the semantics and pragmatics of presupposition...the semantics and pragmatics of presupposition...

Journal cfStmcntus 15- 239-299 © Oxford Uruvemty Preo 1998

The Semantics and Pragmatics of Presupposition

NICHOLAS ASHERUniversity of Texas, Austin

ALEX LASCARIDESUniversity of Edinburgh

Abstract

In this paper, we offer a novel analysis of presuppositions, paving particular attention to theinteraction between the knowledge resources that are required to interpret them. Theanalysis has two main features. First, we capture an analogy between presuppositions,anaphora and scope ambiguity (cf. van der Sandt 1992), by utilizing semantic under-specification (c£ Reyle 1993). Second, resolving this underspccification requires reasoningabout how the presupposition is rhetorically connected to the discourse context.

This has several consequences. First, since pragmatic information plays a role incomputing the rhetorical relation, it also constrains the interpretation of presuppositions.Our account therefore provides a formal framework for analysing problematic data, whichrequire pragmatic reasoning. Second, binding presuppositions to the context via rhetoricallinks replaces accommodating them, in the sense of adding them to the context (cf. Lewis1979). The treatment of presupposition is thus generalized and integrated into thediscourse update procedure.

We formalize this approach in SDKT (Asher 1993; Lascarides & Asher 1993), anddemonstrate that it provides a rich framework for interpreting presuppositions, wheresemantic and pragmatic constraints arc integrated.

1 I N T R O D U C T I O N

The interpretation of a presupposition typically depends on the context inwhich it is made. Consider, for instance, sentences (i) vs. (2), adapted fromvan der Sandt (1992); the presupposition triggered by Jack's son (that Jack hasa son) is implied by (1), but not by (2).

(1) If baldness is hereditary, then Jack's son is bald.(2) If Jack has a son, then Jack's son is bald.

The challenge for a formal semantic theory of presuppositions is to capturecontextual effects such as these in an adequate manner. In particular, such atheory must account for why the presupposition in (1) projects from anembedded context, while the presupposition in (2) does not This is a specialcase of the Projection Problem; If a compound sentence S is made up of

240 The Semantics and Pragmatics of Presupposition

constituent sentences 5, , . . . ,Sn , each with presuppositions P, ,... ,Pn, thenwhat are the presuppositions of 5?

Many recent accounts of presupposition that offer solutions to theProjection Problem have exploited the dynamics in dynamic semantics(e.g. Beaver 1996; Geurts 1996; Heim 1982; van der Sandt 1992). In theseframeworks, assertional meaning is a relation between an input context (orinformation state) and an output context Presuppositions impose tests onthe input context, which researchers have analysed in two ways: either thecontext must satisfy the presuppositions of the clause being interpreted (e.g.Beaver 1996; Heim 1982) or the presuppositions are anaphoric (e.g. van derSandt 1992) and so must be bound to elements in the context But clausescarrying presuppositions can be felicitous even when the context fails thesetests (e.g. (1)). A special purpose procedure known as accommodation is usedto account for this (cf. Lewis 1979): if the context fails the presuppositiontest, then the presupposition is accommodated or added to it, providedvarious constraints are met (e.g. the result must be satisfiable).

This combination of test and accommodation determines the projectionof a presupposition. For example, in (1), the antecedent produces a contextwhich fails the test imposed by the presupposition in the consequent (cithersatisfaction or binding). So it is accommodated. Since it can be added to thecontext outside the scope of the conditional, it can project out from itsembedding. In contrast, the antecedent in (2) ensures that the input contextpasses the presupposition test So the presupposition is not accommodated,the input context is not changed, and the presupposition is not projectedout from the conditional.

Despite these successes, this approach has trouble with some simplepredictions. Compare the following two dialogues (3abc) and (3abd):

(3) a. A: Did you hear about John?b. B: No, what?c A: He had an accident. A car hit him.d. A: He had an accident ??The car hit him.

The classic approach we just outlined would predict no difference betweenthese two discourses and would find them both acceptable. But (3abd) isunacceptable. As it stands it lacks discourse coherence, while (3abc) doesnot; the presupposition of the car cannot be accommodated in (3abd). Wewill argue that the proper treatment of presuppositions in discourse, like aproper treatment of assertions, requires a notion of discourse coherence andmust take into account the rhetorical function of both presupposed andasserted information. We will provide a formal account of presuppositions,which integrates constraints from compositional semantics and pragmaticsin the required manner.

Nicholas Asher and Alex Lascaridn 241

We will start by examining van der Sandt's theory of presuppositionsatisfaction, since he offers the most detailed proposal concerningaccommodatioa We will highlight some difficulties, and offer a newproposal which attempts to overcome them. We will adopt van der Sandt'sview that presuppositions are anaphoric, but give it some new twists. First,like other anaphoric expressions (e.g. anaphoric pronouns), presuppositionshave an underspecified semantic content Interpreting them in contextinvolves resolving the underspecification. The second distinctive featureis the way we resolve underspecification. We assume a formal model ofdiscourse semantics known as SDRT (e.g. Asher 1993; Lascarides & Asher1993). where semantic underspecification in a proposition is resolved byreasoning about the way that proposition rhetorically connects to thediscourse context Thus, interpreting presuppositions becomes a part ofdiscourse update in SDRT.

This has three important consequences. The first concerns pragmatics.SDRT provides an explicit formal account of how semantic and pragmaticinformation interact when computing a rhetorical link between a proposi-tion and its discourse context This interaction will define the interpretationof presuppositions, and thus provide a richer source of constraints onpresuppositions than standard accounts. This account of presuppositionswill exploit pragmatic information over and above the clausal implicaturesof the kind used in Gazdar's (1979) theory of presuppositions. We'll argue insection 2 that going beyond these implicatures is necessary to account forsome of the data.

