success conditions and failure conditions, so we get (3 I). (3 I) -.'Vx ( Wx - (Mx -+ (3!yHyx I\ 3y (Hyx I\ Lyx )))) I\ -.3x ( Wx I\ Mx I\ 3!yHyx I\ 'Vy (Hyx -+ -.Lyx )). By predicate logical reasoning, (3 I ) is equivalent to (32).
2.66
The Dynamics of Description
Acknowledgements This paper has benefited from helpful comments by Krzysztof Apt, Tim Fernando, Marcus Kracht, Reinhard Muskens, Martin Stokhof, and Fer-Jan de Vries. I also wish to thank the twn anonymous referees of this journal for their useful feedback. JAN VAN EIJCK CWI
Kruislaan 4 1 3 1 098 Sf Amsterdam The Netherlands
Received: 1 0-.!-l).! Final revision received: 1 1 - 1 1 -l).Z.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
assignment for the treatment of indefinite and definite descriptions. It turned out that an error state semantics is well suited to take the uniqueness presuppositions of the use of definite descriptions into account. If we adopt a proper state semantics, then both 17 assignment and t assignment can in principle be decomposed. The process of 17 assignment is decomposable in random assignment with subsequent testing, while that for t assignment is only slightly more complicated. In fact, we can read IX : Tl as an abbreviation of 'YJX : n; --. ( 1'/Y : n(y!x); y =I x), where n (y !x) denotes the result of substituting y for all active occurrences of x in n . The active occurrences of x in n are the occurrences that are affected by an assignment of a value to x immediately preceding the execution of n; see van Eijck & de Vries (1 992) for a precise definition. Under an error state semantics 17 assignment is still decomposable, but a decomposition of t assignment has become impossible, because of the way in which the uniqueness presuppositions are handled. It is interesting to speculate about the addition of special error handling constructions to the representation language. In this connection, an obvious question one might ask is: what is the minimal enhancement of the representation language that would make IX : n decomposable again? But irrespective of the answer to this question, the nice thing about the constructs for 17 and t assignment is that they allow us to remain faithful to linguistic form. Both for proper state semantics and for error state semantics I have given an assertion calculus in the style of Hoare and Pratt. For both axiomatizations I have sketched the reasoning for the soundness of the axiom schemata. Both axiomarizations are also complete. Technical details on the first axiomatization (including a completeness prooD can be found in van Eijck (to appear). The completeness of the axiomatization for the error state semantics is proved in van Eijck (1992), where it is also demonstrated how the error state semantics for DPL can be extended for different kinds of presuppositions, how presupposi tion cancellation is handled, and how all these extensions can be incorporated in the axiomatization.
Jan van Eijck
267
R E F E RE N C E S Apt, K. R { I 9 8 I ), 'Ten years of Hoare's logic: a survey-part i', ACM Transactions on
Programming Languages and Systems,
J, 4,
43 1 -8 3 .
Barwise,J. ( I 987), 'Noun phrases, generalized quantifiers and anaphora', in P. Gardenfors (ed.), Generalized Quantifiers: Linguistic and Logical Approaches, D. Reidel, Dordrecht, I -JO.
Theoretical Linguistics,
17, I 59-20 1 .
Eijck, J. van ( I 992), 'Presupposition failure: a comedy oferrors', MS CWI, Amsterdam. Eijck, J. van (to appear), 'Axiomatizing dynamic predicate logic with quantified dynamic logic', in J. van Eijck & A. Visser (eds), Logic and Information Flow , MIT Press, Cambridge, Mass. Eijck,J. van & de Vries F. J. ( I 992), 'Dynamic interpretation and Hoare deduction',jour
nal ofLogic, Language, and Information ,
I,
I-
44·
Enderton, H. B. ( I 972), A Mathematical Intro duction to Logic , Academic Press, New York. Frege, G. ( I 89I ), 'Funktion und Begrifr, translated as 'Function and Concept' in Geach & Black ( I 95 2). Frege, G. ( I 892), 'Ueber Sinn und Bedeu tung', translated as 'On Sense and Ref erence' in Geach & Black ( I 9 5 2). Geach, P. & Black, M. (eds) ( 1 9 5 2), Trans
lations from the Philosophical Writings of Gottlob Frege, Basil Blackwell, Oxford. Gvldblatt, R ( 1 987), Logics of Time and Com putation , Vol. 7 of CSLI Lecture Notes,
CSLI, Stanford. Distributed by University of Chicago Press. Groenendijk, ]. & Stokhof, M. ( 1 98 1 ), 'Dynamic predicate logic', Linguistics and
Philosophy ,
14, 3 9- 1 00.
tions ojthe A CM, 12,
10, 567-80, 5 8 3.
Karttunen, L. ( I 974), 'Presupposition and linguistic context', Theoretical Linguistics , I 8 I --94 ·
Kozen, D. & Tiuryn, J. ( I 990), 'Logics of programs', in ]. van Leeuwen (ed.), Hand book ojTheoretical Computer Science, volume B, Elsevier, Amsterdam, 789-840. Kracht, M. (to appear), 'Logic and control: how they determine the behaviour of presuppositions', in]. van Eij ck & A. Visser (eds), Logic and Information Flow, MIT Press, Cambridge, Mass. Langendoen, D. T. & Savin, H. { I 9 7 I ), 'The projection problem for presuppositions', in C. Filmore & D. T. Langendoen (eds), Studies in Linguistic Semantics , Holt, New York, 5 5-62. Leisenring, A. C. ( 1 969), Mathematical Logic and Hilberts t:-symbol, MacDonald, Lon don. Pratr, V. ( I 976), Semantical considerations on Floyd-Hoare Logic', Proceedings 1 7th IEEE
Symposium on Foundations of Computer Science , 1 09-2 1 . Reichenbach, H . ( 1 947), Elements of Symbolic Logic , Macmillan, London. Russell, B. ( 1 905 ), 'On denoting', Mind, 1 4, 479--9 3·
R A. van der ( 1 98 8 ), Context and Presupposition , Croom Helm, London. Strawson, P. F. ( 1 950), 'On referring', Mind ,
Sandt,
59, 3 2o-44.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Benthem, ]. van, ( I 99 I ), 'General dynamics',
Haddock, N. J. ( 1 987), 'Incremental inter pretation and combinatory categorial grammar', in Proceedings ofiJCAI. Hilbert, D. & Bemays, P. { I 939), Grundlagen der Mathematik , Springer, Berlin. Hoare, C. A. R ( I 969), 'An axiomatic basin for computer programming', Communica
