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JOURNAL OF SEMANTICS AN INTERNATIONAL JoURNAL FOR THE INTERDISCIPLINARY STUDY OF THE SEMANTICS OF NATURAL LANGUAGE MANAG I NG EDITOR : PETER BoscH (IBM Germany) REVI EW EDITOR: BARTGEURTS (Univ. ofTilburg) ASS ISTANT EDITOR: T m oR Kiss (IBM Germany) EDITOR I AL BOA RD:
PeTER BoscH (IBM Germany) SIMON C. GARROD (Univ; of Glasgow)
BARTGEURTS (Univ. ofTilburg) PAuL HOPPER ( Carnegie Mellon Univ., Pittsburgh) lAURENCE R HoRN (Yale Universiry) STEPHEN I SARD (Univ. of Edinburgh) HANs KAMP (Univ. of Srurrgarr) Leo G. M. NooRDMANN (Univ. ofTilburg) RoB A. VAN DBR SANDT (Univ. of Nijmegen) PIETERA.M. SsUREN (Univ. ofNijmegen) CONSULT I NG EDITORS:
R. BARTSCH (Univ. of Amsterdam) J. VAN B ENTHEM (Univ. of Amsterdam) D. S. BREE (Univ. of Manchester) H. E. BREiu.E (Univ. of Regensburg) G. BRoWN (Univ. of Cambridge) H. H. CLARK (Stanford University) 0.DAHL (Univ. of Stockholm) H.-J. EIKMEYER (Univ. of Bielefeld) G. FAucoNNIER (Univ. of California,San Diego) J. HoBBS (SRI ,Menlo Park) D. ISRAEL (SRI, Menlo Park) P. N.JoHNSON-LAIRD (MRC, Cambridge) E. L. KEENAN (Univ. of California, Los Angeles)
E.L ANe (Univ. ofWuppertal)
SIR JoHN LYONS (Univ. of Cambridge)
W. MARSLEN-WILSON (MRC, Cambridge)
J.D. McCAWLEY (Univ. of Chicago)
H. REICHGELT (Univ. of West Indies) B. RICHARDs (Imperial College, London) A.J. SANFORD (Univ. of Glasgow) R. ScHA (Univ. of Amsterdam) H. ScHNELLE (Ruhr Univ. Bochum) A. VON STECHOW (Univ. ofKonstanz) M. STEEDMAN (Univ. of Pennsylvania) D. VANDERVEKBN (Univ. of Quebec) Z. VBNDLER (Univ. of California, San Diego) B. L. WEBBER (Univ. of Pennsylvania) Y. WILKS (New Mexico State Univ., Las Cruces) D. WILSON (Univ. College,London).
EDITOR IAL ADDRESS: Journal ofSemanrics, IBM Germany Scientific Centre, IWBS ?D00-75. Posrfach Hoo8Ho, D-7000 Srurrgarr Ho, Germany. Phone: (49-7II-) 6695-559.Telefa x: (49-7I I ) 6695-500. BITNET: bosch@ds0lilog. New Subscribers to rhe Journal of Semantics should apply ro the Journals Subscription Department, Oxford University Press,Walton Srreet,Oxford, OX2 6DP. For furrher information see the inside back cover. Volumes I-6 are available from Swets and Zeitlinger, PO Box HJo, 216o SZ Lisse,The Netherlands.
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JOURNAL OF SEMANTICS Volume 9 Number 4
SPECIAL ISSUE: PRESUPPOSITION
PART
2
Guest Editors: Rob A. van der Sandt, Henk Zeevat
CONTENTS
RoB A. vAN DER SANDT AND HENK ZEEVAT Editorial Introduction JuoY DEuN Properties of It-Cleft Presupposition WALTER KASPER
Presuppositions, Composition, and Simple Subjunctives RoB A. vAN DER SANDT Presupposition Projection as Anaphora Resolution HENK ZEEVAT
Presupposition and Accommodation in Update Semantics
333 379
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Journal ofSemantics 9: 287-288
© N.I.S. Foundation (1992)
Editorial Introduction
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This is the second special issue on presupposition. As in the previous issue, all contributions derive from a presupposition workshop organized within the DAN DI project (Esprit Working Group 331 s on Dialogue and Discourse). The present issue brings in four new papers which centre around two themes: the connection of the topic-focus distinction with presupposition and two competing views on the formalization of the anaphoric view on presupposition. Judy Delin presents a rich collection of facts about. cleft-sentences and their syntactically unmarked counterparts where topic-focus is marked by means of intonation. She adduces wide variety ofempirical material to show that it -clefts mark information as anaphoric quite independently of their information structure. Of special importance are her observations about the accommodability of topics, which does not seem to fall into the general treatments of presupposi tion produced over the last twenty years. The paper thus brings up the general issue of further classification of presupposition triggers with respect to anaphoricity and accommodability. Walter Kasper's main topic is the semantics of the subjunctive mood. Subjunctive sentences are analysed as 2 kind of counterfactuals with a missing antecedent. It is shown that these unexpressed conditions can be analysed presupposition-like entities induced by the subjunctive itsel£ This simul taneously unravels an important connection between topic-presuppositions and quantification. Topics function as a restriction on quantification (generated by a special implication) in generic sentences and conditions without an explicitly marked condition. The foreground-background distinc tion associated with topic-focus marking in simple assertions leads to a demarcation of presupposed from asserted material. The paper provides an implementation in discourse representation theory incorporating an explicit construction algorithm. Rob van der Sandt elaborates his earlier accounts of presupposition and gives a revised version of his anaphoric treatment. His·claim that presuppositional expressions are anaphors which only differ from pronouns and other semanti cally less loaded anaphors in that they have more descriptive content is further elaborated in the framework of discourse representation theory. It is shown that once their capacity to accommodate is taken into account presuppositional expressions can be treated by basically the same mechanism which handles the resolution of pronouns. Instead of the deterministic algorithm espoused earlier, an indeterministic model is presented. Some aspects of determinism are recaptured by bringing in preference constraints.
288 Editororial Introduction
HENKZEEVAT ROB VAN DER SANDT
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Henk Zeevat's paper contains a detailed comparison of theories of Heim ( 1 98 3) and van der Sandt and develops the latter theory further by restating the anaphoric account of presupposition in update semantics. The resulting theory overcomes some of the problems connected with that framework and yields a compositional treatment of the accommodation process in terms of the notion of stack-updating. Though strictly speaking the notion of accommodation is the only one that requires stack-updating, stack-updating also turns out to be a model of the basic operations in the DRS-constrUction algorithm proposed by Kamp and so allows a top-down compositional interpretation ofDRT. The last three papers all link up with computational work done around presupposition. The statement of the new algorithms reach a high degree of explicitness and could provide the basis for further implementational work.
© N.I.S. Foundation (1992)
Journal ofSemantics 9: 289-300
Properties of It-Cleft Presupposition JUDY DELIN University
Consequent
4.1
Discourse Representation Structures
The following definitions present the basic notions of DRT by defining the syntax and semantics ofDRSs. . The set of basic expressions of the representation language, which I will call DRL , consists of an infinite set of DRF ofdiscourse referents, sets p n of n-place predicate symbols (n � o), and the logical signs �. -, --.. A DRS K is a pair ( UK, CONK) with UK being a set of discourse referents, and CONK being a set of DRS-conditions. DRS-conditions are the expressions of the forms
-.:K K, � K2 The latter ones are the complex conditions, those of predicate-argument-form and the identity statements atomic conditions. A DRS K is superordinated to a DRS K' iff either K' is part of a complex condition of K, or K' is part of a complex condition K" to which K is super ordinated. K' is accessible from K iff K' is superordinated to K or K' is part of a condition K' � K. A discourse referent x is accessible from a DRS K iff x E UK or x E UK. for a DRS K' which is accessible from K. The union K1 + K2 ofDRSs K1 and K2 is the DRS ( UKI u UK2 , CONKI u CONK ). J... ' The semantics is slightly more complicated than the standard one: an interpretation .f is a quintuple ( W, U, E, $, 1"), where
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But the main part of this section will concern the construction ofDRSs. The focus will be on the method for the construction of the implicit antecedents of simple subjunctives, indicated at the end of the last section.
Walter Kasper 321 1. 2.
3· 4·
is a (non-empty) set of 'possible worlds' w is a (non-empty) set of possible objects (individuals) u 1 2 E is a function W -- g; u , giving for each world the set of individuals existing in it $ is a function W -- g;g; W, assigning each world a sphere system in the sense of Lewis (I 97 3 ), which is strongly centred, nested, and closed under union and (non-empty) intersection of spheres. It gives for each world w a set of sets of worlds representing a partial ordering of the possible worlds accord ing to their similarity tc w . Strong centring amounts to the plausible claim that no world can be more or equally similar to the actual world than itsel£ Formally it can be expressed· by the condition that for each world w, {w} e $(w). Nesting means that for all spheres S, T e $, S s; T or T s; S holds. r is a function assigning the elements of p n a set of(n + I)-tuples (u1 , , un, w) (w E w' U; E E ( w)) •
.
•
embeddingfunctionJ for a DRS K is a function UK -- U . g is a K' -extension of an embedding function J for K iff the domain ofg is that ofJ united with UK , and g assigns the elements in the domain off the same value as f. Now we can give the truth conditions for DRS-conditions and for DRSs.J is a true embedding of DRS-conditions C of K in w relative to an interpretation J (1, w, J F C') according to the following rules: An
I . j, W , J F a (u,, . . ., Un) iff ( flu ,), . . ., f(un), w ) E J"(a ) j, w, J F u1 - u2 ifff(u1) = f(u2) 3- j, w ,J I= --. : K iff there is no K -extension g ofj, such that g, w, J I= K 4· j, w, J F K1 � K2 iff (a) either there is no S e $(w) containing a w' such that there is an K1 extension g ofj with g , w', J F K1 , or (b) there is an S e $(w) such that there is w' e S and a K1-extension off such thatg, w',J F K1 and for all w" e S, and for every K1-extensiong' off: if g ' , w", J I= K1 , then there is a Krextension h ofg ' , such that h , w", J I= K2 2.
J is a true embedding of K in a world w relative to an interpretation J ifff is an embedding function for K and for all C e CONK• J, w, J F C. A model of DRL is a pair (J, w ). A DRS is true iff there is a true embedding for it in w. It is consistent iff there is a world w such that there is a true embedding for it in w . It should be obvious how notions like entailment, equivalence, logical truth, etc. could be defined. The truth conditions for conditionals DRSs K1 � K2 differ from the standard ones as given in Kamp (I 98 I), but imply them because of the strong centring of the sphere systems. The (a)-clause of the rule just makes a conditional true if there are no worlds in the sphere system instantiating the
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5·
W
U
322 Presuppositions, Composition, and Simple Subjunctives
4.2
DRS construction
The DRT-language defined above does not contain special components for expressing the subjunctive mood. If one takes serious the claim that simple subjunctives are in some sense conditionals, then semantically they should be represented as such. This is the reason why the question of how to construct such representations becomes important. In the following I will propose a method for constructing DRS-representations especially for those simple subjunctives whose antecedent is not given exclusively by context but rather can be reconstructed from the semantic content of the sentence itself, taking into account the compositional problems that have been pointed out. Essentially the proposal is that during the DRS-construction process two kinds ofDRSs are involved, one called the textual DRS, the other the background DRS which will collect the possible preconditions in the sense described earlier but which can also take up the semantic content of constituents, thereby making them presuppositional in some sense. I assume that after processing a sentence-yielding a textual DRS incre mented by the semantic content of the sentence-the background DRSs can be integrated into the textual DRS by a projection mechanism as used for presuppositions. Here I will adopt Gazdar's concept of compatibility restricted incrementation (c£ Gazdar I 979a, I 979b). The definition of the compatibility restricted incrementation of a DRS K1 by a DRS K2 (denoted by K1 u! K2) can be adapted readily from Gazdar's definition for sets of propositions:
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antecedent DRS of the conditional-a borderline case. Otherwise conditionals are evaluated with respect to the most similar worlds allowing an embedding of the antecedent. Think of the sphere system as a set of concentric circles around the actual word w where the smaller circles are completely contained within the larger ones. Each sphere represents a (minimal) degree of similarity with the actual world. Since the more similar worlds are contained in the set of the less similar worlds the conditional cannot be made true by the less similar worlds if there are more similar ones falsifying it. Therefore, if the actual world allows an embedding of the antecedent, only this world is used for the evaluation on the assumption that no world can be equally or more similar to the actual world than itself, and so the standard truth conditions hold which state that for every embedding of the antecedent there is an embedding of the consequent. So by their interpretation rule conditional DRSs always implicitly involve a universal quantification of all the discourse referents in the antecedent.
Walter Kasper 323
(36) ( U1 , CON1) u! ( U 1 , CON2) ( U 1 u U2, CON1 u ( C I C E CON2 and for all Z � CON1 u CON2 : ( U 1 u U2, Z u (C)) is consistent iff ( U 1 u U2, Z) is consistent].
(37) Ku
EJ
=>
(Ku!BG)-K
main reason for postponing the process of accommodating or relating the background to the textual DRS is that the accommodation of such pre conditions has to wait till all information concerning possible incompatibles is available. But I will now mainly illustrate only the process of building up the textual
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By this rule basically the conditions of the second DRS K2 which are incompatible with those of K1 (or others in K2) are eliminated in that sense that they do not become part of the resulting DRS. But we cannot directly insert the (compatible) conditions of the background DRS into the textual DRS. The reason is that the background DRS might contain discourse referents which should not be made available in the main DRS, e.g. because they had been introduced in the context of a conditional, as will be illustrated later. Then the direct accommodation of the background DRS into the main DRS 1 3 would yield wrong truth conditions because the embedding function for the main DRS would have to take those discourse referents into account. Instead ofmerging background DRS and textual DRS by putting the conditions of the background DRS into the textual one, we insert the background conditions in an existentially quantified fashion which prevents the embedding function from being affected. An existential quantifier can be simulated in DRT by a conditional DRS with an empty antecedent DRS consisting of an empty set of discourse referents and an empty set of conditions. Since any embedding function for such an empty DRS will be identical to that of the superordinated DRS, this structure will only look for some extension embedding the consequent, thereby quantifying all discourse referents in the consequent existentially but leaving the embedding function for the super ordinated DRS unaffected. So our rule for the accommodation of a background DRS BC into the textual DRS K is as shown in (37). This will introduce the compatible background conditions in the consequent of a conditional. Thus the discourse referents of the background DRS will not be available in the main DRS. 1 4 The
324 Presuppositions, Composition, and Simple Subjunctives
(3X) John would win against an amateur. whose F-STRUCTURE could be as in (39) 1 6 (39)
PRED=win-against ((iSUBJ)(iOBJ)) MOOD=subjunctive SUBJ= OBJ =
[ PRED=John ]
[
J
SPEC=a PRED=amateur
For the DRS-construction, the assignments in (40)-(44) are made for the terminal featuresP The rules are to be read as follows: the name John introducesjust the denoted object into the (textual) DRS and its background. I� also is a function which can combine with a DRS. The simple noun amateur just introduces a corresponding condition into textual and background DRS. The rule for the indefinite article corresponds to the actual standard one in logical semantics: it forms the conjunction of the DRS representing the noun's meaning (in the simplest case) and some other DRS, on the textual side as well as in the background DRS. The subjunctive is interpreted as introducing a conditional DRS with the background DRS as antecedent and the proposition it is applied to in the consequent DRS. At the same time it turns the conditional DRS into a counterfactual one by negating the background conditions. This, of course, will only take effect when the background DRS is joined with the
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and background DRSs which are the input to these processes in order to show how they are employed in the process of building up an antecedent for simple subjunctives. The construction process starts out from an analysis of the sentence and builds a pair of semantic structures (DRS, BG-DRS). In Kamp & Reyle ( 1 990) the starting point for the construction of a DRS is a tree structure for the sentence. The construction algorithm consists in a set of transformation rules on these. My illustration, in contrast, will be based on a simpler algorithm for building DRSs from functional structures ofLFG (Bresnan & Kaplan 1 982) first described in Reyle ( 1 98 s). 1 5 The basic operation of this algorithm is Junctional reduction which reduces a set of semantic structures to a single structure by functional application and thus much resembles the construction methods in other grammar frameworks such as categorial grammars. Based on an assignment of semantic structures to terminal feature values, the algorithm recursively computes the semantic structures for the complex valued attributes of the F-STRUCTlJRE. This should become clearer from the examples given below. As a first illustration of the method let us look at the simple subjunctive sentence
Walter Kasper 325
textual DRS in the end. The verb introduces the corresponding event into the texrual DRS and its precondition into the background DRS. (40)
~ lt:J )
v (John)=A.CA.B(
�=john
B
(4 1 ) v(amateur) = (
y
y
amateur(y)
amateur (y)
)
v (win-against((iSUBJ)(iOBJ))) = win (x,y)
I
'
opponent (x,y)
)
(43 )
(44)
v (subjunctive)
WB(�
The Reyle algorithm now computes first a DRS for each of the attributes in the F-sTRUCTURE. Then we get a set of four semantic structures (for the PRED-, SUBJ-, OBJ- and Moon-features) which has to be reduced functionally. One reading will be as set out in (45). 1 8 According to the embedding conditions the (45)
X
x=john
x=john y amateur (y) opponent (x,y)
y :=}
amateur (y) win (x,y)
-, ;
y amateur (y) opponenet (x,y)
)
textual DRS of this structure is true iff in the most similar worlds where John exists and an amateur exists, who isJohn's opponent (taken as a precondition for winning), John always wins. The important feature of this structure is that the condition introduced by the indefinite NP an amateur now appear via the background in the antecedent of the conditional, while its occurrence in the
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(I
326 Presuppositions, Composition, and Simple Subjunctives
consequence is due to the standard rule that the indefinite NP introduces its content in the local DRS (here the consequent) corresponding to the part of the sentence containing the NP. The conditional will usually be a counterfactual, as the background DRS states that in the actual world John is not the opponent of an amateur. If the textual DRS allows it, this can be accommodated there. In addition, it can be shown that on this reading sentence (38) is equivalent to both of the following, one containing a universal quantifier instead of the indefinite article, the other one being a full conditional sentence: (46) a. John would win against every amateur. b. IfJohn's opponent were an amateur, he would win against him.
(4 7)
a.
X
x=john y amateur (y) opponent (x,y)
b.
=>
y amateur (y)
=>
I
win (>,y)
I
X
x=john y amateur (y) opponent (x,y)
y =>
amateur (y) opponent(x,y)
=>
§
specifier every introduces the same background as the indefinite article, i.e. the contents of the noun, and that also the subjunction if passes the backgrounds of antecedent and consequent to the top leveJ.l9 Thereby they can become antecedents for the subjunctive sentences.20 Since the antecedents of the embedded conditionals in the DRSs of (47) are contained in these background DRSs, the DRSs in (47) will be evaluated with respect to exactly the same (most similar) worlds. Any embedding of the 'outer' antecedents in (47) is also an embedding of the antecedents of the embedded conditional DRSs, and so, as a result of the strong centring of the sphere system, the conditionals are evaluated with respect to the same worlds. The construction method also provides a second reading for (3 R), which is achieved by using the object's semantics last in the functional reduction
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The textual DRS of these sentences come out as in (47). Although the DRSs all look a little different, they have the same truth conditions, due to the fact that they all have the same background DRS as (4 5), if we assume here that the
Walter Kasper
327
process, giving the indefinite NP wide scope (see (48)). This says that there is an amateur in the actual world, John would win against, if this amateur were his opponent. It presupposes only that actually they are not opponents. x,y x=john amateur(y) opponent (x,y) x,y
=-§
--, :
opponent (x,y)
Finally, let us have a look at the role of the background DRS in the case of indicative sentences, such as (49) a. John wins against an amateur. b. John wins against every amateur.
The textual DRS of these can be seen in (so). Both of these will have as background DRS that set our in (s I ). The accommodation of the background DRS in the manner described at the beginning of this section will then result in the following DRSs in (s2). In (s2a) the only condition really added is that John (so)
.------, x,y
a.
x=john amateur (y) win (x,y)
b.