The second consequence of interpreting presuppositions is SDRT

concerns accommodation. In all previous dynamic theories of presupposi-tion, accommodation amounts to adding, but not relating, the presupposedcontent to some accessible part of the context This mechanism is peculiarto presuppositions; it does not feature in accounts of any other phenomena,including other anaphoric phenomena. In contrast, we model presupposi-tions entirely in terms of the SDRT discourse update procedure. We replacethe notion that presuppositions are added to the discourse context with thenotion that they are rhetorically linked to it Given that the theory ofrhetorical structure in SDRT is used to model a wide range of linguisticphenomena when applied to assertions, it would be odd if presupposedinformation were to be entirely insensitive to rhetorical function. We willshow that presupposed information is sensitive to rhetorical function andthat the notion of accommodation should be replaced with a moreconstrained notion of discourse update.

The third consequence concerns the compositional treatment ofpresupposition. Our approach affords that one could call a compositionaltreatment of presuppositions. The discourse semantics of SDRT is

The Semantics and Pragmatics of Presupposition

compositional upon discourse structure: the meaning of a discourse is afunction of the meaning of its parts and how they are related to each other.In SDRT presuppositions, like assertions, generate underspecified butinterpretable logical forms. The procedure for constructing the semanticrepresentation of discourse takes these underspecified logical forms, resolvessome of the underspecifications and relates them together by means ofdiscourse relations representing their rhetorical function in the discourse.So presuppositions have a content that contributes to the content of thediscourse as a whole. Indeed, presuppositions have no less a compositionaltreatment than assertions.

Our discourse-based approach affords a wider perspective on presuppo-sitions. Present dynamic accounts of presupposition have concentrated onphenomena like the Projection Problem. For us the Projection Problemamounts to an important special case, which applies to single sentencediscourses, of the more general 'discourse' problem: how do presuppositionstriggered by elements of a multi-sentence discourse affect its structure andcontent? We aim to tackle this question here. And we claim that a richnotion of discourse structure, which utilizes rhetorical relations, is needed.

While we believe that our discourse based theory of presupposition isnovel, we hasten to add that many authors on presupposition like Beaver(1996) and van der Sandt (1992) would agree with us that the treatment ofpresupposition must be integrated with a richer notion of discoursestructure and discourse update than is available in standard dynamicsemantics (e.g. Kamp & Reyle's DRT, Dynamic Predicate Logic or UpdateSemantics), because they believe that pragmatic information constrains theinterpretation of presuppositions. We wish to extend their theories with thisrequisite notion of discourse structure.

2 VAN DER SANDT'S DYNAMIC A C C O U N TAND ITS PROBLEMS

Van der Sandt (1992) views presuppositions as anaphors with semanticcontent He develops this view within the framework of DRT (Kamp &Reyle 1993), in order to exploit its constraints on anaphoric antecedents.

A presupposition can bind to an antecedent only if there is the samecontent in either an accessible part of the DRS which represents thediscourse context, or an accessible part of the DRS which represents thecurrent clause (Le. the clause that introduced the presupposition trigger). In(2), for example, the antecedent of the conditional is accessible to theconsequent, and it contains the same content as the presupposition that'striggered there.

Nicholas Asher and Alex Lascarides 243


So this presupposition binds to it This provides a representation of (2)which can be paraphrased as If Jack has a son, then he is bald, which matchesintuitions.

In contrast, the presupposition in (1) cannot be bound, because thecontext lacks the required content Following Karttunen (1974) and Heim(1982), van der Sandt (1992) resorts to accommodation: he adds thepresupposition to the context (cf. Stalnaker 1974; Lewis 1979).

Van der Sandt provides an algorithm which specifies how binding andaccommodation jointly model presupposition satisfaction. First, the pre-supposed material is separated from the asserted material in the DRS whichrepresents the current sentence (which may be complex in that it containsseveral clauses), in order to allow them to be processed differently. Onehandles the presupposed material first If it can be bound in the mannerspecified above, then it is. Otherwise, it is added to an accessible site. Onethen adds the DRS which represents the asserted material of the currentsentence to the DRS representing the previous sentences in the discourse, orsome subDRS of it, via DRT'S notion of update (note that one of these DRSS

may have been modified with the addition of the presupposition).Essentially, DRT'S notion of update is set union on both the discoursereferents and the DRS conditions.

When the contexts are structurally complex (Le. contain subDRSs andcomplex conditions), different possibilities for accommodation arise. Vander Sandt distinguishes between global accommodation (as in (ia)), intermediateaccommodation (as in (ib)) and local accommodation (as in (ic)).

son(x) has(j,

b

hereditary(b)

X

bald(x)

(ib)son(x) has(j,x)

hereditary(b)

X

bald(x)


(ic) bhereditary{Jb)

XJson(x) has(j,x)

baU{x)

These capture the different possible inferences that presuppositions can giverise to. (ia) means: Jack has a son, and if baldness is hereditary, then Jack'sson is bald, (ib) means: if baldness is hereditary and Jack has a son, thenJack's son is bald, (ic) means: if baldness is hereditary, then Jack has a sonand he is bald. Only (ia) reflects the case where the presupposition projectsfrom the embedding.

Accommodation is subject to certain constraints: the result of theaddition should be logically consistent and should not render any part ofthe asserted content uninformative. Furthermore, van der Sandt argues thatif these constraints yield a choice as to where to accommodate thepresupposition, then one prefers to add it to the most superordinate orhighest DRS context in which the constraints are satisfied. So in (i), globalaccommodation (Le. (ia)) is predicted.

Van der Sandt's account of presupposition is compelling, because heoffers a precise solution to the Projection Problem. A presuppositionprojects from an embedded context only if the above algorithm predictsthat it is accommodated at a superordinate site in the DRS (e.g. (ia)). Thereare, however, a number of difficulties with the theory's predictions, some ofwhich are particular to van der Sandt's formulation of accommodation,others of which are endemic to the semantic notion of accommodationitself—which we will take henceforth to mean the addition of presupposedinformation to the context

The first problem, which is particular to van der Sandt's account, is thatlocal accommodation isn't predicted in certain cases when it should be.Consider (4) (modified from Beaver 1997):

(4) Either John didn't solve the problem or else Mary realizes that theproblem has been solved.

The second disjunct presupposes that the problem has been solved. There'sno suitable accessible antecedent, and so this information has to beaccommodated. (4) is reminiscent of one discussed by van der Sandt(1992):1

(5) Either John has no donkey or his donkey is eating quietly in the stable.

Nicholas Asher and Alex Lascaridcs 245

The presupposition in (5) that John has a donkey cannot be accommodatedglobally in his theory, because this would render the first disjuna of (5)uninformative: assuming 0 is the proposition that John has a donkey, thenaccommodating globally would produce a semantic representation of theform <f> A (-10 V rp), which is equivalent to <f> A rp. So by appealing to theinformativeness constraint we mentioned above, van der Sandt predicts thatglobal accommodation is not possible for (5).*

We cannot block global accommodation in (4) with the informative-ness constraint, however. Adding the presupposition that someone solvedthe problem does not render the first disjunct, that John did not solvethe problem, uninformative. Since this global accommodation alsoresults in a consistent discourse, van der Sandt's representation of (4)amounts to: the problem has been solved, and either John did not solveit or Mary realizes that it has been solved. As Beaver points out, this iscontrary to intuitions, which favor local accommodation: either John didnot solve the problem, or it has been solved and Mary realizes it hasbeen solved

To capture the intuitive semantics of sentence (1), Van der Sandt relieson the preference for global accommodation. But in (4) this preferencecauses problems, because local accommodation should be preferred, and yetthe constraints on accommodation are satisfied at the superordinate site.We shall see in the course of this section that this puzzle arises because of ageneral observation about presuppositions that DRT alone cannot capture:the preferred site for accommodation depends on a variety of pragmaticfactors (c£ Beaver 1996) that are not represented in DHSS.

Nevertheless, (4) is in fact a bit odd unless it is uttered in a particularcontext; we need to know which problem is being talked about Van derSandt's theory fails to capture this as well, because it predicts that thepresupposition that there is a problem, which is triggered by the problem, canbe globally accommodated. But discourse contexts which improve theacceptability of (4) strongly suggest that the way presuppositions aresatisfied depends on the rhetorical structure of the discourse as a whole.Dialogue (6) illustrates this:

(6) a. A: The Problem Solving Group is given a problem each day, and thegroup leader Mary has to assign it to someone in her group. Johnis the best problem solver. But when he solves a problem, healways boasts about it This annoys Mary, and so if she thinks thatthe day's problem is an unsolved one, she gives it to him, to testhim. Otherwise, she gives it to someone else.

b. B: John's being very quiet just now. Did she give him today'sproblem?


(6) c A: Well, I'm not sure she did. Either John didn't solve the problemor else Mary realized that the problem's been solved.

B's question identifies the problem being talked about, and this improvesthe acceptability of (4). In addition, the rhetorical links between the (6a),(6b) and (6c) help one interpret the presupposition that the problem hasbeen solved.

But our more basic problem remains: to explain the local accommoda-tion of the presupposition of realize in (6c). We could with Geurts (1995)integrate in Van der Sandt's theory further constraints on accommodationsuch as those in Gazdar's theory, which are based on Grice's notion ofconversational implicature. Gazdar's theory predicts local accommodationin any context where by uttering the sentence, the speaker implicates thatthe presupposition is not taken for granted (Le. the speaker implicates thathe believes that it is possible that the presupposition is false). Would such aconstraint block global accommodation in (6)? B's question about John'sbehavior in (6b) serves as an elaboration to the generalization about whogets problems in (6a), and so the answer to the question hangs on whetherMary believes that the problem is solved or not A implies by his utterance(6c) that he doesn't know whether Mary gave John the problem. But whatimplicatures does this raise? Given what A said in (6a), A and B would knowthe answer to the question as to whether John got today's problem, if theyknew if Mary believed it was solved. So this context implicates that A and Bdon't know if Mary believes the problems been solved. However, thecontext does not implicate that A and B themselves believe the presupposi-tion—that the problem has been solved—is in doubt; the context is mute onthis issue. So Gazdar's constraints do not predict local accommodation inthis case. Something more is needed to explain why local accommodationoccurs here.

To predict local accommodation in (6), we analyze presuppositions interms of the rhetorical structure of the discourse context Rhetoricalstructure is something about which DRT has little to say. We claim thatrhetorical structure explains why local accommodation is preferred in somecases where global accommodation would be informative and consistent,and furthermore would meet Gazdar's constraints on how Gricean-styleconversational implicatures determine global vs. local accommodation. Theplace where presuppositions get accommodated depends on the rhetoricallinks between propositions in discourse as well as their content Inparticular, presuppositions are interpreted so that the rhetorical links areas strong as possible. We will return to the detailed analysis of (4) in section5.3 and demonstrate that the Contrast relation between the disjuncts in (4) isat its strongest in (6) if the presupposition is accommodated locally.

Nicholas Aiher and Alex Lascarides 247

The difference in acceptability between (3c-d) also demonstrates that theconstraints of infonnativeness and consistency are too weak:

(3) a. A; Did you hear about John?b. B: No, what?c A; He had an accident A car hit him.d. A: He had an accident ??The car hit him.

While (3c) is perfectly felicitous, (3d) is not Most theories would predictthat the presupposition in (3d) is accommodated globally (Le. added to themain context), because the result is informative and consistent So theseconstraints predict coherence where there is none.