X
x=john y amateur (y)
(s I )
x,y
-----l
1--..:...._
x=john amateur(y) opponent (x,y)
=>
I
win (x,y)
I
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x=john amateur(y)
328
Presuppositions, Composition, and Simple Subjunctives x,y x=john amateur (y) win (x,y)
D b.
x,y x=john amateur (y) opponent (x,y)
�
X
amateur (y)
�
I
win (x,y)
I
x,y
u
�
x=john amateur (y) opponent (x,y)
and the amateur introduced in the textual DRS are opponents. The other clauses are redundant as they are contained already in the main DRS. This is different in the case of (52b), the representation of the universal quantified sentence. Here the background DRS adds the information that there is at least one amateur who is John's opponent so that (49b) can only be true ifJohn wins against at least one amateur. Thereby the universal quantifier here carries an existential presupposition (c£ note 20). The case of vacuous quantification is allowed only as a borderline case if there is a positive knowledge as to the falsity of the existential presupposition which would prohibit its accommodation. The example also illustrates why the background DRS should be accommodated as existentially quantified, that is, as consequent of a conditional DRS with empty antecedent. If the background DRS were accommodated directly into the main DRS the universal quantifier would lose its universal force since the quantified discourse referent (the y in (52b)) is then bound existentially by the embedding function for the main DRS so that (49b) becomes equivalent to (49a). Also, the discourse referent would become accessible for pronouns in the main DRS. Looking at the rules for the construction of the backgrounds, one will notice that it is assumed that nouns (and other constituents) contribute their semantic content unchanged to the background, and only in the case of the verb there was a major difference. One might wonder what the rationale behind this is. I can only provide a short, speculative hint as a motivation. The event described by the verb must be regarded as the centre of sentence
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x=john y
Walter Kasper 329
content. Other constituents arc role-fillers, which can also be left indefinite or even be missing. They provide background in so far as they provide the event's participants, locate it, and so on, but do not tell us what happened. Also, it is events which require 'preconditions' for corning about, while other objects in some sense are assumed to be just there. If they do not exist they also cannot participate in events, and there is no question of the event's coming about. If the contents of constituents other than verbs become part of the background, then this just means that the existence of suitable role-fillers of the described kind is assumed as being part of the preconditions for the event. WALTER KASPER
NOTES I
In English, the standard way o fexpressing
amounts to say that John might or might
subjunctive mood is
not have bought a Japanese car. I do not
would
+
infinitive
(present or perfect) though these are exceptions (e.g. auxiliary verbs; also in conditional sentences a past tense form in the antecedent clause can inherit sub junctive mood from the consequent clause). I also want to point our that not every use of
would
+
infinitive
expresses
regard this as a correct reading for (Xa).
c£ the discussion in van der Sandt ( 1 9gg). I will not discuss whether the term cancel
lation
describes the phenomenon adequa
tely. 6 I will not discuss the semantics of the counrerfacrual conditional here in detail.
'subjunctive mood' in the sense discussed
I am assuming a Lewis-sryle semantics for
in this paper. The form has other uses as
it (Lewis
well, such as indicating politeness
world
w
I 97 3 ), saying that it is true in a
if its consequent is true in the
(Could you pass the salt?) and expressing wishes (I would like to . . . ). Also, it may be used as a past future tense Uolm knew that Peter would come) and as marker of indirect
antecedent is true. The similarity relation
discourse.
subjunctives which logically are only
poorer than that in indicative mood. In
regarded as sufficient for simple subjunc
2 The tense system in subjunctive mood is
subjunctive mood there is no formal distinction between past tense, present perfect and past perfect. This problem will not be discussed here. There are some counterexamples to this, such as even if conditionals (Karttunen
I 97 I ); see also Stalnaker ( I 976). They are
not relevant in the current context.
4 A wide-scope reading for the negation
worlds most similar to
w,
in which its
can also be used to explain how the precondition antecedems of the simple necessary, not sufficient conditions can be tives.
7 The concept of P"'P"'
ascription
of pro
perties or relations to objects is a generali
zation of that of 'non trivial' truth which applies only to propositions. X There is a problem with respect to con structionally induced presuppositions, as in the case of clefts, because it is not always clear what in these cases the
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University oJStuttxart IMS Azenbergstr. t 2 D-7ooo Stuttgart 1 Germany
3 3 0 Presuppositions, Composition, and Simple Subjunctives
subjunctive counrerparr is, or if rhere is one. I will ignore this problem here and
1 6 I will ignore here the question of contras
tive stress which could also be marked in the functional structure. It would require
confine myself ro lexically induced pre supposmons.
some
9 A that -clause seems ro be nor very good
with facrive verbs in rhe subjunctive.
Rather, one would prefer a conditional:
John would have regretted it, if his wife left bim . instead of John would have rexretted that his wife left him .
111
the
properry ro be ascribed to rhe focused objects (c£ (8) )
C
and
textual
B
will be used as variables for
and
expression
background
J.. C(DRS)
DRSs.
The
denotes a function
from DRSs to DRSs. Functional applica the
rhar indefinites 111 rhe anrecedenr of
tion
conditionals always are universal quanri
argumenr-DRS inro the DRSs where the
(29)
If John has a dime, he puts it into the parking-meter.
IX
amounrs here
to
mergmg
bound variable occurs. The algorithm can derive several read ings, depending on rhe order of the functional applications. The one given here first has the following derivation:
where one should nor expect John ro put every dime he has inro rhe meter. Interestingly enough, there see1i1s to be a simple subjunctive counrerpart ro that: (3o) I would pur a dime inro the parking meter.
SUBJ(MOOD(OBJ(PRED))).
I 9 On rhis analysis rhe conditional sentence
does not describe a relation between rwo
simple subjunctives-and it should nor. I
regard the subj unctive mood in rhe antecedent of the conditional as resulting from mood agreement The mood IS
given as e.g. an advice. For our discussion
determined by rhe mam clause as 1s
this is not so relevant: our main problem
shown by sentences with prepositional
is, that indefinite NP should belong to rhe
anrecedenrs like
restricting anrecedenr, not so much its universal force.
I I For German,
cf. Kaufmann ( I 97.2).
U should really be a lattice of sets of
S<Jrtcd objects; but I spare myself here this
slight complication. 3 The main DRS is the one superordinared to all others.
In case ofJohn's cominx Mary would leave. These count as subjunc
tive conditionals though rhe conditional adjunct is nor marked for mood. Ir also explains why a past tense in the antece denr of a conditional senrence with a consequent in rhe subjunctive is usually understood as being subjunctive, roo. There are only a few and very special
q Wirh respect to truth conditions the
examples of conditional sentences with really differenr mood in anrecedenr and
the textual DRS. The rule given here also
.zo I just wanr ro poinr our here that on this
neglects the interaction of presupposi
assumption rhe universal quantifier car nes an existential presupposition that
consequenr condition could also more simply be K v ! BG , thus containing also
tions with implicatures, which Gazdar assumes. Another extension might be a quasi-anaphoric treatment of the back ground conditions, as van der Sandt
( I 990) proposed, instead of simply quan
1
consequent clause.
rhere are things of the described kind. I
think this is correct (cf. Srrawson I 9 5 2:
I 67 ff.).
The if should also pass rhe
complete anrecedent to rhe background,
tifying them existentially.
since ir provides rhe background for rhe
( I 99 1 ).
interpretation of rhe consequenr. I n the case of indicative condirionals this might
5 cf. also Wad a & Asher
(I 9tl6) and Kasper
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fiers, such as rhe Dime-example of Schu
bert & Pelletier ( I 9X9):
I
mechanism
.
17
1 o There are counterexamples ro rhe claim
I .2
additional
semanrics construction ro abstract the
Walter Kasper 3 3 I pose a problem with respect to the
that consequence as the antecedent con
accommodation procedure, because it
ditions would be filtered out again by the
ij.
then suggests rhar rhe antecedent might
clausal implicature associated with
be true, a problem which arises in general
(neglected here) which demands that
when the difference of indicative and
epistemically it should be possible that
subjunctive mood is described in terms of
Realis-Irrealis
the
opposition. Bur on
the antecedent and consequent rum our to be false.
Gazdar's account this should nor lead to
RE FERENCES J.
& Kaplan, R ( I 982), 'Lexical
functional grammar: a formal system for
grammatical representation', in J. Bresnan
The Mental Representation of Gram matical Relations, MIT Press, Cambridge,
(ed.),
Mass.
Pragmatics: Implicature, Presuppositions and Logical Form , Academic
Gazdar, G. ( I 979a), Press, New York.
Gazdar, G. ( I 979b), 'A solution to the projec
tion problem', in C.-K. Oh & D. Dineen
Syntax and Semantics 1 1 : Presupposi tion, Academic Press, New York, 5 7-90.
(eds),
Kamp, H. { I 98 I), 'A theory of truth and semantic representation', in
J.
Groenen- .
dijk, T. Janssen & M. Stokhof (eds),
Methods in the Study of Language,
Formal
Mathe
matisch Centrum, Amsterdam, 277-322.
Kamp, H. & Reyle, U. (I 990), 'From discourse to logic', MS, IMS, Stuttgart.
Karttunen, L. (I 97 I), 'Counterfactuals condi
Linguistic Inquiry, 2, 566-9. Kasper, W. ( I 987), Semantik des Konjunktivs II in Deklarativsatzen des Deutschen , Nietionals',
discourse referents and quantification',
Proceedings of the 8th International Joint Conference on Art!ficial Intelligence. Sandt, R van der ( I 9 8 8), Context and Presuppo sition , Croom Helm, London.
Sandt, R van der ( I 990), 'Anaphora and
Presupposition, Lexical Meaning and Discourse Processes , Workshop Reader, Nij megen. accommodation', in
Schubert,
L.
&
Pelletier,
F.J.
( I 989),
'Generically-speaking, or, using discourse representation theory to interpret gener
ics', in G. Chierchia, B. H. Partee & R.
Turner (eds), Properties,
Types and Meaning, Vol. z: Semantic Issues, K.luwer, Dordrecht,
Klu�er. Schwartz,
U.
( I 973), 'Mod us und Satzstruk
tur: Eine syntaktische Srudie zum Modus system in Deutschen', MS, Kronberg.
Stalnaker, R { I 976), 'Indicative conditionals', in A. Kasher (ed.),
Language in Focus,
Dordrechr, Reidel, I 79-96. Srrawson, P. F. { I 9 5 2),
Theory, Methuen,
Introduction to Logical
London, I952.
The Semantic Variability of Absolute Constructions, K.luwer, Dordrechr,
meyer, Tiibingen. . Kasper, W. (I 99 I ), 'Semanrische Reprasenra
Stump, G. T. ( I 9 8 5),
Sprachtheoretische Grundlagen fur die Computerlinguistik , I o, IMS, Stuttgart. Kaufmann, G. { I 972), Das konjunktivische Bedingungsgefuge im heutigen Deutsch , IDS,
Wada, H. & Asher, N. ( I 986), 'BUILDRS: an
tion und LFG: Arbeitsberichte des SFB 340',
Mannheim.
Lewis, D. K. ( I 97 3),
Counterfactuals,
Black
well, Oxford.
Reyle,
U.
( I 98 5), 'Grammatical functions,
r 98 5.
implementation of discourse representa
tion theory and lexical functional gram
Proceedings of the 1 1 th Conference on Computational Linguistics, Bonn. Wilson, D. ( I 9 8 5), Presupposition and Non Truth-Conditional Semantics, Academic mar',
Press, New York.
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Bresnan,
journal ofSemantics 9: 3 3 3-377
© N.I.S. Foundation (1992)
Presupposition Projection as Anaphora Resolution R O B A. V A N D E R S A N D T
University ojNijmegen
Abstract The present paper presents an anaphoric account of presupposition. It is argued that presup
relegated to a pragmatic theory either. Instead presuppositional expressions are claimed to be anaphoric expressions which have internal structure and semantic content. In fact they only differ from pronouns and other semantically less loaded anaphors in that they have more descriptive content. It is this fact which enables them to create an antecedent in case discourse does not provide one. If their capacity to accommodate is taken into account they can be treated by basically the same mechanism which handles the resolution of pronouns. The theory is elaborated in the framework of discourse representation theory. It is shown that pragmatic factors interfere in the resolution of presuppositional anaphors. The resulting account can neither be classified as wholly semantic nor wholly pragmatic. Section
1
presents a
survey of standing problems in the theory of presupposition projection and discusses the major competing approaches. An argumentation for a purely anaphoric account of presupposition is given in section
2. Section 3 presents a coding of presuppositional expressions in an extension
of discourse representation theory. The final section is devoted to
a
discussion of the
constraints which govern the resolution of presuppositional anaphors.
1 RE FERE N C E , B I N D I N G, A N D PRE S U P P O S I T I O N A L EXPRE S S I O N S
The traditional view on presupposition has it that presuppositions are referring expressions. When we use a sentence containing a proper name or definite description. we do not state that some object has a certain property, as the Russellian analysis implies. A proper use of such a sentence rather requires that the referring expression pick out some given object. Only if it does may we check for a particular property whether it holds of this object. If it does not, the sentence will not get an interpretation or, as Strawson phrased it, 'the question of truth or falsity simply does not arise'. This view originally derives from Frege's philosophy of language. For Frege it is referring expressions that give rise to presuppositions. Frege also insists that the reference of a complex expres sion is a function of the references of its parts. Thus, if one component expres sion of a complex expression lacks a reference, the whole expression will lack a
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positional expressions should not be seen as referring expressions, nor is presupposition to be explicated in terms of some non-standard logic. The notion of presupposition should not be
334
Presupposition Projection as Anaphora Resolution
(I a) John has children and his children are bald. (I b) IfJohn has children, his children are bald. (I c) Either John does not have any children or his children are bald. A second problem with the view that presuppositional expressions are referring expressions has been observed as early as I 97 3 by Mates. Presuppositional expressions may contain anaphors and these may be bound by external antecedents. This may seem innocuous with respect to the examples in ( I), for in these sentences the pronoun depends on an antecedent which is a proper name and thus a referring expression itself It does, however, give rise to serious problems as soon as a pronoun in a presuppositional expression is bound by an external quantifier: 1 (2a) Someone had a child and his child was bald. (2b) If a man gets angry, his children get frightened. (2c) Every man kissed thegirl who loved him . In all these cases the description contains a pronoun which is bound by and thus depends on an external quantifier. Consequently there is no uniquely identifiable object on which the 'presuppositional' expression depends and this in turn means that there is no way to analyse these descriptions as referring expressions. Scrawson's revival of presupposition theory in the I9SOS gave rise to two different explications of the semantic notion of presupposition. The first explication is very close to Frege's. A sentence presupposes another sentencejust in case the latter must be true for the first to have a rruch-value.2 On this view presuppositional expressions are referring expressions. It is thus vulnerable to the objection stated above. The second explication takes preservation under negation to be the defining characteristic. Presuppositions are defined as those inferences which are entailed both by their carrier sentence and its negation. Let us call this the inference view on presupposition. According to this view a
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reference. Given his doctrine that the reference of a sentence is its truth value, it is thus predicted that no sentence in which a non-referring expression figures as a part can have a truth-value. This consequence automatically carries over to any extensional compound. Presupposition failure is infectious. If one of the component sentences of a complex sentence suffers from presupposition failure and thus lacks a truth-value, any compound in which it figures as a proper part will lack a truth-value as well. However, as is shown by the standard examples from the literature on presupposition projection, this view gives rise to many counterintuitive predictions. Obviously, all of the following sentences can have a determinate value, even ifJohn doesn't have any children. It is also clear that none of them inherits the presupposition that he has children as is predicted under a purely Fregean account
Rob A. van der Sandt
335
sentence cp presupposes a sentence tp just in case cp I= tp and cp I= tp. This explication actually requires a trivalent or other non-standard logic. However, on its standard definition the notion of entailment adopted is the classic one. This makes it easy to show that this strategy, like any attempt to define presupposition in terms of the classic notion of entailment, cannot succeed. For the entailment relation adopted is a monotonic one and presuppositions generally display a non-monotonic behaviour. Note that in the a-sentence the possessive phrase Harry's child induces the presupposition that Harry has a child: ....,
Note furthermore that we intuitively infer from both (3a) and its negation (3b) that Harry has a child. If we take this inference to be an instance of semantic entailment, the definition of semantic presupposition predicts that Harry has a child is presupposed by both (3a) and (3b). Since the entailment relation employed is a monotonic one, it is simultaneously predicted that this inference is preserved under growth of information. But this last prediction is clearly wrong. If we add the information that Harry may not have a child as in (3c) or that he does not have one as in (3d), the presuppositional inference disappears without a trace. It follows that under its standard definition the inference view of presuppositions is simply wrong. It also follows that any attempt to account for the full range of presuppositional phenomena in terms of the classic notion of entailment is doomed to failure. Two remarks should be made at this point. Firstly, the phenomena just discussed are known from the literature on presupposition projection under the name of presupposition cancellation. This phenomenon actually gave rise to a third view on the nature of presupposition, the pragmatic paradigm. Presuppositional expressions are not taken to be referring expressions, nor are presuppositions viewed as semantic inferences which should be accounted for in terms of truth and entailment. They are instead taken to be purely pragmatic and context-dependent and have one central feature in common with Gricean conversational implicatures: when they conflict with contradictory informa tion they will not give rise to inconsistency. Instead conversational presump tions will be lifted or altered in some way and the original inferences will not be computed with respect to this new situation. It is then important to notice that it need not be conflicting information which is responsible for the removal of presuppositional inferences. In (3c) we added the information that Harry may not have children. This does not conflict with the presupposition that he has one, but nevertheless defeats the inference.
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(3a) It is possible that Harry's child is on holiday. (3b) It is not possible that Harry's child is on holiday. (3c) It is possible that Harry does not have a child, but it is also possible that {he /Harry's child} is on holiday. (3d) Harry does not have a child. So {he/Harry's child} cannot be on holiday.
3 36
Presupposition Projection as Anaphora Resolution
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Secondly, but most importantly, it should be pointed out that the claim that presuppositional inferences can be defeated by the addition of extra informa tion simply is another way ofsaying that presuppositional inferences behave in a non-monotonic way. Cancellability or defeasibility is just non-monotonicity and it is this simple fact which precludes a definition and treatment of presupposition by means of a logic which relies on the classic notion of entailment.3 The alternative approach we just alluded to and which dominated presupposition theory during the 1 970s is to treat presupposition as an essentially pragmatic phenomenon. Inspired by the work of Grice, the informa tional content of natural language utterances was taken to consist of two parts: the proposition expressed in view of the semantic rules of the language and further information conveyed by pragmatic means. The basic tenet of this view is that semantic and pragmatic information constitute two different types of content. Propositional content captures only part of what is intuitively conceived as the meaning of an utterance. Presuppositions and implicatures equally contribute to our understanding of natural language sentences. But the latter are computed in a different way. They are not part of the truth conditional content, but computed on the basis of the propositional content of the sentence uttered, contextual information, and pragmatic principles of a Gricean nature. They are thus computed and represented separately and merged only afterwards into a more substantial proposition. Contextual update will take place both with respect to the propositional content and information which is conveyed by other means. It is the sum of both which will be incre mented into the next context. The general picture derives from Stalnaker's work: utterances are construed as context-sentence pairs. A discourse is conceived as a sequence of utterances. Given an utterance of a sentence cp in a context c we first compute [ cp ]c, the proposition expressed by cp in c. Only then is further pragmatic information computed on the basis of contextual information and the propositional content of the sentence uttered. The proposition expressed and the pragmatic informa tion invoked give, when taken together, the information conveyed by this utterance in this context. Now both the proposition expressed and the informa tion conveyed may be constructed as formal objects of a similar kind. Just take them to be sets of possible worlds. Their intersection will then give us a new and more informative proposition. Let us call this object IC (cp, c), the informative content of the sentence cp in the context c. It is this object which will be incre mented into the next context. The next context will thus comprise all the previously accumulated information + all the semantic and pragmatic infor mation which is conveyed by the utterance itself The following utterance will be interpreted with respect to this information.4 The view just sketched has a number of non-trivial implications. Firstly, it
Rub A. van der Sandt 337
(4) It is not true that the thief stole my Mac. The thief did not steal my Mac. content expression (4a) --.3! x (thief x A steal_Mac x) presupposition (4b) 3! x (thief x) content + presupposition (4c) 3! x (thief x A steal_Mac x) --.