These constraints on accommodation also cause difficulties for exampleswhere the presupposition seems to require an explicit linguistic antecedentto be felicitous. Consider, for instance, the contrast between (7) and (8),taken from Beaver (1997):

(7) ?? I don't know whether the Pope has measles. But every Catholicrealizes the Pope has measles.

(8) I don't know whether the Pope has measles. But for every person, if he'sa Catholic and the Pope has measles, then he realizes the Pope hasmeasles.

Van der Sandt's theory predicts that presupposition that the Pope hasmeasles is globally accommodated in (8). But intuitively, global accommo-dation shouldn't be possible, because a statement akin to Moore's paradox(1912) would be asserted (The Pope has measles but I don't know that the Popehas measles). Van der Sandt's constraints on accommodation do not blockthis. But even if they did, the resulting account would still allowintermediate accommodation. But this incorrectly predicts that (7) isfelicitous. In contrast, the presupposition in (8) is bound to this intermediateposition. But the difference in acceptability between (7) and (8) demon-strates that an explicit linguistic antecedent is required, and accommo-dation at the same site as this antecedent is odd. Van der Sandt fails tocapture this.

There are certain presupposition triggers, such as too, which are like (7) inthat their presuppositions require a linguistic antecedent They pose similarchallenges. Consider (9):

(9) John lived in New York too.

Various people have supposed that (9) presupposes that there is someoneother than John who lived in New York. This content is already commonknowledge to most speakers. However, (9) is odd in a context where the


presupposition or something similar isn't already explicitly introduced intothe discourse context In fact, we think that the received wisdom about thepresuppositional content of too is wrong: (9) is perfectly felicitous if utteredin a context in which other places John has lived have already beenmentioned. The presupposition of too is rather that it requires that there besome proposition in the context that bears the rhetorical relation Parallel tothe content of the sentence in which too occurs.3 In any case thepresupposition triggered by too must be introduced explicitly into thediscourse context, and cannot be accommodated.

Another difficulty for this theory is that it on occasion fails to specify theappropriate content of the presupposition itself Beaver (1997) argues thatthe following minimal pairs show that the content of the presuppositioncannot depend simply on constraints like consistency and informativity:

(10) If David wrote the article, then the knowledge that no good logicianwas involved will confound the editors.

(11) If David wrote the article, then the knowledge that David is acomputer program running on a PC will confound the editors.

The presupposition of (10) is (12), whereas for (11) it is (13):

(12) If David wrote the article, then no good logician was involved.(13) David is a computer program running on a PC.

The factive nominal knowledge triggers the presupposition in both (10)and (11). But whether conditional presuppositions arise or not cannot be astructural matter, since the same structure gives rise to a conditionalpresupposition in (10) but not in (11). So the standard theory ofaccommodation cannot account for the intuitions about these examples;it does not explain the presence of conditional presuppositions in some casesbut not in others. Beaver (1997) argues that presupposition satisfaction mustalso depend on some world knowledge dependent notion of plausibility,but he too does not give an explicit or detailed account that would makethe correct predictions in (10) and (11).

Van der Sandt's conjecture that presuppositions are anaphors is acompelling idea. But it has shortcomings because accommodation is notconstrained enough. Background knowledge such as information about thedomain can block accommodation (Lewis 1979), and the rhetorical functionof the utterance in the text can influence the projection of its presupposi-tions, as shown with (6). Though Van der Sandt and Beaver would bothacknowledge that pragmatic constraints on accommodation are important,these constraints have not been integrated into the formal theory ofpresuppositions or made sufficiently precise to have any predictiveforce. For instance, Van der Sandt's (1992) explicit theory ignores them.


Consequently, presuppositions are sometimes accommodated in the wrongDRS to produce the wrong readings, or they are accommodated when theyshould not be. We will approach these problems by tackling presupposi-tions in a framework of discourse representation that formalizes thesemantics pragmatics interface.

3 THE BASIC PICTURE

Our framework of discourse interpretation, SDRT, extends DRT in twofundamental ways. First, discourse contexts are represented as recursive,relational structures (SDRSS), involving DRSS representing the contents ofclauses, and discourse relations like Parallel, Narration and Backgroundrepresenting the rhetorical functions of these discourse constituents inthe context Second, these discourse relations can affect the content of theclauses they relate, and hence of the discourse in general.

To build such representations of contexts, SDRT proceeds incrementally,interpreting each bit of new information as yielding a change in thediscourse context Like other dynamic theories of interpretation (e.g. DRTand Groenendijk & Stokhof's 1991 DPL), SDRT must specify how newinformation can change an existing discourse context—Le. it must give anaccount of the context change potential (CCP) of an utterance, SDRT does soas follows. First, one uses the grammar to build up compositionally the DRSS

for each clause (cf. Muskens 1995; Fernando 1994; Asher 1993). The SDRS isthen built from these DRSS dynamically. In the simple cases examined hereand in Lascarides & Asher (1993), we update clause by clause.4 Whenupdating the SDRS built so far with a new DRS, one uses the glue logic todecide where to attach this DRS and to infer one or more rhetorical relationsto attach it This last function of the glue logic was spelled out in Lascarides& Asher (1993) and elsewhere in what we have called DICE (Discourse inCommonsense Entailment), but there the glue logic was restricted to thistask. Hence in this paper we will speak more generically and more generallyof a glue logic

The rhetorical relations may trigger modifications to the DRSS that wereproduced by the grammar. For example, in (14), the glue logic determinesthat Narration connects the clauses. Spatio-temporal constraints on Narrationare then used to add to the representation of (14) that the boxcar is inDansville:

(14) a. John took an engine from Avon to Dansville.b. He picked up a boxcar,c and took it to Broxburn.

2 so The Semantics and Pragmatics of Presupposition

The rhetorical relations, their semantic effects and the new information arenow integrated together with the given SDRS representing the context toform a new SDRS. Thus, SDRS construction proceeds dynamically, and eachgiven SDRS and piece of new information produces a new SDRS, which canserve as a representation of a new discourse context

Suppose one were to analyse presuppositions from the perspective of thiskind of discourse semantics. Then standard binding and accommodationboth seem unsatisfactory. First, standard binding is too restrictive: there aremany rhetorical relations that bind propositions together—not just identity,but also relations like Parallel and Background. Binding presuppositions onlywith identity wouldn't reflect these alternatives. Second, accommodation—where it is viewed as addition alone—is unsatisfactory, because in SDRT therepresentation of discourse is well defined or coherent only if each DRS isrelated to another with a rhetorical relation. There is no scope for justadding a proposition to the context; it has to be related to it as well.

This perspective leads us to loosen van der Sandt's notion of binding.Instead of a presupposition binding with identity to an accessible site in thecontext, it will bind with a rhetorical relation. For example, in (15), van derSandt would accommodate the presupposition that there is a King ofFrance, because binding isn't possible.

(15) The King of France is bald.

We take a different view. (15) means: that there is a King of France isBackground to his being bald. Much of this paper focuses on spelling out thisidea in detail.

Our 'rhetorical' approach to presuppositions has at least three advantages.First, as we mentioned in section 1, loosening binding in this way eliminatesthe need for semantic accommodation altogether, where by semanticaccommodation we mean that the presupposition is added to the context,but not related to any element of it Alternatively, accommodation can beviewed as constrained by much more than informativeness and consistencyin this picture, because it is licensed only when the presupposition can bebound to the context with a rhetorical relation (cf. Lascarides & Oberlander1993).* Either way, the accommodation mechanism where information issimply added to the context is removed. This is a very desirable feature ofthe theory, since this 'addition' mechanism is only used to account forpresuppositions. We are replacing it with a general procedure of inter-pretation, which works for assertions too and which is used to model a widerange of linguistic phenomena, particularly semantic ambiguity resolution.

The second advantage of this approach is that it records the influence ofpragmatic information on presupposition satisfaction. Pragmatic constraintson computing rhetorical relations, which are provided by the glue logic

Nicholas Asher and Alex Lascandes 251

(Lascarides & Asher 1993), provide a much more constrained mechanismfor dealing with presupposition than informativeness and consistency alone.As a result this theory will overcome some of the problems discussed insection 2. Third, it maintains a close relationship between presuppositionsatisfaction and discourse coherence. The presupposition failure in (3 a, b, d)will be predicted by the fact that the presupposition that there is a carcannot be rhetorically bound to the propositions in the context This isroughly analogous to the discourses given in (i6a-c) being incoherent; wecannot attach the presupposition anywhere in the context and get acoherent discourse.

(3) a. A; Did you hear about John?b. B: No, what?d. A: He had an accident ??The car hit him.

(16) a. A; Did you hear about John? ??There was a car.b. B: No, what?

A; ??There was a car.c A; John had an accident ??There was a car.

Our account of presupposition will buttress and develop van der Sandt'sview that presupposition satisfaction and discourse coherence are closelyrelated, and we will exploit SDRT'S rich notion of discourse coherence to dothis.

In SDRT, assertions are linked to the context by computing a rhetoricalrelation. We claim that presuppositions are handled this way too. But manylinguists have argued that assertions and presuppositions are differentPresuppositions project from embeddings and assertions don't And Clark(1977) has intuitively described presupposed information as given, andasserted information as new.6 We need to account for this intuitivedifference.

We capture the difference between presuppositions and assertions inthree ways. First, the rules for updating discourse ensure that the rhetoricalrole of presuppositions is in general different from that for assertedinformation. To capture the intuition that by and large, presuppositionsare given, the rules for computing rhetorical relations ensure that pre-suppositions in general bind with Background (Le. the presuppositionprovides background or sets the stage for the main story line). For example,the representation of (15) will include: (a) the proposition a that x is bald,(b) the proposition (3 that there is a King of France and that is x,7 and (c) thecondition Background(a, 0) (so the presupposition provides background tothe main point, which is that x is bald).

Presuppositions may also bind with Def-Consequence in some cases. Thisrelation means that the presupposition is a defeasible consequence of the


proposition it attaches to. If the consequence relation is idempotent (astandard assumption), then binding in van der Sandt's sense turns out to bea species of Def-Consequence. So binding in van der Sandt's sense will ingeneral correspond in this theory to a case where the presupposition isrelated by both Def-Consequence (because it is defeasibly entailed by theproposition it attaches to) and Background (because in our theory pre-suppositions usually bind this way). Presuppositions can be attached withrelations other than Background and Def-Consequence, but in general thisarises because the presupposition trigger itself specifies some otherrhetorical relation. For example, the presupposition trigger too entailsParallel, and because entails Explanation. In contrast to presuppositions,asserted information may be attached to the discourse context with avariety of rhetorical relations other than Background—e.g. Narration, Result,Explanation—even in the absence of words like too and because. Further-more, assertions do not attach with Def-Consequence, unless it is explicitlysignalled by a discourse particle.

A second difference between presuppositions and asserted information isthat there is an important distinction between their compositionalsemantics. The grammar produces a representation of presupposed infor-mation which is always incomplete or underspecified. This is the technicalway of ensuring that presuppositions are always anaphoric, and must bebound. Because of this, asserted information and presupposed informationbehave differently at the start of a discourse. Asserted information is simplyintroduced into the null context But this is not possible for presupposedinformation. It is always bound to some antecedent with a rhetoricalrelation, even if that antecedent is the asserted information in the clausewhich introduced the presupposition—as in e.g. (i 5).