The truth-conditions are taken to be classical. A negated sentence will thus never entail its presupposition, but it will be said to presuppose it by default, that is, it will presuppose it if pragmatic conditions do not forbid accom modation of the presupposition in the context of utterance. It follows that a presupposition which is embedded under a non-entailing operator will never
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means that it is utterances not sentences which are the primary information carrying units. Secondly, it implies that in processing a sentence cp its semantic content should be determined before any pragmatic information can be computed and this in turn implies that pragmatic information is to be represented separately from semantic content. The first of these claims is unconrroversial. The second and third, however, turn out to be wrong. In fact, the postulation of priority of semantic content over implicatures and presuppositions and the representation of semantic and pragmatic information by separate expression give rise to three interconnected problems. We get a notion of propositional content which is rather counter intuitive with respect to extensional contexts and plainly wrong with respect to intensional ones. We run into binding problems when presuppositions and implicatures enter into scope relations with quantified expressions and, finally, we blur the distinction between accommodation as a procedure which adjusts contextual parameters with respect to which the current utterance is to be processed and contextual incrementation as a mapping of the adjusted context into the next one. The basic problem lies in the separation of semantic and pragmatic content. In the remainder of this section I will first discuss how this gives rise to a rather thinned and counterintuitive notion of propositional content. I will then go on to survey the problems which arise out of the fact that all pragmatic information may enter into binding relations with the content expression and conclude with some remarks on the difference between accommodation and contextual incrementation. In the next section I will present an alternative theory which does not run into the problems discussed here. Among the authors who adhere to the pragmatic picture it is generally assumed that logical operators take scope over presuppositional expressions.5 Thus (4) is represented as (4a) and is said to presuppose (4b). In the standard case the full interpretation will thus consist of the sum of the semantic and pragmatic information which is equivalent to the narrow scope reading given in (4c):
338
Presupposition Projection as Anaphora Resolution
(sa) If the thief stole his Mac, John will ensure his next one. (sb) Steal_mac(� x thief x) - Insure_nexc_one j The conditional consists of two independent propositions. The description in the antecedent will thus never take scope over the full conditional. We therefore have to accept the prediction that this sentence can be true even if there is no chie£ The information chat there is such a thief will be computed only after the determination of the propositional content and only chen enter as part of the more informative proposition we just called its informative content. The real problem emerges as soon as it comes to modal embeddings: (6) It is possible that the thief stole my Mac. content expression (6a) 3! x (thief x I\ steal_Mac x) scalar implicature (6b) 0 3! x (chief x I\ steal_Mac x) presupposition (6c) 3! x (thief x) ....,
When we now merge the different expressions into a more substantial proposition, we get the wrong results. For the presuppositional expression states that there is a (unique) thief in this world, the content expression chat in some ocher world there is a possibly different chief who stole my Mac, and the implicature that it does not hold for every world chat it contains a (unique) thief who stole my Mac. However, we would rather want one and the same thief to verify the presuppositional-, content- and implicature-expression as it happens in (7b): (7) It is possible that the chief stole my Mac. (7a) There is a thief . . . . he possibly, but not necessarily stole my Mac. (7b) 3x! (thief (x) . . . stole-Mac (x) . . . ...., 0 stole-my-Mac (x) . . .
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be part of the propositional content, but will be merged with it only afterwards. And since propositional content is one factor in determining whether the pre suppositional expression can be accommodated, it also means that the computation of propositional content has priority over the computation of presuppositions in a very strict sense: the propositional content should be fully determined before any presuppositional information can be computed. Now it might be objected that we could, in the above case, take recourse to scope after all. The presuppositional expression might be computed with respect to a representation on which the negation has a narrow scope. One objection is that we would now gee the prediction chat the existence of a (unique) chief is both asserted and presupposed. But there is another objection which is more relevant to our present purposes.6 The Russellian seance does not work for other types of embedding. Consider (sa) where the presuppositional expression figures in the antecedent of a conditional. In chis environment presuppositions generally survive:
Rob A. van der Sandt
3 39
(2a) Someone had a child and his child was bald.8 (2b) If a man gets angry, his children get frightened. (2c) Every boy kissed thegirl who loved him . In the above cases we find a pronoun in an open presuppositional expression which is bound by a quantifier outside this expression. This prevents a coding of the presuppositional content by means of an independent expression. Karttunen & Peters (1 979) noted that the same problem arises for lexical presuppositions. (8a) induces the presupposition (8b): (8a) John managed to open the door. (8b) It took John some effort to open the door. Their two-dimensional semantics thus predicts that the indefinite (9a) presupposes the corresponding indefinite (9b): (9a) Someone managed to succeed George V on the throne of England. (9b) It took someone some effort to succeed George V on the throne of England. This prediction can easily be shown to be wrong by embedding (9a) in the antecedent of a conditional or by questioning it.9 In the absence of any
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Of course the Russellian would again appeal to scope and claim that both the presuppositional and implicature expression should be computed with respect to the representation in which the modal operator has scope over the description. But apart from the fact that we would run again into the problem that the presupposition would be both asserted and presupposed, it should be noted that it is easy to think up more complicated examples where this strategy does not work. Just embed (7) in the antecedent of a conditional. Now the description may have scope over the modal, but never over the full implication. We thus end up with one thief in this world and a possibly different one in another world who stole my Mac there. Let us look again at the binding problem involved in these examples. In the previous examples the problem arose out of the separation of semantic and presuppositional content which is inherent in the pragmatic picture. On a pragmatic account the semantic content is determined first and it is only then that presuppositional and implicatural information is computed. However, as (7) demonstrates, the computation of propositional content seems to be dependent on a prior determination of the presupposition. It is exactly this the pragmatic scheme does not allow? We run into similar problems when variables in presuppositional expres sions enter into sentence internal scope relations with quantified expressions. Some examples were given in (2a)-(2c) which I repeat here. In all these cases a pronoun in a presuppositional expression depends on an external quantifier:
340
Presupposition Projection as Anaphora Resolution
contextual information presuppositions are preserved in these environments, but ( 1 0) and (I I) clearly do not give rise to a presuppositional inference:
( I o) If someone managed to succeed George V on the throne ofEngland, he will have kept it for years. ( I I) Did someone manage to succeed George V to the throne ofEngland?
(1 2a) A child beats his cat. ( 1 2b) A child has a cat. ( 1 2c) If a child beats his cat, he will be punished.
The truth-conditional content of ( I 2a) can be represented as ( r 3a): (I 3a) 3x3y(child (x) 1\ cat (y) 1\ poss (x, y) 1\ beat (x, y) )
We might try to represent the presuppositional expression as follows: . . (1 3b) 3x3y(child (x) 1\ cat (y) 1\ poss (x, y)) But now the existential quantifiers in (I 3a) and (I 3b) may pick different child/ cat pairs and after accommodation of the presuppositional expression we are likely to end up with the wrong result that there is a child who has a cat and yet another child who has a cat and beats it. The final problem with the pragmatic point of view is that it obscures the difference between accommodation and contextual incrementation. Intuitively presuppositional information is information which is taken for granted. The understanding of a sentence which contains some presuppositional construc tions normally requires some context in which it can be interpreted. In many cases the context of utterance will already contain the presupposition, but this need not be the case. If a presupposition is not already there, the context of utterance may be adjusted. The default option is to add the presupposition so as to make the utterance interpretable after all. Lewis (I 979) coined the term accommodation for this strategy. It should be noted then that the accom modation is a strategy of repair. It does not simply add some information to the propositional content of the sentence uttered, nor is it part of the process of incrt:mentation thereby affecting the next context in the same way that propositional or implicatural information does. On the contrary, accommoda-
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Again the problem arises from having to bind the indefinite NP in the presup positional and the content expression by different quantifiers. Instead, we would want to identify the actual successor of George V with the person who is presupposed to have had difficulties doing so. But this is precisely what the use of two different quantifiers prevents. It should be noted that this problem is a general and fundamental one. It will arise whenever a quantifier binds some variable in a presuppositional expression. Consider ( I 2a)-( I 2c).
Rob A. van der Sandt
341
tion is a strategy of repairing the context of utterance in order to get an inter pretation for the sentence to be processed. If a relevant contextual parameter does not have an appropriate value, the hearer will infer it and adjust the con text so as to provide an interpretation for the utterance after all. Accommodation is thus best seen as a kind of pre-processing of an utterance in order to adjust contextual parameters so as to create an auxiliary content in which it can be interpreted. It is the context thus established which enters in the computation of the content, implicarures, and other pragmatic information. Contextual incrementation will then map the adjusted context into the next one.
P RE S U PP O S I T I O N AS A N A P H O R A
I n the previous section I tried to establish three claims. Presuppositional expressions cannot be conceived of as referring expressions, nor should presuppositions be conceived as logical inferences to be accounted for in some multi-valent or partial logic. I also argued that the pragmatic account cannot be maintained in its standard formulation. A principled division of informational content into a semantic and a pragmatic part gives rise to binding problems whenever presuppositional expressions enter into scope relations with quanti fied expressions. In the present section I will present an alternative and elaborate on van der Sandt ( 1 989) and van der Sandt & Geurts ( 1 99 1 ). I will claim that presupposi tions are just anaphors. They can be treated by basically the same mechanism that handles the resolution of pronominal and other anaphoric expressions. In fact, they differ in only two respects. Firstly, unlike pronouns they contain descriptive content which enables them to accommodate an antecedent in case discourse does not provide one. And, secondly, they have internal structure of their own. They can thus contain free variables and be incomplete in the sense descriptions may be and they thus may be bound in exactly the same way by external quantifiers. In sections 3 and 4 we will present a resolution mechanism for presuppositional expressions. It will turn out that the very same mechanism which handles the resolution of presuppositional anaphora simultaneously takes care of pronominal resolution. Let me first point our that it has been noted by several authors that definite descriptions can be used anaphorically. It was, however, simultaneously taken for granted that their presuppasitional properties had to be handled by a separate mechanism. Anaphoric treatments of definite descriptions are found, among others, in McCawley (1 979), Lewis ( 1 979) and many workers in AI. 10 However, McCawley takes Karttunen's ( 1 97 4) rules of contextual satisfaction as
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2
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Presupposition Projection as Anaphora Resolution
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a starting point in order to explain their projection behaviour. Lewis requires for a definite description to denote some individual that this individual is the most salient one having the relevant properties according to some contextually determined salience ranking. He does not, however, discuss the projection properties of the associated presuppositions. The closest to the position defended here is the view put forward in Heim's thesis (1982). Her statement of the novelty/familiarity condition simply comes down to the claim that definiteness is anaphoricity. However, Heim simultaneously states that definites have, apart from their anaphoric property, a presuppositional prop erty11 and this property simply is a species of a felicity condition which gives rise to the problems involved in presupposition projection. 1 2 A related but dif ferent view is taken in a subsequent paper devoted to presupposition projection (Heim 1 98 3).B Here Heim takes Karttunen's conditions of contextual satisfac tion as a starting point and reinterprets them as definedness conditions on con texts. First, the presuppositional property has to be defined for each trigger. The inheritance property, that is, what happens to the presuppositional property under embedding, should then fall out as a consequence of the rules of context change.1 4 The present paper follows van der Sandt ( 1 989), and van der Sandt & Geurts ( 1 991) and defends the claim that presupposition projection and anaphora resolution should not be handled by separate mechanisms. This claim applies basically to all paradigm cases of presupposition. It is therefore not just definite descriptions which are anaphoric. Once we take VP-anaphora and full propositional anaphora into account the claim that presuppositions are anaphoric expressions covers presuppositional adverbs like too and even , aspectual verbs like begin , stop and continue, cleft constructions, temporal clauses and factives. All these triggers are anaphoric in the same sense, though they may differ in their capacity to accommodate. 1 5 The claim that definites are anaphoric is thus seen as a special case of the more general phenomenon that all presuppositions are anaphoric expressions. In this section I will first present some suggestive material to illustrate a number of non-trivial correspondences between anaphora resolution and presupposition projection. I will then go on to show that this parallelism generalizes to the paradigm cases ofpresupposition inducers, I will correlate the basic terminology from the literature on presupposition projection to the basic notions of anaphora theory, and finally point out how such a view on presupposition and anaphora extends the scope of testability of theories of presupposition projection. In the next sections I will develop these ideas in the framework of discourse representation theory. The first attempt to give an account of presupposition projection is Karttunen ( 1 973). In this article he presents (1 4a)-(r6a) as his paradigm cases:
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(1 4a) Jack has children and all ofjack's children are bald. (I sa) IfJack has children, then all ofjack's children are bald. (I 6a) Either Jack has no children or all ofjack's children are bald. Compare these sentences with the well-known donkey sentences which gave rise to the development of discourse representation theory: (I 4b) John owns a donkey. He beats it. (I sb) IfJohn owns a donkey, he beats·it. (I 6b) EitherJohn does not own a donkey or he beats it.
(I 7a) IfJack has children, then they are bald. (I 7b) IfJohn owns a donkey, he beats his donkey.
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Now the problem as Karttunen formulated it for the theory of presupposi tion was rather different from the problem donkey sentences posed for anaphora theory. For Karttunen the problem came down to the following. In contrast to logical inferences, presuppositions normally do not enter into any scope relations with embedding operators, but tend to survive any depth of embedding, quite independently of the logical properties of the embedding operators. In the above cases they somehow disappear, however, and this is exactly what the projection problem for presuppositions comes down to. How do we determine the parameters needed to compute the presuppositions of a complex sentence out of the triggers and their components and, given these parameters, how do we define a recursive procedure which yields the actual presuppositions on the basis of these triggers and the composition of the sentence? So the actual problem was how to account for the fact that none of the sentences ( I 4a)-( I 6a) preserves presupposition that Jack has children. The problem as it was formulated with respect to the donkey sentences was quite a different one. It was to find a mechanism which would account in a uniform way for the anaphoric links between the pronouns and their antecedents in the (b)-sentences. The terminology in which the problems were discussed was equally different. While presuppositions were said to be filtered, cancelled or satisfied by the context of utterance, anaphora theory focused on the analysis of pronouns which were analysed in terms of co reference and binding. The parallelism between the (a)- and (b)-sentences will be obvious. Wherever we find a full NP in the (a)-sentences we find a pronoun in the (b) sentences. We could as well pronominalize the presupposition triggers in the (a)-sentences, thus turning them into donkey sentences, or expand the pro nouns in the (b)-sentences to full definite NPs, thus turning them into para digm cases of presupposition filtering. No difference in interpretation results in either case.
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These observations at least suggest that a similar mechanism underlies both pronoun resolution and presuppositional filtering. They also suggest another terminology of describing the presuppositional phenomena. I nstead of saying that the presuppositions in the (a)-sentences are suspended, cancelled or neutralized, we should say rather that they are linked up or bound to a previously established antecedent j ust like the pronouns. Note that the behaviour just observed is not confined to NP-anaphora (that is, definite descriptions and the related possessives and restrictive relative clauses). Once we look at VP- and full propositional anaphora, the parallelism extends quite naturally to other kinds of presupposition inducers:
Full propositional anaphora ([actives , temporal clauses): (1 9a) IfJohn is ill, Mary regrets (that/that he is ill). (1 9b) If]ohn died, he did see his children before (that/he did/he/died). Just as in the case of the NP-anaphors we find no difference in interpretation between the VP-and propositional anaphors and their full lexical expansion. And j ust as in the previous cases the presuppositional expressions seem to be bound by a previously established antecedent. It is only when we look at presuppositional constructions which cannot be linked directly with a proper antecedent that we find a crucial difference. In case a pronoun cannot be linked with a suitable antecedent, the whole sentence will not get an interpretation. However, under the same conditions presupposi tional sentences may get a determinate value. There is an obvious explanation for this. Presuppositional constructions differ from pronouns, VP- or proposi tional anaphors in that they have semantic content of their own. This accounts for the fact that presuppositional constructions unlike pronouns or other unloaded anaphors have a capacity to accommodate. In case a semantically empty anaphor does not succeed in finding a proper antecedent it will not get a determinate value. However, presuppositional expressions will generally contain enough descriptive content of their own to establish an antecedent in case the previous discourse does not provide one. The discourse will be repaired so as to provide an accessible antecedent and the anaphoric expression may get an interpretation after all. The following pairs illustrate the effect of accom modation: (2oa) All ofJack's children are bald. (2ob) They are all bald. (2 I a) If baldness is hereditary, then all ofjack's children are bald. (2 I b) If baldness is hereditary, then they are all bald.
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VP-anaphora (clefts , aspectual verbs , presuppositional adverbs): (1 8a) If someone solved the problem it was Julius who (solved it/did). ( 1 8b) If Harry stopped smoking,John (stopped/did) too.
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This brings me to the basic explanation. Presuppositions are simply anaphors. They only differ from pronouns or other kinds of semantically less loaded anaphors in that they contain enough descriptive content to establish a reference marker in case discourse does not provide one. In this case the lexical material will be accommodated. A further observation which will tum our to be crucial is that accommodation normally takes place with respect to the context established by the previous discourse. In the terminology of discourse representation theory this means that the antecedent will preferably be accommodated at top level of discourse structure. In contrast to the situation where a presupposition is bound at some subordinate level, the information contained in the trigger will be entailed by the DRS and be preserved intuitively. Note that this is what we would expect given the intuitive notion of presupposition as information taken for granted and note also that this explains the intuition that presuppositions, unless filtered, cancelled or neutralized, are entailed by their matrix sentence. In (2 1 a) the information contained in the presuppositional expression is accommodated at top level and thus entailed by the DRS thus adjusted. It should nevertheless be pointed out that certain principles of a pragmatic nature may force accommodation at some sub ordinate level. In these cases the presupposition will still be there. It will not, however, be entailed by the adjusted context, but it will remain invisible and not surface as an intuitive inference. This picture allows us to reinterpret the central theoretical notion of presupposition theory. To say that a presupposition is projected (in a given discourse) _simply means that the lexical information contained in the 'presup positional anaphor' has been accommodated at some level of discourse struc ture, thus providing an accessible antecedent after all. In this view projection is a repair strategy which enables us to establish an anaphoric link even if the current discourse does not provide a suitable antecedent. To say that a sentence is presupposing (or that its presupposition is preserved in a context of utterance) is a special case of accommodation. It tells us that the presupposition has been accommodated at the top level of discourse structure. Neutralization or pre suppositional satisfaction boils down to anaphoric binding at some level of representation. And the notion of cancellation makes no sense anymore. We can do away with it as a misleading label which was introduced to cover those cases where a presupposition is not perceived as an intuitive inference, that is, · those cases where a presupposition is bound to (and its descriptive content thus absorbed by) some antecedent, as well as those cases where a presupposition has been accommodated at some subordinate level, because projection to the top level would result in inconsistency or otherwise violate pragmatic constraints on accommodation. Before giving a more precise account of the ideas put forward I still have to elaborate on two points. The first concerns the difference between the notion of
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The context of utterance will thus only admit a sentence cp if it already entails all of cp's elementary presuppositions, or, in Heim's terms, the contextual update of a sentence in cp in a context c will only be defined if c entails all its elementary presuppositions. If cp is complex, presuppositional admittance can be defined recursively by associating with each constituent sentence of cp its own, so-called 'local' context and requiring that each of the constituent sentences is admitted by its local context: (23) A context c admits a complex sentence cp iff each of cp 's constituent sentences are admitted by their local contexts. For a negated sentence the local context simply is the global context. A context will thus admit the negation of a sentence just in case it admits its unnegated counterpart, or c + cp, the contextual update of a negative sentence will be defined just in case c + cp, the contextual update of its non-negated counterpart, is defined. This captures the fact that sentences tend to preserve their presuppositions under negation. In case cp is a conjunction or conditional the local context is determined as follows: (24) In case cp is of the form '1/J and X ' or 'if 1/J then X ', c is the local context for 1/J and c + 1/J is the local context for X . ....,
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anaphoric binding envisaged here and the notion of contextual satisfaction adopted by Karttunen and Heim. This difference will tum out to yield different predictions both with respect to the neutralization of presuppositional information and the interpretation of accommodation as a contextual repair mechanism. The second question concerns the testability of the claim that presupposition is a species of anaphora. The basic claim in Karttunen ( 1 974), Stalnaker (1973, 1974) and Heim ( 1 983) is that the presuppositions of a carrier sentence must be entailed by the context in order for them to satiifj thepresuppositions if this sentence, or, to use a shorter but equivalent terminology, these presuppositions must be entailed by the context of utterance in order for this context to admit this sentence. Admittance or presuppositional satisfaction is thus defined in terms of entailment. Heim (1983) reinterprets these requirements as definedness conditions on the contextual update. On her account no contextual update will take place unless the presuppositions of a sentence are satisfied, i.e. unless their descriptive content is entailed by the context of utterance. Remember that linguistic presuppositions are conventionally associited with lexical items and syntactic constructions. This allows us to assign to each simple sentence a finite lise of elementary presuppositions.16 Call this set Pres( cp) for a given sentence cp. The presuppositional requirement that simple sentences impose upon the context can then be characterized as follows: (22) A context c admits a simple sentence cp just in case c entails Pres(cp).