Finally, there will be differences in the preferences for which part of thediscourse structure presuppositions vs. assertions attach to. Presuppositionsare freer in their attachment possibilities than assertions; those clausalconstituents of the assertion that are combined with logical operators havetheir attachment sites determined by the grammar, whereas presuppositionsare always free in principle to attach outside the SDRS constituent in whichthey were generated. The preferences for attachment predict that pre-suppositions can project from embeddings in a way that assertions cannot

The underspecification in presuppositions is used to record the influenceof pragmatics on presupposition satisfaction. A distinguishing feature ofSDRT is that computing a rhetorical connection between propositions in theglue logic can result in those propositions receiving additional contentUpdate in SDRT is defined so that if this additional content can resolveunderspecified conditions that arose in the grammar, then it does. Thiscaptures the intuition that when processing discourse, people are expected


to and often do fill in gaps in what's been made linguistically explicit Thisfeature of SDRT provides a formal model for how pragmatics (whichinfluences the rhetorical relation) affects semantics (i.e. the resolution ofunderspecification). We will use this feature to record the influence ofpragmatics on the semantics of presuppositions.

The grammar typically introduces at least two underspecified elements ina presupposition: one is the rhetorical relation used to bind the presupposedinformation, and the other is the other term of this relation, which is knownas the attachment point The latter underspecification ensures that thestructural position in the discourse context in which the presupposedinformation is entered is not determined by the syntactic position of thepresupposition trigger that generates it, because the attachment point that ispart of the representation of the discourse context could be a propositionthat was introduced by an earlier sentence (this is explained in more detail insection 4.2). This captures the intuition that that presuppositions mayproject from the embedded contexts in which they are introduced.

Underspecification for presuppositions actually comes in a variety oftypes, which depend on the presupposition trigger. We will examine someof these in section 4.1. In all cases, however, in processing a presuppositionone must resolve the underspecified elements with respect to the discoursecontext So presupposition projection, binding and accommodation alloccur as a byproduct of the SDRT update procedure. They occur bycomputing how the presupposition rhetorically connects to the contextSince this update procedure is determined by the pragmatic informationspecified in the glue logic, presuppositions are influenced by pragmatics aswell as compositional semantics.8

4 PRESUPPOSITIONS IN MORE DETAIL

Having given the basic picture, we will now turn to the details of thetheory. First, we will give an overview of the SDRT compositional semanticsof presupposition triggers. Processing the presupposition relative to thecontext amounts to resolving its underspecified elements, and this ishandled via the SDRT update function. We will illustrate how this works,by analysing some simple sentences (Le. sentences that do not containlogical operators such as [for not). We will then examine the interpretationof presuppositions in more complex sentences (e.g. (10) and (11)), andcompare our treatment to that of other dynamic accounts, such as Beaver's(1996) and van der Sandt's (1992). Using SDRT makes comparisons andreformulations of van der Sandt's DRT-based theory of presuppositionsrelatively straightforward. We will demonstrate that at least some of the

2$4 The Semantics and Pragmatics of Presupposition

problems concerning conditional presuppositions can be overcome, becauseof the role of pragmatics in SDRT. Finally, we will examine presuppositionsin multi-sentence discourse, and then return to some cases that one mightthink are difficult to handle in a proposal where semantic accommodationis excluded.

4.1 Semantics of clauses

We first examine some important aspects of the compositional semantics ofthe clauses. Following Reyle (1993) and Asher & Fernando (1997), thegrammar utilizes underspecification to represent semantic ambiguity. Thegrammar produces a set of labelled pieces of information and a set ofconstraints about how these labels can combine. Semantic ambiguity occurswhen the constraints underdetermine the combination of these labels. Sincethe combination of labels is underspecified, so is the representation of themeaning of the clause. Resolving the relative scopes of the labels is thendone by updating the discourse context with this (underspecified) meaning.Discourse update in SDRT is specifically designed to resolve underspecifiedelements when it can.

To avoid clutter in notation, semantic information that must be groupedtogether according to syntax receives just one label. Moreover, as in HPSG

(Pollard & Sag 1994), these labels may appear in conditions. A special case ofthis labelling procedure is the following: if the grammar produces the DRSKw for some clause, then the SDRS for the discourse will include (17) wherethe label n is a discourse referent, which we call a 'speech act discoursereferent' since it labels a DRS (we will always assume a notational conventionthat n labels Kn):

(i?)

Updating the discourse with information such as that in (17) will involvecomputing a rhetorical relation R between TT and some accessible speech actdiscourse referent n' in the discourse context Computing this rhetoricalrelation may include resolving underspecified conditions that are in KT, aswe shall see in section 4.2. Note that R's arguments are the labels, and notthe DRSS themselves. We explain why in section 4.2.

A presupposition that is introduced by a clause can receive differentscope from the assertion. For example, in (1), the presupposed informationhas wider scope than the conditional, but the asserted information doesnot9 In section 2, we showed that the relative scopes of the asserted andpresupposed content of the clause is not syntactically determined; and so, inline with the general strategy for representing ambiguity, the grammar

Nicholas Aster and Alex Lascandes 255

groups asserted information under one label, and the presupposed informa-tion under another. Consequently, the grammar produces an SDRS like thatin (17) for the asserted content of a clause, and it will produce another SDRS

with speech act discourse referent TT', and condition TT' : K^ for thepresupposed content of this clause, where Kv> will be the DRS discourseconstituent that represents the presupposition (cjg.Jack has a son for (1)). Thegrammar does not determine the scope of n and TT'. Rather, all of theseSDRSS must be attached to the representation of the discourse achieved so farthrough the SDRT discourse update procedure: that is, they must be attachedto the context with a rhetorical relation. Rhetorical relations producehierarchical structures for the labels TT, TT' etc, since some rhetorical relationsare subordinating and some are coordinating. So this discourse structurewill resolve die relative scope of the asserted and presupposed content

As well as separating asserted content and presupposed content in thisway and providing them with different labels, the grammar distinguishesbetween presuppositions and assertions in one other important respectPresuppositions are explicitly encoded as anaphoric, since the grammarinvokes for each presupposition an underspecified attachment point andunderspecified rhetorical relation. These are given respectively by u = ?and R = ? in the canonical representation of presuppositions, given in (18):

This distinguishes this treatment of presuppositions from van der Sandt's,because this underspecification means that the presuppositions must alwaysbe rhetorically bound to the context, rather than added.

The Projection Problem is challenging, because the scope of presupposedinformation is contextually rather than grammatically determined. Oursemantic representation of presuppositions allows for this through the useof the underspecified attachment site u = ?. The scope of a presuppositionis determined by resolving u = ?. Since this is done via the discourse updateprocedure, and hence via the glue logic, pragmatics will influence the scopeof presuppositions. Moreover, for presupposition triggers that are intro-duced in an embedded context such as a conditional, SDRT allows thepresupposition to access attachment points that are outside the scope of theembedding. If discourse update resolves the antecedent attachment point uto one of these, then the presupposition has essentially projected out from


its embedded context. This contrasts with the assertions in the conditional,which cannot project in this way.

To illustrate the ideas, let us examine the compositional semantics ofsome example clauses that contain presupposition triggers. Presuppositionsof abstract type—lc. propositional or factual presuppositions—are triggered byexpressions such as u'/i-questions, focus, comparatives, stop/start verbs,manage and succeed verbs, factive verbs like know, regret, realize, andpresuppositional adverbs like again. Let us consider, for instance, a factiveverb like regret. The grammar will produce two SDRSS for a sentencecontaining regret as shown in (19): a is the asserted information, and p isthe presupposed information; [1] is filled in with the subject NP and [2] withthe sentential complement of regret. So the grammar produces therepresentation (20') for sentence (20). a and p below each label bits ofstructure that are produced by the grammar, but they are not discoursereferents themselves. They merely provide ways of talking about the wholestructures, and therefore act as guides for putting the SDRS together, they willdisappear after SDRS update. This will involve binding TT, TT' etc to availablereferents with rhetorical relations. Note also that the DRS representing JO/JH issick forms part of the representation of the asserted content, and also part ofthe representation of the presupposition. We use the DRS in a rather than thelabel because the intensional operator works over a DRS and not a term.

(19) a:TT:

regret(s,[i)*{2})

P-

(20) John regretted that he was sick

(20') a:

TT

TT:regret

holds(s, t)

t -< n

P-

TT',R,U

TT1:

R(u,

R =

u =

j,s",t"

sick(s"j)

holds(s",t")

t" <n

*')?

?


The SDRS p contains the underspecified conditions R = ? and u = ?, whichmust be resolved by updating the context with/?, i.e. by computing a rhetoricalrelation between n' and an antecedent site in the context Resolving theattachment site u will determine the scope of the presupposition.

As we have mentioned before, some cue phrases are presuppositiontriggers which actually specify the rhetorical relation (e.g. too specifies therelation to be Parallel). The presupposed information triggered by too andalso is represented in (21), where [1] is to be filled in by a label for the SDRS

over which too (or also) is assigned scope by the grammar

Such cue phrases presuppose that an antecedent of an appropriate sortexists. This is represented by the anaphoric condition u = ?. Other cuephrases may introduce different discourse relations—e.g. because introducesExplanation; although introduces Contrast. All of these will generate the samesort of conditions as (21). Such conditions impose constraints on what u canbe, because each rhetorical relation specifies constraints on the relationshipbetween the semantic content of the propositions it connects. Theseconstraints are described in section 4.2.

Let us consider now the presuppositions of definites. In line with Chierchia(1995) and Asher & Lascarides (in press), we assume that definites introduce anunderspecified bridging relation, which connects the object denoted by thedefinite to some antecedent in the context. In Asher & Lascandes (in press), wedemonstrated that this bridging relation could be computed as a byproductof SDRT Update, which is how we also treat presuppositions.10

Definites introduce not only underspecified 'bridging' relations at the'micro-structure' level to connect the denoted objects together, but in linewith other presupposition triggers, they also introduce underspecified'rhetorical' relations at the 'macro-structure' level of the from R(u, TT),R = ? and u = ?, which connect the propositions together:

(22) a:MM P-

*':

r;

x, u,B,e,t

MMB(e,*,«)/*&(,,<),

« = ?

2$8 The Semantics and Pragmatics of Presupposition

The definite NP furnishes argument [i], while the VP contributes toargument [2] (depending on whether the definite occurs in subject orobject position).

As an illustrative example, sentence (23) has the compositional semanticsgiven in (23'):

(23) The man walked

walk{e, x)

holsd(e, t)

t -< n

n'

R

R

V

,R,v

x,u,e',

man(x)

B(e',x,

holds(e'

:»,*')= ?= ?

t',B

•0

The presupposition must be bound to the content via a rhetoricalrelation. In addition, the man denoted by the definite must be (bridging)related to an antecedent object (so (23) couldn't be uttered in a nullcontext).

Our treatment of definites extends to quantified NPS, which also conveypresuppositions (cf. von Fintel 1994). The restrictor includes underspecifiedbridging conditions, which require the objects denoted by the NP to berelated to antecedent objects. This is intended to capture the bridging thatoccurs in discourses such as (24): the strikers mentioned in (24b) played inthe football match mentioned in (24a):

(24) a. I went to the Scotland vs. Latvia football match yesterday,b. Every striker attempted to score a goal.

We reflect this in the semantics of quantified NPS by invoking under-specified conditions of the type found in definites, which are placed in therestrictor of the DRS duplex condition. For example, the compositionalsemantics oi every is specified in (25), where [1] is derived in the grammarfrom the NP that contains the determiner every, and [2] is derived fromwhatever the NP combines with to form a clause:


(25)

7T, R, U

TT:

B,x,e,t,y

holds{e, t)

y = ?