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Talking again in terms of definedness conditions, this means that c + tp -+ X will be defined just in case c + tp and (c + cp) + tp are defined. It is thus required that all presuppositions of the antecedent are entailed by the context of utterance and that the presuppositions of the consequent are entailed by c + tp . This predicts that the presuppositions of the antecedent always carry over to the matrix. The requirement that the local context for the consequent c + tp should entail the presuppositions of X comes down to the requirement that the global context c should entail tp -+ Pres (x ). The presuppositions of the consequent of a conditional thus always surface in a weakened form. The limiting case is where tp already entails the presuppositions of X . Now tp Pres (X ) is trivially true and presuppositional satisfaction is guaranteed automatically. Falsity of the presupposition cannot give rise to undefinedness of the contextual update. The presupposition is effectively neutralized. A simple example may illustrate this. According to the rules given above a context c will admit (25a) just in case c entails (25b): .....
The consequent of (25a) triggers the presupposition that John has a wife. The clauses given above require that this presupposition should be entailed by the local context for the contextual update to be defined, i.e. it should be entailed by c + John is married . The global context c should consequently entail the implicative proposition (25b). Since this is a tautology, and since tautologies give no new information whatsoever, the condition for definedness is a trivial one. Definedness is guaranteed automatically and the content of the presup position is effectively neutralized. The following sentence poses a more substantial requirement on the context of utterance: (26a) IfJohn made coffee, his wife will be happy. (26b) IfJohn made coffee, he has a wife. Assuming that it is not known beforehand that John has a wife, the local context, c +John made coffee , does not entail that John has a wife. Again the requirement that the local context should entail this elementary presupposition comes down to the requirement that c should entail the implicative proposition Ifjohn made coffee, he has a wife . The prediction therefore is that an utterance of (26a) presupposes that John has a wife, on the assumption that he made coffee. In other words it presupposes (26b). This brings us to the question as to what happens when the presuppositions of a sentence are not entailed by the context of utterance which, according to the view just sketched, would make the contextual update undefined. Here Lewis's ( 1 979) notion of accommodation comes inY Accommodation is a
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(25a) IfJohn is married, his wife will be happy. (25b) IfJohn is married, John has a wife.
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mechanism which, if applicable, will simply insert the required presupposition into the context of utterance. 1 8 It is thus a mechanism which under certain conditions adjusts the context of utterance by accommodating the required presupposition so as to make the utterance defined after all. The absence of a 'required' presupposition need not therefore result in infelicity. It is by means of this notion of accommodation that Karttunen and Heim account for the fact that utterances may introduce new information simply by presupposing it. If presuppositions are not neutralized, they can be accommodated so as to restore definedness after all. On Heim's account definedness can be restored in either of two ways. We may either accommodate the missing presupposition globally, that is, into the context of utterance, or insert it locally, which in the above case would amount co inserting in the antecedent of the conditional. Ceteris paribus, global accommodation is the preferred option. With respect to examples like (26a) it does not make much difference whether we globally or locally accommodate. Consider a sentence of the form cp -+ tp , where tjJ triggers a presupposition X . Global accommodation would put the implicative proposition cp -+ x into the context of utterance. Local accommodation would put X into the local context that is in c + cp . Both operations would satisfy the presuppositional requirement and thus guarantee contextual update, but in both cases the resulting context will only entail the conditionalized presupposition. The alternative would be globally to accom modate the descriptive material contained in the trigger straight away, instead of the sentential presupposition computed according to the clauses above. This would also restore definedness, but not minimally. It also requires an answer to the question why we should compute a weak sentential presupposition, but accommodate a stronger one. 1 9 It has been argued (Zeevat 1 99 1 , chis volume) that anaphoric binding can be reduced to entailment and that the view on presuppositional requirements put forward in chis paper can be amalgamated to the one which has been defended by Karttunen and Heim, provided we make some proper adaptation to both theories. I have my doubts about this claim. There are a number of non-trivial differences between anaphotic binding on the one hand and contextual satisfaction in the Heim/Karttunen sense on the other. As we saw, the basic requirement put forward on the Karttunen/Heim account is that the presuppositions of an utterance should be entailed by the local context. If they are, definedness of the contextual update is guaranteed and the presuppositions are not felt to have a true presuppositional status any more. The reductionist account would thus predict that as soon as the information triggered by a presupposition inducer is found in an accessible position, the material thus found constitutes the antecedent for the anaphoric expression. Let me first remark that we should not require chat there be an entailment relation between an antecedent and an anaphoric expression but rather that this relation
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(27) IfJohn has grandchildren, his children must be happy. The Karttunen/Heim account predicts that the presupposition is satisfied trivially and that this sentence thus cannot have a presuppositional reading. I contend that this sentence has both a presuppositional and a non-presupposi tional reading and that for this particular example the presuppositional reading is strongly preferred. Note that the grandchildren in the antecedent of the conditional cannot serve as a proper antecedent for the presuppositional expression in the consequent. The presupposition thus cannot be bound and will be accommodated so as to provide an antecedent after all. The preference for global accommodation moreover predicts accommodation at top level and
c
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should be one of subsumption. However, even if the requirement that an anaphor must be entailed by its antecedent can be defended, this requirement can only be maintained as a necessary but certainly not as a sufficient condition. A discourse will normally contain many male individuals. If we adopt the requirement that an antecedent expression should entail the anaphor, each male individual is a potential antecedent for a pronoun which requires the . antecedent to be of the male gender. The actual antecedent still has to be selected from these. It is here that the differences between an anaphoric view and the contextual satisfaction view come out most clearly. The satisfaction view predicts that once the presuppositional material has been found the presupposition is effectively neutralized. This is not quite what we expect on an anaphoric view. The latter predicts that if some discourse referent with suitable properties is found this referent is a potential antecedent. Such a potential antecedent will, however, only absorb the descriptive content associated with the presuppositional anaphor if it is actually selected as its antecedent. If not, this material may be absorbed by another suitable candidate or b� accom modated after all. An anaphoric view thus predicts that presuppositional anaphors may be genuinely ambiguous, that is, there should be cases where we can either select among different antecedents or have the choice between either binding or accommodating. It thus simultaneously predicts that we should find cases which allow a certain variability in interpretation and in particular a choice between a presupposing and a non-presupposing reading, where the satisfaction account predicts just presuppositional neutralization. This vari ability in interpretation is what we actually find. In order to bring out the differences between the two views, I will first consider a case where the lexical material contained in the presuppositional trigger is entailed by the local context but nevertheless cannot serve as a proper antecedent, and then discuss some cases which actually give rise to the variability in interpretation we would expect on a purely anaphoric view. In the following sentence the antecedent entails the information induced by the presuppositional trigger in the consequenc:20
3 so Presupposition Projection as Anaphora Resolution
(28) IfJohn has an oriental girlfriend, his girlfriend won't be happy. (29) IfJohn murdered his wife, he will be glad that she is dead. (3o) If someone at the conference solved the problem, it was Julius who solved it. I argued before that sentences of this type display a genuine ambiguity.22 The presuppositional interpretation is most easily perceived in the following continuations, which eliminate the presupposing reading: (28 ) IfJohn has an oriental girlfriend, his girlfriend won't be happy, but if he has one from France . . . (29 ') IfJohn murdered his wife, he will be glad that she is dead, but if she took those pills herself . . . (3o') If someone at the conference solved the problem, it was Julius who solved it, but if it was solved at Nijmegen University, it certainly was not Julius. '
Which interpretation we get depends on whether or not we resolve the presuppositional anaphor in the antecedent. If we take the first option the descriptive material associated with the presuppositional expression will be absorbed in the antecedent. The second option yields accommodation of the presuppositional material into the context of utterance.23 An important feature of the theory presented here is that it is notjust testable with respect to our intuitive judgements with respect to the survival of presuppositions, but also with respect to the possibility of pronominal uptake. One of the most salient characteristics which distinguishes presuppositions from logical inferences is their tendency to survive embedding, no matter what the logical properties of the embedding operators are. Presuppositional con structions thus do not normally enter into scope relations with quantifiers or
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consequently a presupposing interpretation for this sentence on its preferred interpretation. The non-presupposing interpretation comes about by accom modating the presupposition in the antecedent of the conditional.21 The second type ofexamples consist ofcases where a presupposition may but need not be bound. Soames observed that conditionals in which there is a one sided entailment relation between the antecedent and the presupposition of the consequent allow a non-presupposing reading and claimed that they were completely neutral with respect to the truth of the presuppositions. Of course, if we think in terms of cancellation such a claim makes sense. A presupposition is either cancelled or not. So if we perceive a non-presupposing reading for a particular sentence, we have no other choice than to maintain that the presupposition does not survive. On the present account there is no need to entertain this assumption. If I am right in claiming that in many cases presuppositions may but need not be bound to a potential antecedent, such examples display exactly the variability we would expect.
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(3 1) If John has an oriental girlfriend, his girlfriend won't be happy. She has always been rather jealous.
(32) IfJohn has grandchildren, his children will be happy. They wanted to have
offspring long ago. (33) If the problem was solved at the conference, it was Julius who solved it. But whether he did or not, the solution was brilliant anyway. It should be observed that these continuations cannot be treated as an instance of modal subordination. Neither the pronouns nor the description can access the anaphoric antecedent in the antecedent clause of the conditional. Both require an antecedent at the main level of discourse. This shows that the presuppositions in these conditionals are neither neutralized nor weakened to an implicative proposition. For this would deprive us of the possibility of accounting for the anaphoric links in the above sentences.
3 A N A P H O R I C S T R U C T U R E S I N D I S C O U RS E
RE P R E S E NTAT I O N T H E O R Y
In the present section I will develop the informal ideas outlined above in discourse representation theory. The account of anaphoric structures in discourse representation theory follows van der Sandt & Geurts ( 1 99 1 ). For details concerning the actual construction mechanism out of the syntactic parse of a sentence I refer to the same paper. In Kamp's original formulation a discourse representation structure or DRS K is an ordered pair (U(K), Con(K)), where U(K) is a universe of discourse markers and Con(K) a set of conditions. Indefinite NPs introduce discourse markers into the universe of a DRS. These discourse markers then serve as the referent for the NP for tpe remainder of the discourse. Pronouns or other
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logical operators. If they survive they behave like indexicals or other context dependent expressions. On the current account this is a consequence of their capacity to accommodate. As I pointed out before, accommodation of the presuppositional material creates a discourse referent, provides it with descrip tive material associated with the presuppositional expression, and thus estab lishes an accessible antecedent. If accommodation takes place at top level, this creates a discourse marker, which can subsequently function as an antecedent for pronouns or other anaphoric expressions to come. This gives us a further test to distinguish presuppositional from non presuppositional readings. If a sentence is presupposing in a given context the discourse marker thus created should allow anaphoric take-up in subsequent sentences. So let us consider the above examples again:
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{34) Every girl loves her cat . ( 3 s ) I f every farmer would fondle his donkey, donkeys would b e happier. {36} John has a goose and every farmer loves his goose . In (34) and (35) a pronoun inside a presuppositional expression is bound by the quantified NP in subject position. As I pointed out in section 1 , chis is exactly
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anaphoric expressions may pick them up. Conditions assign properties to the members of U(K} and thus encode the descriptive content of the predicates. Discourse markers thus store whatever information accumulates on them when discourse proceeds. Two salient features of Kamp's original formulation are that the construc tion procedure works top-down and that pronouns are resolved on-line during the construction procedure. The construction of each new DRS is based on the DRS representing the previous discourse and the syntactic parse of the sentence to be processed. The syntactic tree of the sentence under analysis is taken apart top-down and during this process new markers and conditions are added immediately to the main DRS. The same applies to anaphoric expressions. When the conscruction algorithm encounters a pronoun or other anaphoric construct it is resolved immediately against the universe of the main DRS. The present account differs in three respects. Firstly, the construction pro cess works bottom-up. Secondly, the construction procedure is indirect in that we will first construct a provisional DRS from the syntactic parse of the sent ence. Such a 'sentence'-DRS is an auxiliary construct which only after the com pletion of the construction procedure is merged with the incoming DRS.24 The final and most important difference is that anaphoric elements are encoded separately in a DRS. They are therefore not resolved straight away against the content of the main DRS, but they are processed only after the DRS constructed for the incoming sentence has been completed and merged with the main DRS. I will refer to chis construct as a resolved or proper DRS. A proper DRS will thus not contain any unresolved anaphoric expressions and ·it is to chis construct that the standard interpretation rules apply. So we will construe a DRS as consisting ofthree components, a universe of discourse markers, a set of conditions, and its so-called A-structure. The latter component is a set of DRSs. They collect the anaphoric elements of the sentence to be processed. This last difference is a crucial one and derives from the fact chat presuppositional expressions differ from pronouns or other anaphoric elements in that they may have the same internal complexity that non-presuppositional phrases of the same syntactic category exhibit. As I said before, presuppositions need not be independent of each other. In fact presuppositions may embed further presuppositional concructions or other anaphors. Some obvious, but in the literature on presupposition unfortunately neglected examples are found in open descriptions:
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(37) Mary didn't realize that it was Harry who bought the butcher's goose. (38) John didn't know that the thieflost his watch in the backyard. (39) IfJohn has children, he will regret that all of his children are bald. In (3 7) a factive complement, which is itself a presuppositional anaphor, embeds a presupposition inducing cleft, which contains a possessive construction, which in tum contains a definite description. We thus arrive at the following hierarchy of presuppositional anaphors: (37a) (37b) (37c) (37d)
It was Harry who bought the butcher's goose. Someone bought the butcher's goose. The butcher had a goose. There is a butcher.
Sentence (38) illustrates a presuppositional construction which embeds several other presuppositional anaphors at the same level of embedding. This example also shows that the latter may both enter into scope relations with expressions inside and outside the embedding presuppositional expression. Processing and interpreting the embedding anaphor obviously depends on a prior resolution of the embedded ones. Sentence (39) differs in that a presuppositional anaphor (the possessive construction) embedded in another one (a factive complement) is bound in the antecedent of a conditional. Note that no antecedent can be found for the embedding anaphor. This might invite one to accommodate the factive presupposition at top level of representation. That would, however, yield the wrong prediction that (39) presupposes that all ofJohn's children are bald. It transpires that the natural accommodation site for this presupposition is the antecedent ofthe conditional and the reason is obvious. Accommodation at top level would project the anaphoric expressionJohn's children up to a position where it could not access its antecedent marker any more. The above observations give rise to a natural and central constraint on
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the reason why it is wrong to analyse presuppositional expressions as referring expressions. Sentence (36) shows how the interpretation of a presuppositional expression may vary depending on the antecedent chosen for the embedded anaphor. This turns out to be the general case both for pronouns and presup positional anaphors and is one of the reasons for choosing an indirect construc tion procedure. We will see that in order to determine the correct interpretation of a sentence we first have to process the deepest embedded anaphor. The resolution and interpretation of the embedding anaphor will then depend on the result of this. Note that once we allow anaphoric expressions to have internal structure there is no limit on the depth of embedding. The following presuppositional constructions embed other presuppositional constructions, which again contain further anaphoric expressions:
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. accommodation, which I mention now and which I will discuss later in more detail. If an embedded anaphor is bound to some accessible antecedent, none of the embedding anaphoric expressions can be accommodated any higher. As I said, the reason is obvious. Accommodating the full expression beyond the binding site of an embedded anaphor would unbind a variable in the latter. Before giving some examples I will first give the formulation for the language. The definition extends the standard definitions for the language of discourse representation theory in that they allow an explicit coding of multiply embedded anaphoric expressions:
DRS dt'finition
•
•
•
•
•
•
A DRS K is a triple (U(K), Con(K), A(K)), where (i) U(K) is a finite and possibly empty set of discourse markers. (ii) Con(K) is a set of simple or complex conditions. (iii) A(K) is a (possibly empty) set of DRSs. A condition is an expression of the following form: un are discourse markers, then P(u1, (i) If P is an n-place predicate and u1 . . ., un) is a simple condition. (ii) If u; and uj are discourse markers then U; = uj is a simple condition. (iii) If K and K ' are DRSs, then --.K, K ..... K ' and K V K ' are complex conditions. •
•
•
For a given DRS K we will refer to A(K) as its A-structure. This structure collects the anaphoric elements of K. As we pointed out, an anaphoric expression may simultaneously contain any number of other anaphoric expres sions. An A-structure is thus defined as a set of DRSs. We noted furthermore that each anaphoric expression may itself embed other anaphoric expressions up to any depth. Any member of an A-structure is thus itself a DRS. This gives us a simple way to embed anaphoric expressions inside larger anaphoric expres stons. An example may demonstrate the function of an A-structure. Consider the following sentences: (4o) John's cat purrs. (4 1) John has a cat. It purrs. (42) John has a cat. His cat purrs. The construction algorithm will associate the following structure with sentence (40):25
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The vocabulary is identical to the language of disco"urse representation theory. It consists of a set U of discourse markers: u, v, w, u., U2, , a set of n-place predicates: P 1 Pn and the operators --., ....., and V to form complex conditions.
Rob A. van der Sandt 355
(43) (
0, {purr (x)),
{( {x), {cat (x), poss (x, y)), {( {y), ijohn (y)),
0 )>-+)} )
In the pictorial representation (44) I use dotted boxes as a mnemonic device to indicate the members of an A-structure. Italicizing will be used throughout as a means to indicate anaphoric material. Bold indicates material which has been accommodated. This is just for clarity. Nothing substantial hinges on it. It Ko purr (x)
. - -- - - - - - - .., I X -I
�- - - - - - - ., 1 cat (x) I I I : poss (y.X)
: I I I I ...J :
: r;------, I r - - - - - - - - -1
I
L - - -- - - - - - -
J
II
(y) I L.: _ _ _ _ _ _ _ _ I I John
is easy to read off from this representation that (40) contains two anaphoric expressions, one for the full possessive construction and one for the proper name which is contained in it.26 Its universe is empty and so is the A-structure ofthe deepest embedded anaphor. Though Ko is a DRS according to the above definitions it is as yet unresolved and does not allow an interpretation. In order to make clear how an A-structure is resolved we need some more definitions. As I said, DRSs are constructed in two stages. First, a DRS is constructed for the incoming sentence. This DRS is then merged with the main DRS, which result in a new DRS in which the anaphoric structures still await processing. Only then are the anaphoric expressions resolved against the content of the new DRS, thus yielding a proper DRS. Merging the DRS for the incoming sentence with the content of the main DRS is a rather simple operation which involves taking the union of the universe of both DRSs and merging their conditions and A-structures.
Merging Given two DRSs K and K ', the merge ofK with K ' is defined as follows: K U K ' :- (U(K) u U(K '), Con(K) u Con(K '), A(K) u A(K ')) Anaphora resolution is now a partial function from DRSs to DRSs, which should obey the standard constraints on accessibility. On the current account
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(44)
3 56
Presupposition Projection as Anaphora Resolution
accessibility is a relation between members of the universe of an A-structure and established markers. Accessibility is the first and foremost constraint on the possibility of anaphoric binding and regulates the projection of presupposi tional material upwards through DRSs. Again we have to extend the definitions in order to take the contribution of A-stnictures into account. Subordination A DRS K; immediately subordinates a DRS � if one of the following holds: There is a Kk such that � -+ Kk e Con(K;) There is a Kk such that K; � e Con(Kk) There is a Kk such that � V Kk e Con(K;) There is a Kk such that Kk V � e Con(K;) ....., � e Con(K;). � E A(K;). -+
A DRS K; subordinates a DRS � just in case (i) � immediately subordinates �(ii) There is a Kk such that K; subordinates Kk and Kk subordinates �Accessibility Let u e U(�). where � is an element of some A-structure and v an established marker in some U(K;). Now v is accessible to u just in case K; subordinates �We furthermore distinguish between the local domain and the accessible domain of an anaphoric DRS. Let K be an anaphoric DRS, that is, an element of some A-structure. Its local domain is U(K). Its accessible domain Acc(K) is the set of all markers which are accessible from the elements of U(K). Note that according to these definitions no anaphoric marker in an A-structure A(K) can access a marker in its local domain, nor any other marker in a superordinate A-structure. Anaphoric markers will thus always be resolved outside an A-structure. Subordination imposes a tree-structure on DRSs, which extends inside A-structures. It tells us which markers are accessible from a given marker and thus can be identified with it. On the present account anaphora resolution is not limited to the identification of discourse markers, as is the standard case with pronominal anaphora. Instead it is an operation on (sub) DRSs. It is then convenient to have the notion of a projection line. A projection line is one path through an accessibility tree from a sub-DRS to the root of the tree. It tells us which route an anaphor must take when it is projected to a higher position in a DRS.
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(i) (ii) (iii) (iv) (v) (vi)
Rob A van der Sandt
3 57
Projection lines Let Ko be a main DRS and K., a member of some A-structure. The projection line ofK., is a sequence ofDRSs (Ko . K.,) each member ofwhich immediately subordinates the next one. A DRS � will be said to be lower on K.,'s projection line than K;just in case K; subordinates �- � is higher on K.,'s projection line than K;, if� subordinates K;. .
.
Proper DRS Let K; be a member of some A-structure. (i) K; is simple or non-anaphorically-embeddingjust in case A{K;) 0. (ii) K; is empty just in case K; (0, 0, 0). (iii) IfK; is empty and K;' is immediately superordinate to K;, then K;' is empty just in case K;' (0, 0, K;). =
=
=
A DRS is proper just in case it does not contain any non-empty A-structure. This brings me to the notions of binding and accommodation. Both are operations on DRSs. In order to see whether a presuppositional anaphor can be bound to some pre-established antecedent we follow up its projection line in order to find a suitable antecedent. If we do, the anaphoric marker can be identified with the established marker. The associated conditions will be transferred to the binding site and the antecedent thus inherits all the descrip tive information associated with the presuppositional anaphor. If no suitable antecedent for a presuppositional anaphor can be found, it will be accommo dated. Accommodation generally will take place at the highest accessible level such that the resulting structure does not violate general constraints on (un)binding and acceptability. Technically, accornrnodation consists in trans ferring the anaphoric marker plus its conditions to the level of accommodation,
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DRSs may contain any number of unresolved anaphors. Resolution of all anaphoric expressions contained in a DRS will yield a proper DRS which can be interpreted with respect to a model according to the standard embedding conditions.2' Anaphora resolution is thus a complex function from DRSs to DRSs. In the case of anaphoric binding the resolver puts in equations which link discourse markers and transfer the conditions associated with the anaphoric expression to the binding site. In case of accommodation the resolver will percolate an A-structure upward along its projection line and add both its markers and the conditions to the accommodation site. If this process is suc cessfully completed for all A-structures in a given DRS we end up with a resolved or proper DRS. A proper DRS is thus a DRS with an empty A-structure.
3 5 8 Presupposition Projection as Anaphora Resolution
thus adjusting the discourse structure by establishing an accessible antecedent after all. The following definition tells us how binding and accommodation can transform an unresolved DRS into a resolved one. In the next section we will give the constraints which allow us to determine what admissible binding and accommodation sites are for an anaphoric expression in a given DRS. Resolution Let K be a DRS and let K. be the source of an anaphoric expression, that is an element of an A-structure of some sub-DRS ofK and let A(K.) be empty. Let its target be a (sub)DRS � on K.'s projection line. Let K. have the markers y1 Ym and Ace(�) the markers x 1 "n· Let J be a function from U(K.) to Ace(�). such that the conditions of� are compatible with the conditions of K. under the substitution of y1 Yo for x 1 "n· The resolution of the anaphoric structure K, with respect to K1 yields a DRS K ', which differs from K in the following respects. •
•
•
•
•
•
•
•
.
•
•
Binding (i) U(K.') CON(K.') 0 (ii) U(�') U(K.) u U(�) (iii) CON(�') CON(K.) u CON(�) u {x =
=
=
=
=
y I x f(y)} =
Accommodation (i) U(K.') CON(K.') 0 (ii) U(�') U(K.) u U(�) (iii) CON(� ') CON(K.) u CON(�) =
=
=
=
Accommodation of K. into � is thus just like binding with the one exception that no restrictions on compatibility are required and no anaphoric equations are added to Con(�). It is worth running through an example and to look in some more detail how the resolution algorithm would map the unresolved DRS (44) into a proper DRS. The deepest embedded anaphor we find is the A-structure set up for the proper name. Going upwards along its projection line we check whether a suit able antecedent can be found. In this case we will not. Hence we add y to U(�) and the associated condition to Con(�). This yields �·. Next we start process ing its embedder. Again we will not find an antecedent for the embedding pre suppositional expression. It will be :!Ccommodated as well, yielding �*. This is precisely the DRS which the conventional construction rules would yield
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.
Rob A. van der Sande 3 59
(44 ' )
Ko'
Ko" .---y.x--------,
)'
._______---i John (y)
John (y)
purr (x)
cat (x)
r - ..,- - - - - - - -, �-.:. _ _ _ _ _ _ _ _ ...J I I cat (x) I I I I poss (y.t) 1 I 1 r - - - - - - -, 1 I t- - - - - - - --1I I I 1 I I J.,. _ _ _ _ _ _ _ j I L- - - - - - - - - - - J
poss (y,x) purr (x)
,.. -- - -
- - - - - - --, 1- -- - - - - - - - - -1 I ,.. - - - - - - -- ., I I I I 1- - - - - - - - - ..l I I I I 1 I L. - - - - - - - - - � I J.,. _ _ _ _ _ _ _ _ _ _ _j
(45) His cat purrs. The representation is K1, which is exactly like �. except that we find a pronoun where � has a proper name. Again we will not find an antecedent. And since pronouns lack the capacity to accommodate, no interpretation would come about if (45) were processed in isolation. However, if (4 5) were processed given an incoming DRS, which already contains the information that John has a cat, the embedding presupposition will be bound to this pre-established animal: (46) John has a cat. His cat purrs. Merging K1 with the incoming DRS yields (47). Resolution is now straight forward. We first equate the pronominal y with u and subsequently the x with v and transfer the associated conditions to the main DRS, which yields the K1". (47)
Kt
Kt
1------l purr
(x)
r - ---------, I X 1- - - - - - - - - - - ,I 1 cat (x) I I
: 1
poss (y,x)
- - - "1 : jym:; - I :---------i II I I I
�:
I I I 1 I L.--------....1 I �----------J
John (u) cat (v) poss (u,v) purr (x)
poss (u,v) purr (v)
c:.x.:.: ::- ::-.:::-.:::-.:::-.:=::- ::-J I cat (x)
I
I
u,v John (u) cat (v)
poss (y,x)
�--------,
: I Ymasc
:
1 I
: :
I r- - - - - - - - - '1 I I L- - - - - - - - - � I L--- - - - - - --- J
���-=-��-=-��=]I I
I r - - - - - - - --, I 1- - - - - - - --� I 1 1 I L- - - - - - - - - .l
I
I I I
L - - - - - - - - - - ...J
Note that K1" is like Ko". They only differ in the way they are constructed. In �· John's cat comes about by accommodation, in K1" the possessive construction is bound to a previously established antecedent. Note furthermore that (44) is intuitively presupposing while the discourse in (46) is not. This illustrates our informal discussion in the previous section. On the current
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Consider now (45) which is like (4o) except that we find a pronoun where (40) has a proper name.
360 Presupposition Projection as Anaphora Resolution
account the intuitive notion of presupposition coincides with accommodation at top level of discourse structure. However, if some presupposition is bound to some previously established antecedent, the presuppositional construction will be absorbed in its antecedent and not be felt to have a presuppositional status any more. This captures the common intuition that presupposition and assertion are complementary notions. It also shows how presuppositional material can be entailed without being presupposed. Sentence (48) is one of the paradigm cases of cancellation or filtering in conditionals: (48) IfJohn has a child, his child is happy.
(49)
K2
r-------� y
happy (z)
r-;----- - - -: t- - - - - - -- -t
child (y) poss (x,y)
: 1
r-------- , I X I
r- - - - - - - - ..., 1 1 John (x)
child (z)
poss {w,z)
: r.v-1
:
1 1
:
1 L - -- - - - - - - ..J
r:.::J
1- - - - - - - - - �
K2' r----, John (x) y child (y) poss (x,y)
happy (y)
..... - - - - - - --, 1- - - - - - - ..J I
I
L _ _ _ _ _ _ _j
�
;::: :-.=-:-.::::::J
I I I I I -I I I --L--------�
f--j
Next the pronominal marker in the consequent will be processed and equated with the marker just established for John. Processing the remainder of the possessive construction is then straightforward. Following up its projection line we will find a perfect match for the presuppositional anaphor in the antecedent if we equate z with y and w with x. Transferring the conditions to the ante cedent box then results in K,', which is identical to the DRS we would have derived straight away for its pronominal counterpart under a coreferential reading for John and the pronoun.
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The initial representation is depicted in (49). Again we will not find an antecedent for the proper name. Thus accommodation at top level will ensue.
Rob A van der Sandt 361
(so) IfJohn has a child, he is happy. Binding and accommodation are subject to a variety of constraints. I will discuss these constraints in the next section in order to determine what proper binding and accommodation sites are. This will bring us back to the standard problems involved in presupposition projection.
4
PROJE CTI O N A S RE SOLUTION
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Let me recapitulate what we have done up to now. Assuming a bottom-up construction procedure, we opted for an indirect construction mechanism. First, a DRS is put together from the syntactic parse of the sentence. This DRS collects but does not resolve the anaphoric elements in its A-structure. Merging this DRS with the main DRS yields a new DRS in which the anaphoric elements still await resolution. Only then does the actual processing of anaphoric elements take place. The anaphoric expressions are either linked to some previously established antecedent or, if they have enough descriptive content, accommodated at some level of representation. In order to see whether a presuppositional anaphor can be bound to some pre-established antecedent we follow up its projection line and link it to a marker that is a suitable antecedent. The marker in the A-structure encoding the anaphoric expression will be identified with the antecedent marker, which after transfer of the conditions inherits all the descriptive information associated with the pre suppositional anaphor. If no suitable antecedent for the anaphor can be found, it will be accommodated. Accommodation will generally take place at the highest accessible level such that the resulting structure does not violate general constraints on (un)binding and acceptability. Once we have resolved all anaphoric expressions, we end up with a proper DRS to which the standard rules of semantic interpretation apply. The task which faces us then is to specify under what conditions the anaphoric expressions coded in the A-structures of a DRS can be resolved with respect to a certain target. In the proposal put forward here this simply comes down to giving the principles which constrain binding and accommodation. We can look at this in either of two ways. The first way is rather procedural and leads to a backtracking mechanism. The second way is more declarative. It sorts out possible resolutions by filtering them through a series of successive constramts. In the first process, anaphora resolution proceeds as follows. Beginning with the most deeply embedded anaphor, anaphoric material will climb up along projection lines until a proper binding site is found, that is, a site which contains or is compatible with the (presuppositional) anaphor. If so, we will identify the
362 Presupposition Projection as Anaphora Resolution
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markers of the A-structure with the relevant markers in the binding site and transfer the associated conditions. If we reach the root of the accessibility tree and no binding site is found, we will try to accommodate the anaphoric material, that is, we will insert the discourse marker ofA-structure and add the associated conditions. But now it might tum out that this violates the constraints on accommodation which we will discuss shortly. If so, we will go back along the anaphor's projection line and try to accommodate one level lower, repeating this procedure until a proper accommodation site is found. Next, the same procedure will be applied to the anaphoric expression which resides one level higher on the same projection line. If this procedure can be completed for all A-structures we will end up with a full DRS. If no binding or accommodation site can be found, the construction algorithm will come to an end and the whole discourse will lack an interpretation, just as would happen with sentences containing pronouns, which cannot be linked to a suitable antecedent. The process just sketched automatically gives binding priority over accom modation. Both binding and accommodation can only cake place at accessible positions. But binding involves a search upwards along the anaphor's projection line and will thus normally take place at the nearest accessible position. Accommodation, on the other hand, goes downwards. If accommodation at top level is blocked due to an imminent violation ofwell-formedness conditions on discourse structures, the next attempt at accommodation will be made one level lower. In the process of resolving a presuppositional anaphor we thus trace a loop along the anaphor's projection line. Implementing this strategy, though possible, gives rise to some technical problems and leads to further complications when pragmatic factors interfere during an attempt at resolution. The first obstacle we encounter is that the constraints on contextual acceptability, which are crucial co determine whether a presuppositional expression can be accommodated, are essentially dependent on logical properties. These, however, are only defined for full DRSs. Remember that a DRS may contain any number of unresolved anaphors. This obviously leads to problems when we check for logical properties like consistency or entailment. For interpretation and determination ofthese logical properties can only ensue after full resolution of all anaphoric expressions. Except for the simplest cases, implementing this strategy will thus involve a substantial amount of backtracking. In this paper I will explore a simpler alternative. Note that a DRS can only contain a finite number of anaphoric expressions each of which can only be resolved at a limited number of sites along its projection line. The strategy I envisage is to collect the possible solutions and sort these out by applying a series of successive constraints. These will sort out the possible solutions to a number of admissible ones. If this successive sorting out does not yield a single
Rob A. van der Sandt 363
( 5 I ) A man loves his wife. (52) If a man loves his wife, she is happy. (53) Every man loves his wife. (54) If every man would love his wife, women would be happier. (55) Every man who loves his wife will be rewarded. (56) Nobody loves his mother in law. In section I I noted that such sentences present problems for the view that presuppositions are referring expressions, since they contain free variables
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solution, further discourse constraints will define a preference order over the resulting set. This procedure minimizes the need for backtracking and will still yield a preferred interpretation. It has moreover the conceptual advantage of separating absolute constraints like conditions on variable binding and accept ability from discourse properties like recency or salience and the contribution of non-linguistic knowledge in determining a suitable antecedent.28 The picture as I will present it here is as follows. For an unresolved DRS the accessibility constraints and the constraints on binding allow a number of possible resolutions. Resolution of all anaphoric expressions in accordance with these constraints determines a proper DRS, which is subject to the standard rules of interpretation. Let us call this the set of logically possible interpretations . However, only a part of the possible interpretations may respect the restrictions on acceptability. Acceptability will thus sort out this set to a smaller one which we call the set of admissible interpretations . But, as I said, the set determined by the previous constraints may still not single out a unique interpretation, as happens in (27}-(30). I will furthermore assume that the resulting set is ranked by a preference order, which is determined by full versus partial matching, relative distance along its projection line, discourse principles, and non linguistic knowledge. These factors then finally single out the preferred inter pretation . A full discussion of the discourse factors that co-determine the choice of the preferred interpretation if the resolver leaves open a number of logical possibilities is beyond the scope of this paper. In the following I will limit myself to the constraints on binding and acceptability and make some short remarks on the latter constraints when we come back to the matter of 'prag matic' ambiguity. The accessibility constraint has been discussed in the previous section. Thus in order to pin down what admissible interpretations are I will first discuss the constraints on binding. Then I will show how the acceptability constraints further sort out the possible interpretations to the set of admissible inter pretations. The constraints on binding involve the interaction between quantified expressions and presuppositional anaphors. Consider the following sentences:
364 Presupposition Projection as Anaphora Resolution
(57) Every man who has a wife loves her. (58) If every man who has a wife would love her, women would be happier. Similarly I want for (56) the interpretation that no man who has a mother in law loves her. The source of the problem is clear. Consider (5 3). The presuppositional expression his wife contains another anaphor which depends on the quantified NP every man . Thus projection of the full expression to top level would cut the link between the pronoun and its binder, thus creating a free variable in a condition which cannot access its antecedent any more. It was to prevent this that we set up the hierarchical ordering of A-structures and required that in case of multiple embedding the deepest embedded anaphor has to be processed first. The solution is then simple. When we start processing the embedder, the embedded anaphor will already be resolved. The embedder thus cannot be projected any higher along its projection line without creating a free variable in a condition which cannot be bound by its intended antecedent. Note that it would be wrong to insert a variable at top level and to interpret it by means of its existential or universal closure. Such a procedure would, in fact, yield exactly the same predictions as emerge on Heim's or Cooper's account. The correct way to proceed is to start processing with the deepest embedded anaphor and to put a natural ban on the unbinding of anaphoric links already established. This procedure intercepts an embedding anaphor at the place where an embedded expression is bound, and prevents the resolver from accommodating the embedding expression any higher along its projection line. The definition requires the notion of a discourse marker occurring free in some condition. Free discourse markers A discourse marker u is free in a condition C of a DRS K just in case u occurs in C and u f. Acc(K).
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which are bound externally by a quantified NP. If we derive for (5 I ) the presup position that a man has a wife and accommodate this presupposition into the main DRS, we end up with the awkward prediction that some man has a wife and a possibly different one loves her. With respect to (5 3), we would get an equally bad prediction. This sentence would presuppose that every man has a wife. This is in fact the presupposition that Heim's theory predicts for (5 I ) and (5 3), and, even worse also for (5 5) and (56).29 When we embed these sentences it is easy to see that both predictions are wrong. Neither does the truth of (52) require that a man has a wife, nor does (56) require that every man has a wife. The current theory predicts that no sentence which contains an open phrase in which a variable is bound by an outside quantifier can ever have a presuppos ing reading. Instead (53) will come out as equivalent with (57) and (54) as equivalent with (58):
Rob A. van der Sandr 365
Possible resolutions Let Ko be a DRS, � an element of the A-strucrure of some sub-DRS ofKo and (Ko, . . . �) its projection line. Resolution of� with respect to some (sub)DRS � is subject to the following constraints: (i) (ii) (iii) (iv)
� is on �·s projection line. A�) is empty. There is no � on �·s projection line such that A(K;.) is non-empty. No condition in � contains a variable which occurs free.
Clause (i) e1:1codes the basic requirement of accessibility; (ii) guarantees that no anaphoric expression will be processed until all embedded anaphors have been resolved; (iii) imposes a left-right ordering on the resolution process-it guarantees that the resolver will not find any unresolved anaphor on its path when processing an anaphoric expression. Finally, (iv) encodes the central constraint: no attempt at resolution may result in unbinding a variable. Example (59) illustrates how an embedded anaphor may intercept its embedder. The construction rules yield the inner box of Ko as the initial representation for (51 ). Assuming that the pronoun is coreferential with the subject NP Ko transforms in Ko' by identifying z with x. When we start processing the remaining A-strucrure we will not find a proper binding site. Thus accommodation will ensue. Clause (iv) ensures that the highest place this anaphoric expression can be accommodated is sub-DRS where it originates. This correctly yields Ko". Note that the same prediction ensues for (56). The resulting DRS only differs in that the embedded box is prefixed with a negation operator. Since the relevant anaphoric expression can never escape the box
(59) Ko l----
Ko'
r-----
X man
(x)
man
love (x,y)
[�---_-_-:_���-:_-_-_] : wife (y)
: ;
1 pass (z,y)
I I
r - - - - -.
I I
1-:_ _ _ _ _ .J
L1::.: :::.-� - -
__
J
(x)
love (x,y)
[!-=--= =--=--:_-_-_--=-.=) : wife (y) : pass (x.y)
: :' �
I r- ---, I L _ _ _ _ .J
L�---..: ::�
_ ___
J
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Any DRS which has been resolved in accordance with these constraints is a possible resolution. The standard interpretation rules apply to it.
366
Presupposition Projection as Anaphora Resolution Kon .----x,y man (x) love (x,y)
(y) poss (x,y) ,.. - -- - - - - - - ..., 1----- -------l wife
·
: 1- - - - - -1 I
I
r - - - - ..,
I I
:
L�:.::----�----J ..
(6o)
---.. K0 ..X
love (x,y)
man (x)
�
r - - - - - - - - - ..., I I Y t- - - - - - - - - -;
: wije (y)
I poss (z.y)
I ,.. --..,
I I Z
I
���-�
: I I I
_..!
accommodation sites, the antecedent- and the consequent-box. Given the first option, the anaphoric material will be transferred to the antecedent of the conditional, yielding Ku' ( (6 I )). The second possibility will leave the anaphoric (6 1 )
K0'
1;:::==== ::: ==;-----;:;:::== ::::; ====� x,y love (x ,y)
man (x)
(y) poss (x,y) wife
r - - - - --- ---, 1- - - - - - - - - - .... I I I I .- ---, I I I I I L- - -' I L -- - - - - - - - .J
material at the posmon where it ongmates. (53) thus allows two possible resolutions. But given the preference to accommodate as highly as possible, the first option which yields the interpretation given in (57) is the preferred one. Accessibility and the conditions on binding determine the set of possible
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where it originates, it is predicted that no sentence which contains (5 I ) or (56) as a component part can ever be presupposing. (53) differs in that it allows two possible solutions. The initial representation can be seen in (6o). After processing the pronoun we end up with two possible
Rob A. van der Sandt 367
interpretations of a sentence in a given discourse. But as we said before, not all possible interpretations are admissible. In previous work I have argued at length that contextual acceptability is the crucial constraint governing accommoda tion. The view put forward there is that a presupposition can never be accommodated into the context of utterance in case this would violate the con straints on contextual acceptability.30 On the current account this principle still holds. However, since our DRT implementation also allows accommodation on subordinate levels we will have to revise our formulation so as to make it applicable to subordinate levels of representation. For the extensional fragment presented here the following constraints on acceptability suffice.
(i) K1' is informative with respect to �. that is � does not entail K1'. (ii) Resolving � to K1' maintains consistency. (iii) Resolving � to K1' does not give rise to a structure in which (a) some subordinate DRS � is entailed by the DRSs which are superordinate to it, (b) -.K, is entailed by the DRSs which are superordinate to it. The first two clauses encode Stalnaker's (1978) conditions on assertions. The requirement of consistency requires no further discussion. Informativeness arises from independently motivated conversational principles. The main purpose of discourse is to convey information, and information is conveyed relative to background information, which is already part of the current DRS. In DRT an assertion is thus incremental in the following sense. After an asser tion has been made, its content will be added to the DRS under construction. The informational status of its content thereby changes. It will become part of the DRS from then on and can function as an antecedent for coming anaphoric expressions. Now the point of an assertion is to introduce new information. Its utterance would be superfluous in a discourse which already contained or entailed its content. Processing such an utterance would result in a trivial mapping of the current DRS on to itself no information would be added. Thus the informativeness constraint accounts, among other things, for the unaccept ability resulting from iteration of sentences which have been uttered before or which contain information which has already been established in the current DRS. The following pieces of discourse are unacceptable precisely because they violate this condition.
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Admissible resolutions Let � be the incoming DRS, K1 the merge of a DRS with � and K1' a possible resolution of K1• The resolution of � to K1' is subject to the following conditions in order to be admissible:
368 Presupposition Projection as Anaphora Resolution
(62a) John has a dog. John has a dog. John has a dog. (62b) John managed to buy a dog. John has a dog. (62c) John has a dog. Either he has a dog or he has a cat. Clause (iii) requires that the principles of informativeness and efficiency carry over to subordinate DRSs with respect to the information established in their local context, that is, the (sub) DRSs they are subordinate to.3 1 In incremental terms one could say that no provisional update may lead to inconsistency and each provisional update should at least provide some new information.32 It marks, inter alia , the following pieces of discourse as unacceptable:
Acceptability constrains resolution. In fact it sorts out the set of possible resolutions to a smaller set of admissible ones. The underlying reason is obvious. When processing a sentence, a cooperative hearer will take care that the resulting strucrure is acceptable and coherent. The following two sentences illustrate this: (64a) Either John has no donkey or his donkey is eating quietly in the stable. (64b) Either John is out of hay or his donkey is eating quietly in the stable. Note that the first sentence can never have a presupposing reading, and it is easy to see why. The contruction mechanism yields K 1 ( (65) ). Resolution proceeds X
(6 s )
John (x) z
z eating (z)
...,
donkey (z)
·--- ---�
y donkey (y) poss (x,y)
,.. - - - - -.....,
1-!- -----1 LJ.£hn (x) __
J
v
1- - - - - - - --t t donke (z) t y t I
(w,z) I' r-poss w - - - -, 1 1'" ., t
_ __ _
I �---- - 1 I
t
I
I II t
y donkey (y) -,
poss (x,y)
r- - - - - - --,
I1- - - - - --l I L ....J
poss (x,z) eating (z)
v
t= = =:::.::-=i :.
I f-----; -�
I _ __ ...J .. _
I
I I .J
in the same way as before. First, the A-strucrure in the first disjunct will be resolved which results in accommodation of the proper name at top level. Then the pronoun will be bound to the marker which has just been established. The interesting part lies in the processing of the A-strucrure for the donkey. The accessibiliry constraint forbids binding of the anaphoric expression in the first disjunct. The only possible solutions are accommodation at top level or one level lower along its projection line, i.e. the box where it originates. Both are possible resolutions in the sense that neither violates the constraints on binding. But
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(6 3a) John has a dog. If he has a dog, he has a cat. (63b) John has a dog. If he has a cat, he has no dog. (63c) John has a no dog. Either he has a dog or he has a cat.
Rob A. van der Sandt 369
only accommodation in the subordinate box is admissible, since accom modation at top level would violate clause (iii) of the acceptability constraint. It would, in effect, represent the following unacceptable discourse: (66) John has a donkey. Either he has no donkey or his donkey is eating quietly in the stable. The resulting structure is K' which is admissible and correctly represents the meaning of (64a) and its paraphrase (67): (67) Either John has no donkey or he has one and it is eating quietly in the stable.
(68) Either the king or the president of france opened the exhibition. (69) IfJohn is married, his wife is happy. Assuming that countries cannot have both monarchs and presidents, (68) admits only one solution. Given our discussion thus far the reason will be clear. Accommodation of both the king and the president at top level would violate the consistency requirement. Accommodation of only one of the presupposi tional expressions is not allowed either. Although this would not result in an inconsistent DRS, it would yield a sub DRS being inconsistent with the superordinate one, thus violating clause (iiib). It will also be clear why (69) can never have a presupposing reading. Accommodation of the presuppositional anaphor at the top level would enduce an entailment relation between the main DRS and the antecedent of the conditional, thus violating (iiia). In section 3, I pointed out that on an anaphoric account of presupposition we would expect a genuine ambiguity in presuppositional expressions. We already met some such examples at the end of section 2 where I discussed the data that Soames (1 979) adduced against the implicature-cancelling account. I will conclude this paper with two types of cases. The first one allows both binding and accommodation. In the second one the ambiguity derives from the possibility to accommodate at different levels of representation. Consider first (70): (7o) IfJohn has sons, his children are happy.
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Compare this result with the predictions with respect to (64b). Here the first disjunct is logically independent of the presuppositional expression in the second one. Accommodation can thus take place at top level without violating the acceptability constraint, and given the general preference for accommoda tion at top level it is predicted that the preferred reading of this sentence is the presupposmg one. I will give here only two more examples to show how acceptability constrains the resolution of presuppositional anaphors. Many more can be found in the literature on presupposition projection.
3 70 Presupposition Projection as Anaphora Resolution
The initial processing of the DRS constructed for this sentence yields Ko ( (7 1 ) ). X
John (x)
z
happy (Z)
r - - - - - - -, ·
y sons (Y) poss (x,Y)
�
1- - - - - - - '1 1 child (l) 1 1 pass (w,Z) I
: rl; -, �-- -1 I L=:..--� - - - .J
:
I
•
(72)
f-x
--------------1 John (x)
z
happy (Z)
,- - - - - - - - - ,
y
sons (Y) poss (x,Y)
_...
1-- - - - - - - -4 I chi/d (l}
I : I I
poss (w.Z)
ra-;- -1 1-- --j
: : I
x,Z John (x) child (Z)
happy
poss (x,Z)
1- - - - - - - --l
y
sons (Y) poss (x,Y)
L:.::�� - - - .-1
(Z)
r-------,
�
I
l
r - - -,
1- - --i
I L '- - - -'
-
I I I I I _.J
The second case (73) finally gives an example where a genuine ambiguity arises our of different accommodation possibilities. (7 3)
IfJohn has grandchildren, his children are
happy.
ThoughJohn's having grandchildren entails that he has children, it will be clear that the grandchildren in the antecedent clause do not provide an anaphoric antecedent for the children in the consequent. Again the entailment relation is one-sided. Accommodation at top level now yields the presupposing reading. The preference for accommodation at the top of the projection line predicts
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Notice that the antecedent entails the presuppositional expressions in the consequent and note furthermore that the lexical material matches only partially. We thus may, but do not have to identify the marker for the sons in the antece dent with the presuppositional anaphor in the consequent. Further processing thus yields (at least) two readings.33 Anaphoric binding absorbs the presupposi tional expression in the antecedent and thus gives a non-presuppositional inter pretation. However, the constraints given above also allow accommodation of the presuppositional expression at top level. Since the entailment relation between the antecedent and the presuppositional expression is only one-sided, accommodation of the presuppositional expression at top level will not yield a structure in which the main DRS entails a subordinate one. The resulting structure is K which represents the reading thatJohn has children and if he lias sons (or, if there are sons among them), (all of) his children are happy ( (72) ).
Rob A. van der Sandt 37I
that this reading is, ceteris paribus , the preferred one. Note that this also predicts the possibility of pronominal take-up as (74) illustrates: (74) If John has grandchildren, his children are happy. They wanted to have offspring long ago. The second possibility is accommodation in the antecedent. This gives the non presupposirional reading which states that ifJohn has grandchildren and (thus) children, his children will be happy. Acknowledgements
ROB A. VAN DER SANDT Filosoftsch lnstituut Universiteit Nijmegen Postbus 9 1 o8 65 00 HK Nijmegen The Netherlands
N OTE S I Benson Mates (I973) points out that (i) descriptions containing open descriptive phrases present problems for a theory which analyses presuppositional expres sions as referring expressions and (ii) these descriptions can be handled by Russell's theory. The basic argument is that the theory of descriptions applies to all expressions which can be represented by means of his description operator which allows us to eliminate such descriptions from all contexts in which they might occur. Mates takes this as an argument for rhe superiority of a Russellian analysis over a presuppositional one. Mates's paper contains a number of other obser vations rhar have nor been discussed in rhe literature on presupposition and which are relevant ro rhe purposes of this paper. See also Neale (I 990) for further
discussion of the relevance of open descriptions for anaphora theory. 2 See van Fraassen (I 969) for a formaliza tion of this account. 3 The idea of restoring the inference view on presupposition by adopting of a non monronic logic is found in Mercer (I 992) However, Mercer does not rake rhe classic semantic account as a starring point, but reinterprets and elaborates Gazdar's ( I979) pragmatic theory in rerms of Reiter's (I 98o) default logic. He shows in particular that once we extend the notion of logical inference so as to include non monotonic ones a number of phenomena which seem to elude a logical treatment can be integrated in the logical paradigm. Wirh respect to the orthodox semantic notion of presupposition no such attempt has been undertaken up to now. .
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The basic idea underlying this paper derives from work which was done from I987 to I 989 on a Huygens fellowship granted by the Dutch Organization for Pure Research (NWO). The initial idea is found in a preliminary form in van der Sandt (I987/9) and in van der Sandt and Geurts (I99I). I owe thanks to many people who commented on earlier presentations of the ideas contained in this paper. Here I want to mention in particular Bart Geurts and Henk Zeevat, who commented on earlier versions of this paper.
3 72 Presupposition Projection as Anaphora Resolution 4-
(i) It is possible that a thief took my Mac. Scalar implicature It is not necessary that he took my Mac. Note that it would be wrong to compute the implicature that it is not necessary that a thief took my Mac. The same holds for the following generalized variant: (ii) A: L am out of gas. B: There is a gasoline station around the corner. Generalized conversational implicature It is open . The main difference is the following. In case presuppositions are not already there they will be accommodated and the material thus accommodated may bind the anaphoric expression in the content or implicature expression. In the case of implicatures both the presupposition and the content expression may provide the antecedent for the anaphor in the impli cature expression. 8 I adopt the common view that possessive constructions like John's child or his child are analysed as complex definite descrip tions. 9 Karttunen & Peters point out that (9a) sounds odd precisely because it pre supposes the falsehood that it was diffi cult for the actual successor of George V to succeed him to the throne. However, the presupposition computed is trivially true: for almost everyone except the actual successor it would have been extremely difficult to succeed George V. 10 Webber (I 978) is a representative ex ample. I I 'Generalizing from example (4-) [i.e. The cat is at the door], I am proposing that the present theory be augmented by the following assumption: Definites contrast with indefinites in yet another respect, aside from their different behaviour with respect to Quantifier Indexing and the Novelty Conditions: In definites, the descriptive content of the NP is pre-
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The scheme given here is roughly the picture Stalnaker sketched in a series of papers starring in the early 1 970s (see in particular 1 970, 1974-, 1978). An. explicit statement is found in the appendix of Stalnaker (1 976), where he makes a formal distinction between the notion of semantic and pragmatic interpretation and where the notion of pragmatic inter pretation is made dependent on a prior determination of the semantic content. I am, however, reluctant to attribute the view as I sketch and criticize it here to Stalnaker in its full generality. For one thing, Stalnaker never explicitly defended the separation of semantic and pragmatic content in the way it is found in, for example, Gazdar ( 1979), Karttunen & Peters ( 1 979) and-based on Stalnaker's scheme-in van der Sandt ( 1 988). Heim (1992) treats Stalnaker's writings as a precursor of current theories of dynamic semantics, and the latter need not be vulnerable to the arguments given here with respect to the strict semantics/ pragmatics dichotomy found in the writings just mentione& The mistaken assumption that logical operators always take scope over pre suppositional expressions and that the presupposition can be derived separately is found, among others, in Gazdar ( I 979) and van der Sandt (I988). 6 A further problem is that it is rather unclear how scope generalizes to kinds of presupposition inducers other than defi nite descriptions and constructions which can be analysed as such. 7 Note that the above arguments don't just hold for presuppositions, but apply to pragmatic information in general. It turns out that all pragmatic information may entertain anaphoric links to the content expression they are associated with. While presupposirional expressions may provide antecedents for anaphoric expressions in the content expression, implicatures may be anaphorically linked to both. Consider.
Rob A. van der Sandt 373
I2
I3
Is
I6
I7
say something that will be unacceptable for lack of a required presupposition. Say something that requires a missing pre supposition, and straightaway that pre su pposmon springs into existence, making what you said acceptable after all . . . call it the rule of accommodation for presupposition . If at rime t something is said that requires presupposition P to be accept able, and if P is not presupposed just before t, then-ceteris paribus and within certain limits-presupposition P comes into existence at t.' (Lewis I979= 340) I 8 A general requirement for accommoda tion is that the sentence uttered should contain some conventional mark or some feature of interpretation which requires a readjustment of contextual parameters for its utterance to be felicitous. Accom modation will then have the following effect If a relevant contextual parameter does not have an appropriate value, the hearer will infer it and adjust the context so as to make the utterance felicitous after all. It will be clear that in the absence of any substantial constraints the whole notion of accommodation would be vacuous. Heim requires just consistency. See section 4 for a discussion of con textual acceptability as a constraint on accommodation. I 9 Accommodation of the. trigger instead of the sentential presupposition is the option taken by Zeevat in his reconstruction of Heim's theory in update semantics. Irene Heim (p.c.) informed me that she is indeed committed to the prediction that all else being equal, the preferred accom modation for a sentence like (26a) is the global accommodation of If John made coffee, he has a wifo. She suggests, however, that the global/local hierarchy is not the only (or even the most important} factor to determine accommodation. Factors like (un)controversiality and having ade quate grounds for believing the propo sition in question might play an equally
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I4
supposed, whereas in indefinites it is (merely} asserted' (Heim I 982: 23 3). 'Felicity conditions of any sort give rise to a problem analogous to the famous projection problem for presuppositions' (Heim I 982: 320). Heim (p.c.) pointed out that the views of her thesis are only partially compatible with her I 98 3 approach to presupposition projection. A full comparison between the two views and the account presented here would take me too far afield and has to await another paper. A comparison and elaboration in terms of update semantics ofHeim's ( I 983) account and the account given here is given in Zeevat (this volume). For yet a further elaboration of an appli cation of her account to attitude contexts, see Heim (I992). Possible exceptions are Fillmore's lexical presuppositions that are triggered by such lexical items as bachelor which may perhaps be better tteated as sortal restric tions on these predicates. They do, how ever, display the same type of projection behaviour as the above-mentioned trig gers. Zeevat (I99 I , this volume) points out that they differ with respect to their behaviour in attitude contexts. I refer to Zeevat's paper where the same phenome non is observed with respect to facrives. Such a procedure to exttact the descrip tive material from their lexical or syntac tic sources is either assumed or given for all theories of presupposition projection. Gazdar (I979) calls them pre-supposi tions, Karttunen & Peters (I 979) conven tional implicatures, van der Sandt (I 988} elementary presupposmons. Seuren (I98S} distinguishes between precondi tions and satisfaction conditions for pre dicates, where the preconditions code the presupposirional properties. 'Some things might be said to require suitable presuppositions. They are accept able if the required presuppositions are present; not otherwise. . . . Be that as it may, it's not as easy as you might think to
374 Presupposition Projection as Anaphora Resolution
(i) If John has an ORIENTAL girlfriend, his girlfriend won't be happy. (ii) IfJohn MURDERED his wife, he will be glad that she is dead.
(iii) If someone AT THE CONFERENCE solved the pr.oblem it was Julius who solved it.
·
In view of this fact Henk Zeevat (p.c.) objected to this picture and claimed that the presupposing reading comes about as a result of projecting a presupposition rriggered by the intonation pattern in the antecedent. This requires the assumption that the (a)-sentences trigger the putative presuppositions in the (b)-sentences: (iva) John MURDERED his wife (ivb) John's wife is dead (va) Someone AT THE CONFERENCE solved the problem (vb) Someone solved the problem. I am far from sure that intonation patterns induce resolution presupposi tions in the sense of this paper, but even if they do this argument certainly cannot be upheld for the second example. Accord ing to the standard view its intonation patterns would induce the presupposition that John did something to his wife, not that she is dead. It is easy to check that the latter is not a presupposition of (iva). Modal embedding or questioning (iva) gives no suggestion whatsoever as to the truth of the putatative presupposition: (vi) Did John MURDER his wife? (vii) It is possible that John MURDERED his wife. 24 A formulation of the actual construction procedure is beyond the scope of this paper. The notion of sentence-DRS derives from Asher (1 989) and Asher & Wada (1 988). Alternative bottom-up versions are, among others, found in Reyle (1985) and Zeevat (1 989); van der Sandt & Geurts (1991) contains a con strUction algorithm for sDRSs in a CUG style grammar incorporating an explicit coding of presuppositional anaphors. 25 See van der Sandt & Geurts (1991) for details. 26 We do not therefore introduce proper names at the highest level of representa-
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important role. Similar defences which shift the burden to a (Gricean) prag matics are found in Karttunen & Peters {1979), and Soames ( 1982). I will not go into this question here but refer to the authors mentioned and the criticism of this view in Gazdar (1 979) and van der Sandt (1988). · 20 I assume some coding of the· fact that someone who has grandchildren has children. For the present argument it is irrelevant whether this is taken to be world knowledge or results from the lexi cal content ofgrandchildren . David Beaver (p.c.) objected to this example on the grounds that someone having grandchil dren entails having at least one child and not having children in general. Note first that this does not greatly improve the predictions of the satisfaction view. Instead of the presupposition that John · has children we still get the weaker 'If John has gtiuidchildren, he has children'. Note furthermore that it is easy to adapt this example to circumvent his difficulty. Firstly, the more grandchildren someone has the less plausible it is that he has only one child. But Jfjohn has 1 oo grandchildren, his children must be veryfertile suggests even more strongly that John has children. The same happens if we adapt our example so as to exclude the possibility that they all spring from the same parent, which excludes the possibility that he has only one child: IfJohn has grandchildren from different parents, his children will compare their qualities. ' 21 For me the non-presuppositional reading is strongly preferred for this particular example and so it was for most people whose intuitions I asked. 22 See van der Sandt {1 988: 1 5 8-6o). 2 3 Contrastive stress partially disambigu ates:
Rob A. van der Sandt 375
28 29
30 31
32
making the embedding function depen dent on the status of the relevant markers. See Asher & Wada (1988) for a similar approach to pronoun resolution. Cooper (198 3) predicts an existential presupposition for (s 1 ). For the other cases his predictions coincide with Heim's. See van der Sandt ( 1988). The notion of local context envisaged here is just the DRT counterpart of Karttunen's and Heim's notion. It is, however, important that this notion plays a very different role in this theory than in Karttunen's or Heim's. Contrary to Karrunnen's and Heim's theory, it is not required that a presuppositional expres sion originating in a subsenrential constituent be satisfied by its local con text. In the current theory the local con text has the function of constraining the process of accommodation. The require ment put forward here is not that a pre supposition should be entailed by its local context, but merely that it should be accommodable without violating the acceptability requirements. Note that a local violation of consistency or informativeness need not give rise to uninformativeness of the whole utterance processed. It often signals that the infor mation carried by the utterance is con veyed in an unnecessarily redundant and complex way. Suppose, for example that q; has already been established in the incoming DRS. In this situation the utterance of 'If q; then 1/J ' is clearly informative since it tells us that 1/J is the case. However, the same information could have been conveyed in a shorter and thus more efficient way simply by staring 1/J. Or suppose that we want to convey the information that x when 1/1 is already established. 'If not 1/J, then x or '1/1 V x ' are rwo candidates. But again, the mere utterance of x would be a more straightforward and efficient way. Effi ciency and informativeness are thus distinct notions. If 1/J is contextually � ·
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rion as is standard in DRT to account for the fact that proper names normally escape any depth of embedding. Nor are they considered to be rigid, which would force us to treat them as external anchors. I will here ignore Kripke's (1 972) rather forceful arguments and not go into the question whether proper names are directly referential in the same sense indexicals are. Instead we treat them, as is common in presupposition theory, on a par with other presupposition inducers. When we come to the treatment of the resolution algorithm we will see that their tendency to accommodate at the highest structural level can easily be explained by their relative lack of descriptive content. This feature makes them insensitive to the constraints on accommodation, which might otherwise push them back to subordinate levels of representation. The way the resolution mechanism is set up will nearly always give proper names the widest scope possible. This has the advantage that we do not need a stipula tion to the effect that discourse markers for proper names should always be inserted at top level, as Kamp (1981) requires. 2 7 I have to put in one caveat here. We need the additional constraint that no marker should occur free in a condition. We will discuss this constraint in detail in the next section. In this paper I furthermore assume the standard extensional seman tics for the DRS language, which is set out well in the literature; see e.g. Kamp ( 1 98 1 ) o r Kamp & Reyle (forthcoming). One consequence is that when a 'failing' presupposition is accommodated the resulting discourse is false, and not undefined as Frege or Strawson would have it. Undefinedness will only ensue when a presupposition can neither be bound nor accommodated so that the construction algorithm will come to a halt. The Fregeau institution can, how ever, be restored by explicitly marking accommodated material as such and
376
33
Presupposition Projection as Anaphora Resolution
given, an urrerance of 'if cp then !p ' may be informative, bur the very same utter ance would simultaneously be inefficient, since there is a simpler way of getting this message across, namely the mere utter ance of !p. A further reading which I ignore here
results from accommodating rhe presup positional expression in the antecedent of the conditional. This gives rhe inter pretation that if he has children, part of them are sons and that the sons are happy. See van Deemter ( 1 991 ) for a different view of how this reading comes about.
RE F E RE N C E S
272-309.
Cooper, R. ( 1 9 8 3), Quantification and Syntactic Theory, Reidel, Dordrecht. Deemter, K. van ( 1 99 1 ), 'Towards a general ization of anaphora', journal ofSemantics 9, 1: 27- S I . Fraassen, B. van ( 1969), 'Presuppositions, supervaluations and free logic', in K. · Lambert (ed.), The Logical Way of Doing Things , Yale University Press, New Haven, Conn., 67-9 1. Gazdar, G. ( 1979), Pragmatics: Implicature, Presupposition, and Logical Form , Academic Press, New York. Heim, I. ( 1 982), 'The semantics of definite and indefinite noun phrases', Ph.D. thesis, University of Massachusetts, Amherst. Heim, I. ( 1 9 8 3), 'On the projection problem for presuppositions', Proceedings ofthe West Coast Conference on Formal Linguistics, :z.: 144-26. Reprinted in S. Davis (ed.) ( 1991 ), Pragmatics, Oxford University Press, Oxford, 3 97-40;. Heim, I. ( 1 992), 'Presupposition projection and the semantics of attitude verbs', Jour nal ofSemantics , 9, 3: 1 8 3-22 1 . Kamp, H. ( 1 9 8 1 ), 'A theory of rruth and semantic representation', in J. A G. Groe nendijk, T. M. V. Janssen & M. B. J.
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Asher, N . ( 1 989), 'Absrract objects, semantics and anaphora', MS, Department of Philo sophy and Center for Cognitive Science, University of Texas, Austin. Asher, N. & Wada, H. ( 1988), 'A com putational account of syntactic, semantic and discourse principles for anaphora resolution', journal of Semantics , 6, 3/4:
Rob A. van der Sandt 377 Soames, S. ( 1 989), 'Presupposition', in D. Gabbay & F. Guenthner (eds), Handbook of Philosophical Lagic , Volume W, Reidel, Dordrecht, 5 5 2-616. Stalnaker, R C. ( 1 970), 'Pragmatics', Synthese , 2.2.: 272-89. Reprinted in D. Davidson & G. Harman (eds), ( 1 972), Semantics ofNatural Language , Reidel, Dordrecht, 38-97. Stalnaker, R C. ( 1 973). 'Presuppositions', journal oJPhilosophical Lagic, 2., 4: 447-57. Stalnaker, R C. ( 1 974), 'Pragmatic presup positions', in M. K. Munitz & P. K. Unger (eds), Semantics and Philosophy , New York University Press, New York, I 97-2 I 3· Stalnaker, R C. ( 1 976), 'Indicative condition als', in A. Kasher (ed.), Language in Focus: Foundations Methods and Systems , Reidel, Dordrecht, 1 79-96. Stalnaker, R C. ( 1 978), 'Assertion', in P. Cole (ed.), Syntax and Semantics g: Pragmatics , Academic Press, New York. 3 r 5-32. Webber, A. ( 1 978), A Formal Approach to Discourse Anaphora , Bole, Beranek & Newman, Report 376 1 , Boston, Mass. Zeevat, H. ( 1 989). 'A compositional approach to discourse representation theory', Lin guistics and Philosophy , n: 95-1 3 1 . Zeevat, H . ( 1 99 1 ), 'Aspects of discourse semantics and unification grammar', Ph.D. thesis, University of Amsterdam, Amster dam. Zeevac, H. ( 1 992), 'Presupposition and accommodation in update semantics', this volume.
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Dinneen (eds), Syntax and Semantics 1 1 : Presupposition , Academic Press, New York, 37 I-88. Mates, B. ( I 97 3), 'Descriptions and reference', Foundations oJLanguage , 10, 3: 409-I 8. Mercer, R ( I992), 'Default logic and presup position', journal OJSemantics , 9, 3: 223-50. Neale, S. ( 1 990), Descriptions , MIT Press, Cambridge, Mass. Reiter, R ( 1980), 'A logic for default reason ing', Art!ficial lntelligence , 13: 8 r-1 32. Reyle, U. ( I985 ), 'Grammatical functions, quantification and discourse referents', I]CAl 9: 829-8 3 r . Sandt, R A . van der ( 1 98 8), Context and Pre supposition , Croom Helm, London. Sandt, R A. van der ( 1 989), 'Presupposition and discourse strucrure', in R Bartsch, J. van Benthem & P. van Emde Boas (eds), Semantics and Contextual Expression , Foris, Dordrecht, 287-94. Sandt, R A. van der & Geurts, B. ( 199 1 ), 'Presupposition, anaphora, and lexical content', in 0. Herzog & C.-R Rollinger (eds), Text Understanding in LiLOG , Springer, Berlin, 259-96. Seuren, P. A. M. ( 1985), Discourse Semantics , Blackwell, Oxford. Soames, S. ( r 979), 'A projection problem for speaker presuppositions', Linguistic Inquiry , 10: 623-66. Soames, S. ( 1 982), 'How presuppositions are inherited: A solution to the projection problem', Linguistic Inquiry 13, 483-545.
© N.l.S. Foundation (1992)
journal oJ&mantics 9: 379-412
Presupposition and Accommodation in Update Semantics H E N K ZE E V A T
University ofAmsterdam
Abstract
I NTRO D UC T I O N Presuppositions in natural language put a classical puzzle to the theorist known as the projection problem. Certain expressions and constructions in natural language can give rise to inferences of the utterances in which they occur regardless of any operator (such as negation, implication, modal operators, attitude verbs) that has scope over their occurrence. Such expressions and constructions are called presupposition triggers. The implicatures to which they give rise are called presuppositions and the content of the presuppositions can be determined from the trigger and its arguments. The problem is that these inferences do not arise in all circumstances. The projection problem is the problem of describing precisely when this happens and when not. Some prime examples of triggers and their (traditional) presuppositions are given in ( 1 ).
( I ) Trigger definite descriptions names cleft pseudocleft quantifiers factives
Example the N Bill (it was NP, WH SINP) (WH S/NP, is NP) all N x regrets that S
Presupposition
3x N(x) 3x-x - bill 3x S!NP(x) 3x S/NP(x) 3x N(x) s
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A reconstruction is presented of van der Sandt's theory of presupposition in the framework of update semantics and extended to belief sentences. The resulting view is confronted with earlier approaches to presupposition (especially Heim's) in update semantics, concentrating on the approach to accommodation. It is shown in some detail that the anaphoric view of presupposition can be maintained for only a subclass of presuppositional triggers and must be given up for another class. The paper shows that the treatment of presuppositional anaphora and presuppositional accommodation is compositional with respect to stacks of information states. The brief development of the approach in section 7 shows, however, that, contrary to what one would expect, an approach in terms of stacks of information states is a powerful method in the study of DRT and other dynamic systems.
3 80 Presupposition and Accommodation in Update Semantics
Trigger subordinate clausal PPs iterative lexical
Presupposition s
3e1 (S(e1) 1\ past (e1)) male(x) 1\ adult(x)
The first modern treatment of the projection problem was provided by Karttunen, taking an essentially semantic approach. Counterexamples to Karttunen gave rise to influential approaches (Gazdar I 979; Soames I982; van der Sandt I 988) starting from pragmatic intuitions. Both Heim (I 98 I) and van der Sandt {I989) can (but need not) be described as mixed approaches, combining semantic and pragmatic elements. In van der Sandt (I989), the projection problem is handled by two concepts: anaphora resolution (a seman tic process) and presupposition accommodation (a pragmatic notion). In Heim {I98I), the relation oflogical consequence holding between the local informa tion state and a presupposition is the contribution of semantics, and accom modation is again the pragmatic element. Both approaches seem to relate well to the empirical data and also to restore the insights of Frege and Strawson in the study of presupposition, in particular their view that a presupposition is a precondition on the use of its trigger and that its falsity results in an anomaly of the utterance. Van der Sandt's later approach to presupposition is couched in the framework of Discourse Representation Theory (Kamp I 98 I ; Kamp & Reyle I 9CJO). This is a fortunate choice since the operations the theory employs and the relations that constrain presupposition resolution and accommodation have a direct visualization and also because the use of the DRS development algorithm is natural for the treatment of presupposition triggers. At the same time it obscures the relationship to the treatment of Karrrunen and Heim which were formulated in terms of update operations and opens the question to what degree the theory depends on syntactic manipulation. This paper tries to give a reformulation in terms of update semantics and in particular to answer the question as to what the meaning of accommodation is within update semantics. The reformulation will allow a comparison between van der Sandt and the update theories of presupposition. In the following I assume a version of DRT, where DRSs are defined as in (de£ I ). Here ordered pairs of DRSs formalize implications and variable labelled DRSs belief reports. De£ I : Discourse representation structure, SubDRS
A DRS A consists of two sets AnR and AeoN> where AnR is a finite set of
variables and AeoN is a finite set of conditions. A condition is either an atomic formula, the sign .l, a pair (B, C) ofDRSs, or a DRS B"' labelled with a variable x .
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·
Example when S, P S(eo) again bachelor(x)
Henk Zeevat 3 8 I
If (B , C) is a condition of A , then B and C are subDRSs of A . If Bx is a condition of A , B is a subDRS of A . If C is a subDRS of B and B is a subDRS of A , C is a subDRS of A .
(2 ) Presuppositional trigger development To develop a trigger T with a presupposition P in a subDRS B in a DRS A , we first test whether P can be found in a DRS C on the accessibility path of B in A . If so, the discourse markers in P occurring in B are replaced by the corresponding markers in C. Or else we proceed from A to B down the accessibility path and try to add P. This fails if adding P to one of the DRSs on the path leads to a conflict with the correcmess conditions on the assertion at hand or if formal demands are not satisfied. If failure occurs everywhere on the path, the development as a whole fails. This sketch draws on the definition of an accessibility path, given in (de£ 2 ), finding a presupposition (de£ 3) and adding a presupposition (de£ 4). De£ 2: Accessibility path
1 . If A is the topmost DRS, path (A ) - (A). If (C, D ) is a condition of B then path (C) - (C.path (B)) and path (D) = (C.path (C)) 3· If Bx is a condition of A then path (B ) = (B .path (A )
2.
We assume that the trigger gives a syntactic form to its presupposition, a form which needs development by the other rules of the system. To this end we open a notepad box in which we place the syntactic form of the presupposition and to which we make accessible all the material that is accessible from the site of the trigger. The notepad is discarded if the presupposition is found or when its contents have been added to some part of the DRS under development.
D
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Within this framework, van der Sandt's theory can be briefly sketched as in (2 ), a complex rule in the DRS-development algorithm. This algorithm starts by putting a syntactic analysis tree in a DRS. There is a set of rules allowing a reduction of the tree under the insertion of new discourse referents, conditions and subDRSs. The process stops when there are no longer any (semi-) syntactic objects in the DRS or its subDRSs. We assume that we have some mechanism that produces the undeveloped version (a schematic analysis tree analogous to the analysis trees provided by the syntactic theory for which the development algorithm is defined) of the presupposition triggered by the trigger we have to deal with.
3 8 2 Presupposition and Accommodation in Update Semantics
De£ 3: Finding a presupposition P in A A DRS P is found in a DRS A with respect to Z iff A and its subDRSs have discourse markers x1 . . . xn that stand in 1 - 1 correspondence with discourse Yn such that P's (simple or complex) markers of P and its subDRSs y1 x". conditions are conditions of A under the substitution ofy1 Yn for x1 • .
.
•
•
•
•
•
•
De£ 4: Adding P to A Adding P to a subDRS A of B consists of adding each of P's discourse markers to the markers ofA and of adding each of the conditions of P to the conditions ofA . Adding is undefined if a condition P contains a marker that does not have accessible discourse referent in P or A or in a DRS accessible from A . The process of looking up a presupposition is analogous to answering a question in Prolog: it instantiates variables. As a simple example, consider (3).
{3) John saw a donkey. The donkey was ill.
A donkey sets up a discourse marker x. In processing the donkey , we try to find a DRS consisting of a discourse marker y and the condition donkey (y ). This succeeds as we can substitute x for y and find both the condition and the marker in the DRS resulting from processing the first sentence. Substituting the y in y was ill completes the development of the trigger. If we consider a single discourse marker to be a proposition as well, anaphoric binding can be reduced to presupposition. The development of anaphoric pronouns can be defined by inserting a discourse marker in the matrix for the pronoun and by triggering the presupposition that this marker is a discourse marker. (Extra restrictions need to be imposed here though.) This development rule would transform the expression he sleeps into the condition sleep(x) where the proposition x would have to be resolved. The resolution to a marker y would result in a substitution transforming sleep (x) into sleep (y ). Notice that the identification of presupposed material is a purely syntactic notion. We will come back to this point later on. The last notion that is crucial to van der Sandt's theory is the notion of a
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(De£ 3 ) imposes a purely syntactic relationship between the presupposition and the DRS in which it is found. The definition can be made more semantical by recursively defining a subsumption relation, so that complex conditions need not have literal counterparts under the substitution, but have counterparts which subsume them. For our purposes, however, the current definition is good enough, as the problem disappears completely when we switch from DRSs to information states.
Henk Zeevat 383
correct assertion. An assertion is correct (van der Sandt refers to van der Sandt (I989)) ifit meets the conditions in (de£ s). De£ s: Correctness
An assertion is correct iff
it does not follow from the DRS it is developed in. It is not in contradiction with the DRS it is developed in. 3· If a DRS A contains a condition (P, Q ), ( I ) and (2) also apply to P w.r.t. A and to Q w.r.t. to the DRS obtained by merging A and P. 1.
2.
(4) It rains. It rains. It does not rain. It rains. It rains. It does not rain. It does not rain. It does not rain. It rains. If it rains, John is bringing his umbrella It does not rain. If it rains, John is bringing his umbrella. It rains. If it is Monday, it rains. It rains. If it is Monday, it does not rain. It does not rain. If it is Monday, it rains. It does not rain. If it is Monday, it does not rain. For presupposition projection, the crucial effect of correcmess is the absence of projection in case the addition of the presupposition before the assertion made the whole assertion incorrect. In van der Sandt, the other explanation of the absence of projection is the case where the content of the presupposition is found in a proper subDRS accessible from the position of the trigger. Gazdar handles these cases by means of clausal implicatures as well. I
B A S I C U P DATE SEMANT I C S
If pursued in a principled way, update semantics characterize the meaning of expressions by stating the contribution an expression makes to information
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The correcmess conditions derive from Stalnaker's assertion conditions (de£ s.I and 5.2) and are extended to some subsentential cases in (de£ 5.3). The conditions should be compared with Gazdar's definition of clausal implica tures, responsible in his system for the cancellation of presuppositions. (4) spells out some immediate consequences of (de£ s) in the form of a list of incorrect texts. The correcmess conditions are weaker than clausal implicatures, since they require for the assertion A that the common ground does not yet contain A or -.A , not that the speaker does not know these. Full clausal implicatures still require the Gricean maxims.
384 Presupposition and Accommodation in Update Semantics
Def. 6: Propositional updates
a[p] = {i e a: i F= p} a[-. cp] = a - a [cp] a[cp 1\ 1/J] = a[cp] [l/J] a[cp - lp] - a (-. (cp l\ --. ¥' )]
First order with discourse referents In order to reach first-order logic we must generalize slightly. We will consider not first-order logic but a formalism similar to DRT, where variables are treated as atomic formulas and formulas (DRSs) are built up using the connec tives:
......,, 1\, As an example, ( s) gives a formulation of the donkey sentence: �.
( s ) (x 1\ Jarmer(x) 1\ y 1\ donkey (y) 1\ own (x , y)) .... beat(x, y) For the interpretation, we start with possibilities i e I that are functions assigning appropriate values to predicate constants, variables, and individual constants. Variables and individual constants are mapped to the elements of some non-empty set U, n-place predicate constants to subsets of U". We do not require that every information index is defined for all variables or for constants. Undefinedness for constants will play no role in the sequel, however. I is again I and o the empty set. Independently of the updating process, the discourse referents are given by a recursive definition (de£ 7). De£ 7: Discourse referents 1.
DM ( " 0 then pres l: ((�0 n �10}.l: 1) e. otherwise undefined =
-
=
=
=
=
Clause (a) appeals to a notion of cfi which relabels discourse referents. cfi
=
{if: i e a)
where ig is defined by putting ig(x) i (g (x ) ) for x e dorn g , and ig(x) i (x) otherwise.' So ig is an information index like i itself with the difference-if it is used as in clause (a)-that the discourse markers of the information state of which it is an element are made identical to discourse markers of an information state further down the stack. The intersections in clause (b) and (d) push this identification down the stack. So clause (a) describes presupposition resolution, clause (b) deals with com plete global accommodation, clause (c) with skipping and clause (d) with local accommodation. The operation fails if no accommodation or resolution is possible, but does not cover the case of lexical presuppositions in their local contexts. Failure can here be ensured by demanding that the non-presupposi tional meanings of triggers entail the truth of their lexical presuppositions. This would cause information states to become inconsistent ifthe requirement is not met, and seems natural enough in most cases. =
=
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(de£ 3 1 ) follows the presupposition operation. It is based on Heim but allows skipping of intermediate contexts (when there is a reason for it) by clause c.
Henk Zeevat
403
We give some simple examples for the operation of (de£ 3 I). Consider the update of (3 I) to I : ( 3 I ) There is a king. The king sings.
(32) Th�re is no king. The king sings. Here the condition on clause (d) is not met. For (b) and (c) we need more complex examples. Consider updating I with (3 3) (33) There is a king. John believes the king sings. The trigger update leads to ( I [y ] [king(y )], I , I , [x ] [ king (x )]). Oohn's belief state still has no information after the first update.) (a) does not apply therefore. But (a) gives the result ( I [x] [king (x)] [x = y]) when applied to ( I [y] [king(y)], I [x] king(x)]). This meets the conditions in (b) so we get the result (I [y ] [king (y )], I [x ] [ king (x )] [x = y ]) and finally (34). (34) beloutj ( I [y ] [king (y)] [sing (y)], I [x] [king (x)] [x - y]) A very similar result is obtained when the addition of the king to the initial
context results by clause (d) (accommodation). For clause (c) consider the update of (35) to 1 .
(3 s ) John believes there is no king. John believes the king sings. The initial update for the trigger gives (36). (36) (I [y ] [king (y )], neg (I [x ] [ king (x )], I , I ))
(belinj composed with beloutj is an identity). Clause (a) and (b) do not apply, as the second element does not have the information that there is a king or can consistently be updated with their information. The third and last clause can, however, be updated in chat way, so that clause (c) applies, giving (3 7) by the entailment requirement for lexical presuppositions.9
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Updating I with the first clause gives I [x ] [king (x)]. Presupposing y 1\ king (y) starts by forming the complex stack (I [y ][ king (y )], I [x] [king (x )]). Clause (a) now applies for g = {) and delivers ( I [x] [king (x)] [x = y ]). The final update gives: (I [x ] [king(x )] [x = y ] [sing (y )]). Clause (d) applies when (a), (b) and (c) do not. Updating I with the second sentence of (3 I) is an example. We first get ( I [y] [king (y)], I ), and from that ( I [y ] [king(y )]), and finally ( I [y ] [ king (y )] [sing (y )]). (a) does not apply because I does not have the required information and the conditions for (b) and (c) are not met on an empty stack. Clause (e) applies to (32)
404 Presupposition and Accommodation in Update Semantics
(3 7) (y ] neg ( 1 [x) [king (x)), I , 1 [x) [king (x)]) This then finally gives ( 3 8).
De£ 32: DRS updates ass -
(merge(I0, I10).I11) neg = (I01 u {NOTI0}.I11 ) up - one = belin = ((0, 0).I ) beloutx = (I01 u [BEL.):0}.I 1 1 ) .8 = substitute markers according to g pres see van der Sandt. The fact that DRSs are formal objects obliterates some of the distinctions we were able to make. We distinguish three types of subordinate boxes by initializing them in different ways. Because of the obliteration of these distinctions, correcmess cannot be expressed directly any more. The relation can also be turned around. Then our efforts can be seen as giving a semantic interpretation of what goes on when we add material to subordinate DRSs as the DRS development algorithm instructs us to do. A semantics for these operations is not available in the bottom-up semantics that have been proposed for DRT, e.g. in Zeevat (1 989) and Stokhof & Groenendijk (1991). In the following section, a grammatical formalism will be interpreted directly in terms of the stack operations defined in the current section and atomic updates. This completes the formalization ofvan der Sandt, as after all a solution to the projection problem is in the end a grammatical and compositional treatment of the syntactic and semantic properties of pre supposition triggers. 7.2
Grammar
I will define a small fragment using a mock-Prolog without the pretence that any of this will run. We use a Prolog notation (capital letters for variables). The
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(38) beloutj[si ng (y))[y)neg ( I [x) [king (x)), I , I [y) [king (y)]) The operation ( cp) we had before, can be rendered as pres [ cp ]one. The relation with DRT must be reasonably clear by now. We render atomic updates by putting things in boxes and negations by prefixing a negation sign to the update corresponding with the scope. The operation up corresponds with opening a new box, one with opening a notepad box, belin with a belief box, etc. It is even possible to attempt to give a DRT 'semantics' for our operations, as in (de£ 32). This time the operations apply to stacks ofDRSs. (Here (0, 0) is the empty DRS and merge(A , B) = (41 u Eo. A1 , B1 ).)
Henk Zeevat 405
( 39) (NP, believes, that, S): sentence: � : beloutxT� NP:np(X):�:P S:sentence:belinx P:T. The following two clauses are presuppositional referential phrases. Names are treated as involving two presuppositions: an existential one and an anaphoric one. To treat names as anaphoric has-under the pressure of problems-become the accepted practice in computational linguistics but can be justified theoretically precisely by the different treatment that one is forced to, meet out to names in discourse representation theory: this shows that they are meant to refer to an already accessible discourse referent. Other arguments can be found in the distribution of(short) names in discourse. First, they can (in resumptions) be used in exactly the positions where pronouns and other short definites could occur. Second, they can be used referentially (but only supported by more explicit references that serve as antecedents, i.e. long versions of the name or compounds such as myfriend Doctor Watson ), also in situations where local uniqueness is not satisfied, e.g. discourses where two persons named John are around. In the case of the determiner the which still needs a noun, the behaviour is the same. The noun is put on a new empty information state (it consists of an existence statement for the new variable and the statement that the property associated with the noun holds of that new variable) which then is presupposed to obtain the semantic contribution of the whole NP. Mary:np(X):� : pres [mary - X) [X]one �. ( the, N) :np(X):� : pres T � N:noun(X):one � : T
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notation A : B : � : T stands for the statement that A : B : � : T is an expression with form A , category B , that transforms an information stack � into an information stack T. To give some flavour, let us consider a treatment of the verb believe. The incoming information state � is enriched with the new information state that is the belief state of the subject of the verb according to the first information state of�. after taking in the information coming from the subject NP, which maps � to P. This forms the incoming stack belin,.P for the belief complement which updates belin,.P to become T. From T the first element is removed by the beloutx operator which codes the information in the next element on �. Meeting the goals after the � means that the updates are found for the subject NP and the belief complement so that, if� is instantiated to a particular information stack, the clause ofwhich believes is the head will denote a concrete update of�.
406 Presupposition and Accommodation in Update Semantics
The following two examples are two verbs leave and regret , where I take regret to add a property attribution sad(e) to the belief state of the subject of regret and to presuppose the complement clause in the same belief state. (NP, leaves): sentence(E): � : [leave(E , X)] [EJ T � NP:np(X):� : � 1 (NP, regrets, that, S) : sentence � � � NP:np(X):�:P, S:sentence:one bellnx P:T, � � = beloutx[sad(E)] pres T))
(if, S I , S):sentence:� : neg neg T � SI :sentence:up � : P, S:sentence:up P : T . (it,is,NP, who, S):sentence:� : [X - Y] pres T) � NP:np(X):� : P, S:sentence/Y:one P : T bachelor:noun(X): � : [unmarried (X)] pres [male (X)] [adult (X)] [X]one � man:noun(X):� : [man (X)] [X]�
8 A PROBLEM W I T H A C C O M M O D AT I O N
The process we used here is a default process: accommodation happens as far down the stack as possible and on the intervening states as long as doing so does not lead to conflict with the correcmess conditions. There is a philosophical reason to be unhappy with the notion of accommodation we developed, since it does not seem to follow from the nature of presupposition as such. From what we understand of presupposition and why it occurs, it would follow rather that accommodation should always be as local as possible, as indeed Karttunen predicts. But there are more empirical problems as well. First of all, the view of accommodation we developed does not lead to the right characterization of the resolution of definite descriptions. There is a class of definite descriptions that
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Of the following examples, the only one that needs a special comment is the tentative treatment of the cleft statement. For this it is necessary to assign an exhaustive interpretation to the WH-variable in the complement. Though exhaustivity can be treated in update semantics (see Zeevat forthcoming), it essentially involves use of the technique of pre-order updating pioneered by Veltman (to appear). Partly for this reason10 no treatment of proper quantifica tion is offered.
Henk Zeevat
407
are not meant to be resolved: their content is already sufficient to yield a referent without any contextual dependency. If one wants, these could be subject to accommodation to make their behaviour as much like proper names as possible. But the definite descriptions outside this class do not seem to participate in accommodation at all. They can either be resolved by finding a discourse object that meets the description or one that meets the description well enough or by being functionally related to a high focus discourse object. For the first case compare (4o): (40) A soldier entered the room. The man asked for a beer.
(4 1) A man died in a car crash yesterday evening. The &nsterdam father of four was found to have been drinking. For bridging cases, compare (42): (42) John went into the kitchen. The tap was running. John got married last April. The priest was bald. Here the definites are linked to the kitchen and the marriage respectively: they are the tap in the kitchen and the priest who celebrated the wedding respectively. The problem for our accommodation account is that if we do not have antecedents in each of the four cases the interpretation process is blocked and not as accommodation predicts continued in a routine way. This is not to say that the resolution does not add new information in both cases. We infer that the soldier is a man, and that the man who crashed was an Amsterdam family father, that the kitchen had a tap, that the marriage was performed by a priest, etc. But this is not accommodation proper, which would also create the antecedents themselves. It would be an improvement to add for presupposition resolution precisely the possibilities for the definites: the possibility of adding some not implausible material and the possibility of bridging to high focus elements. The conditions under which these resolutions are possible are not very sharply demarcated but nevertheless quite restrictive. It is possible to go from soldier to man, but not as easily from man to soldierY Similarly, linking calls on a relation of part and whole is hard to formalize, but nevertheless intuitively obvious. Here a marriage normally has a performer, a kitchen normally a tap, etc., but not the other way around. What this comes down to is giving resolution a larger and more realistic role in presupposition, which would decrease the role of accommodation. Perhaps it is then possible to reduce the explanation of projection tojust global and strictly
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Though the predicate soldier does not strictly imply the predicate man, there is certainly a strong expectation here, which makes the resolution unproblematic. But it can be worse, as in (41 ), where genuinely new information is added.
408 Presupposition and Accommodation in Update Semantics
local accommodation, a position that is easier to defend than the one we arrived at. Global accommodation-unlike intermediate accommodation-can be seen as the further determination of an object that is not completely explicit from the ongoing discourse. A sketch of the resulting algorithm would be: Try to resolve allowing also bridging and adding material at the site of antecedent accompanied by accommodation between the antecedent and the trigger. 2. If this fails and the trigger is suitable for its global accommodation and accommodation of the intervening path. J. Try local accommodation. 4· Give up. 1.
(43) a. LBJ dreamt that he was a homosexual and that everybody knew that his foreign policy was a failure. b. LBJ dreamt that he was a homosexual and that everybody knew that he waited for boys in the restroom of the YMCA.
In the (b) example, the recognition ofLBJ's behaviour in his dream as implying �9p10sexuality provides a relationship like the one in (42), so that projection is prevented. In the (a) example, such a relationship cannot be constructed and projection occurs. In addition it provides an approach to van der Sandt's partial matching, as the resolution processes we now assume have the required soft boundaries. For the grandchildren-children example, it would be possible but difficult to bridge from his children to hisgrandchildren . If a bridge is built, John's having children is not projected; otherwise it is. 9
C O N C LUS I O N S A N D O PE N Q UES T I O N S
What did we learn from our comparison? I n the first place we have established a strong similarity between Karttunen & Heim on the one hand and van der Sandt on the other. The similarity is strengthened by our construction of discourse markers as proper names in the information states. This prevents a good many of the problems arising from logical omniscience. This is not to say that the problem oflogical omniscience has been solved. The information states can still not distinguish between e.g. two equivalent mathematical statements if they involve the same discourse referents. Second, we have provided a reconstruction ofHeim's theory of accommoda tion, in which global accommodation obtains the properties needed for dealing
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A version of this could deal with examples like McCawley's (43 ).
Henk Zeevat 409
(44) Mary met a man; and John believes that Harry thinks he; stole his watch.
it is necessary to accommodate the existence of the man in Harry's belief state according to John as well as in John's belief state. (c) De re readings for definites in belief contexts can be described as resolution and accommodation without (full) local accommodation. These should be allowed, even in Heim's position. Fourth, we have established a difference in the behaviour with respect to accommodation of two classes ofpresuppositions, the lexical and the resolution ones. The second class is rather well understood since the recent wave of philosophical attention to anaphora. Or, more prudently, the concepttial problems by resolution problems are the same as addressed in the literature on anaphora. It is different with lexical presuppositions. Though the role of sortal concepts for individuation and identity has been investigated in depth, so that it may now be feasible to explain the presuppositional character of sortal information in terms of the concepts that have been dug out in that discussion, it does not hold that all lexical presupposition can be thought of as sortal information. Though preconditions for action are significant in explaining another class, there are important other cases. Seuren (1 988) mentions the case of the English bald , whose lexical presuppositions rule out that it can be used to translate the Dutch een kaal landschap or the German eine kahle Landschafi as a bald landscape, although the kernel meaning of bald and kaal or kahl is the same. So it seems that much remains to be done here. The notion of updating stacks of information states may worry the theoretician. I have no argument to pacify such worries, but hope that the method contributes to clarify the postulated accommodation processes. The
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with the problems involved in Karttunen's earlier version of update semantics for presuppositions. Under this view, global accommodation is the default case. Unfortunately, we are in the same position as Gazdar ( 1 979), Soames ( 1 982), van der Sandt (1988, 1 989), and Heim (1 982) in being unable to provide an explanation of the fact that there is this default. Also, we have not succeeded in solving the scheduling problem in a satisfactory way. Future work will have to tell whether the approach to accommodation following Mercer (1992) is the way to go. Third, we have been able to correct a number of details. (a) It is necessary for developing a theory of presupposition under belief in DRT to involve the whole belief state of that person rather than limit oneself to the current belief report. (Unwanted accommodations are the result.) In this respect update accounts are crucially better since they do not have the alternative of ignoring a person's other beliefs. (b) Resolution is more complex than we thought since it often involves local accommodations as well. This may seem a point against anaphoric theories of presupposition, but it is not as personal pronouns behave in exactly the same way. In (44):
410 Presupposition and Accommodation in Update Semantics
formalization is closely related to DRT and could be used as an alternative model by those who prefer information states and constructs from information states to syntactic objects. Unlike other 'semantics' for DRT (Zeevat 1 989; Stokhof & Groenendijk 1 990; Asher 1 990), the present one is top-down rather than bottom-up and provides therefore e.g. a more appropriate reconstruction ofKamp's proper name rule than the bottom-up approach.12 At the same time, as a semantical approach, it can be useful in ruling out syntactical operations on DRSs that could not be meaningfully interpreted within stack-updating. This paper will have sequels where a formalization of accommodation in default logic will be described and one which will document computational work along the lines set out in this paper.
Thanks go to Noor van Leusen, David Beaver, Friederike Moltmann and Remko Scha for spotting mistakes in and suggesting improvements to earlier drafts of this paper. All remaining errors are entirely my own responsibiliry. HENK ZEEVAT Vakgroep A lfa-Informatica Faculteit der Letteren Universiteit van Amsterdam Spuistraat 134 1 0 1 2 VB Amsterdam The Netherlands
N O TES I
To maintain determinism, we will require throughout that such functions are unique. As van der Sandt points out, it is more realistic to switch to a non deterministic resolution scheme, where more solutions are allowed. Such a scheme can be easily defined as in (de£ I4). but at the price of losing the clariry of a deterministic update notion. De£ I 4: Non-deterministic presupposition resolution
3g [at[P] - at � a(P) E [at:3gal[P] - al) 2
David Beaver (p.c.) rightly objects to this example that his children forces the resol ver to have made a choice that John would have more than one child, some-
thing that does not follow from his having grandchildren. He reports coming up in collaboration with Kamp with (6) where this problem does not seem to arise. (6) If Pete and John have grandchildren, their children must be adult. This modification gets rid of the uneasi ness that one feels with the original example but seems to retain the same two readings. In later work (this volume) van der Sandt abandons determinism and so obtains a (non-preferred) reading where the chil dren are accommodated at the site of the grandchildren. Strict matching still pre-
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Acknowledgements
Henk Zeevat 4 1 1 marion state if y is an object that is existent according to x. This makes .it possible to express that an object is both an object ofJohn and an existent object, or that an object is shared berween John and Bill. What we do not capture, however, is the mechanism by which such relationships arise, i.e. the causal effects of objects and representations of objects on belief subjects that cause them to repre sent these objects themselves and the epistemic effects of such causations. 10 The other reason is type-raising in the current formalism, a discussion of which seems a distraction here. 1 1 (4 1) is an apparent exception but can be brought into line by making a distinction berween restrictive and non-restrictive parts in definite descriptions. Here the restrictive material is about the same as that of a male pronoun and the rest must be seen as an adjectival non-restrictive modifier. 12 In Zeevat (1 989), the best result obtain able seemed to be that any text in which a name acts as an antecedent for a pronoun can be reconstructed by a quantification rule ambiguity. This is empirically ade quate but does not do justice to the intui tion behind the proper name rule in the DRS-development algorithm. On the current account, the proper name rule is a special case of presupposition and so provides an explanation of names for non-existent objects as in Santa Claus does not exist or The Greeks believed that Pegasus was a winged horse .
RE FE RE NCE S Asher, N. (1 990), 'Abstract objects, semantics and anaphora', MS, Center for Cognitive Science, University ofTexas, Austin. Gazdar, G. (1 978), Pragmatics: Implicature, Presupposition, and Logical Form , Academic Press, New York.
Heim, I. (1 982), 'The semantics of definite and indefinite noun phrases', Ph.D. thesis, University of Massachusetts, Amherst. Heim, I. ( 1 98 3), On the Projection Problem for Presuppositions , WCCFL , 2: 1 1 4-26. Heim, I. (1 992), 'Presupposition projection
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vents a proper anaphoric reading where a conceptual link berween the children and the grandchildren is established. 4 This notion can be defined properly only in a discourse grammar as cancellation can be caused by the next sentence or even after an interruption or elaboration. The notion ofincorrecmess involved here is usually identified with the incorrect ness notion of discourse grammar. The observation that this incorrectness is less dramatic than the one arising from sentence grammar has been often made and is usually explained by our superior ability to correct incorrect discourses. Nevertheless, discourse mistakes are easily recognized and form a reliable starring point for the study of discourse. 6 See Seuren (1 988) for a defence of the view that it is the matrix that is respon sible for the existence presupposition. 7 The first line of the table brings out a weakness of van der Sandt's treatment. Intuitively, resolution should be possible to both the actual king and the king John assumes, with possibly an identification of both kings. 8 The accommodation of John believes that Mary left if Mary did not leave seems impossible. It is as if projection is obliga tory if John only has an implicit belief that Mary left. This seems a problem for the current account of regret . 9 Though the requirement that y exists in John's beliefstate is a necessary condition, it seems too minimalisric an account of de re belie£ What we could define here is a relation object(x, y) holding in an infor-
4 1 2 Presupposition and Accommodation in Update Semantics
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Semantics and Contextual Expression , Foris, Dordrecht, 26-94. Seuren, P. ( 1 988), 'Lexical meaning and presupposition', in W. Huellen & R Schulze (eds), Understanding the Lexicon , Niemeyer, Tubingen, I 70-87. Soames, S. (1 982), 'How presuppositions are inherited: a solution to the projection problem', Linguistic Inquiry, 13, 48 3-545· Stalnaker, R. (1978), 'Assertion', in P. Cole (ed.), Syntax and Semantics 9: Pragmatics , Academic Press, New York, 3 I 5-32. Stokhof, M. & Groenendijk, J. {I99I), 'Dynamic predicate logic', Linguistics and Philosophy , 14: 39-100. Stenning, K., Levy, ]. & Shepherd, M. {I 988), 'On the construction of representations for individuals from descriptions in text', Language and Cognitive Processes , 3: I 29-63. Veltman, F. {to appear) 'Defaults in update semantics', accepted by Journal of Philo sophical Lagic . Zeevat, H. {I 989), 'A compositional approach to discourse representation theory', Lin guistics and Philosophy , 12: 95- I 3 1. Zeevat, H. {I 992), 'Questions and exhaustiv ity in update semantics', MS, University of Amsterdam.
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