« = ?

n"

n":MM

In (24) for example, [i](x) is replaced with stnker(x); [2](x) is replaced withthe vp attempted to score a goal, and B, y and u will be computed through SDRT

Update, so that the quantified NP connects with (24a) in the right way. Thatis, B will be resolved to play, y identified with a discourse referent denotingthe football match, u identified with the label for the DRS which represents(24a), and R resolved to Background (as we will see shortly). Note that unlikedefinites, the presupposition associated with every is restricted in scope tobeing in the restrictor, it isn't free to take wider (or in DRT, 'higher') scope.This restriction ensures that every striker V-ed does not entail that there areany strikers. Of course, these observations hold provided that the discoursereferents within the constituent labelled by 7r get the appropriatequantificational force from =>. This is assured if R is a veridical relation(c£ section 4.3), because then any embedding of the right hand side of theconditional must perforce be a proper embedding of the TT constituent

These examples illustrate the variety of underspecifications that pre-supposition triggers generate. The update task involves resolving theunderspecified conditions where possible. This includes scope resolution.So using underspecification to represent the compositional semantics ofpresuppositions allows us to assimilate presupposition projection to a moregeneral problem—that of assigning a scope to various informational units.

We now turn to the problem of defining discourse update, and the waydiscourse update resolves underspecification.

4.2 From clauses to discourse

The SDRSS produced by the grammar must be dynamically integratedtogether, into a representation of the semantics of the discourse. In SDRT,


one updates the discourse context r that has been built so far with somenew information /3, by attaching 0 to a with a rhetorical relation, where ais an available attachment site (i.e. speech act discourse referent) in r.

But which a's are available attachment sites? Rhetorical relations provide aricher discourse structure than DRT alone gives: Elaboration, Jj- (a ij- @ can beglossed as 'a is a topic for /T) and Explanation are subordinating relations; therest are not Therefore, the notion of accessibility in SDHT (which is termedavailability to distinguish it from DRT) is more constrained than in DRT.Available labels in an SDRS are those on its right frontier: that is, the previouslyattached label, and ones which elaborate or explain it, or are a topic to it So,for example, new information could attach to vr' in (26) but not to TV.

And hence the antecedents to anaphora must be picked up from Kni, butnot from K^. In general, this offers a much smaller set of possibilitiesthan DRT itself would offer. This is one way in which interpretingpresuppositions will be more constrained in SDRT than in DRT.

To compute which rhetorical relation to use, it is essential to use anonmonotonic, 'glue' logic, as we have argued in many places (e.g.Lascarides & Asher 1993). It is also essential to make use of nonmonotinicityto place constraints on where to attach new information, especially whenthis information to be attached is presupposed. The glue logic is expressedin a quantifier-free language augmented with a weak conditional con-nective: A > B means 'If A, then normally B\ This glue logic forconstructing logical forms for discourse is quite simple, even though thecontent of the discourse may be very complex. To build logical forms, theglue logic must have access to the contents of the discourse, but to keepthe logic simple it has only limited access to the full contents of thepropositions—namely the SDRSS. More specifically, we suppose that the gluelogic has access to the form of the SDRSS, but not what they denote (Asher &Fernando 1997). To this end, we suppose that there is an informationtransfer function n from the language of information content to the gluelanguage, which takes conditions inside a given SDRS and turns them intopredicates on that SDRS'S label. So /j.(Ka)(a), where 0 is a predicate on thepropositional variable a, and it corresponds to an SDRS condition in Ka.

The glue language uses various nonlogical predicates in describing ruleswhich constrain where new informarion should attach, and what rhetoricalrelation should be used to attach it We exploit the labels of SDRSS in the


glue language, as arguments to our nonlogical predicates (Asher 1996). Oneof these is (T , a, /?), which can be glossed as 'the constituent labelled by /3 isto be attached to the constituent labelled by a with a rhetorical relation,where a is an available label in the SDRS labelled r that's built so far'. Thereare also: relation symbols for the discourse relations, whose arguments arethe labels (e.g. Explanation(a, /?)); predicates on labels, which allow us tospecify whether the main eventuality described in the SDRS with that label isan event or a state (e.g. event(a) and state(a)); and predicates on the labels,which describe conditions within the SDRSS (e.g. overlap(e,e')(a)). Forexample, the Narration axiom of our glue logic below states: If theconstituent labelled by /? is to be attached to the constituent labelled bya with a rhetorical relation, and those constituents describe events, thennormally, the rhetorical relation is Narration. On the other hand, if /? isstative, then by Background, the rhetorical relation is normally Background:

• Narration: ((T, a, /?) A event(a) Aevent(P)) > Narration(a, 0)• Background: ((T,a,P) Astate(fi)) > Background(a, 0)

For example, Background ensures that Background relates the contents of thefirst and second sentences in (27):

(27) Jack has a son. He is bald.

The language also includes a predicate [ and a function symbol Update.Updatc{r,a,0) returns the SDRS constructed by the glue logic given aninput SDRS T, an attachment point a and T, and a new labelled SDRS /?. [Updatc{r, a, 0) means that updating r with j3 by attaching it to a producesa well-defined SDRS (i.e. there are no unresolved conditions x = ?, and everyconstituent is rhetorically attached to another). We will define SDRS Updateprecisely in a minute and use this to specify constraints on which site a newmaterial /3 should attach to. Once again, it is important to stress that whilethe glue logic has access to the structure of SDRSS—e.g. the conditions withinthem—and indeed reasons about SDRSS, it does not have access to theirdenotations. The glue logic reasons about logical forms of discourses, not(except in the very limited way we have mentioned) about their content

Because the majority of the glue logic axioms feature the connective >,and > does not support a modus ponens-like rule, computing rhetoricalrelations is nonmonotonic The nonmonotonic notion of validity (=» thatunderlies the SDRT glue logic has several desirable properties, which we havediscussed in detail elsewhere (Lascarides & Asher 1993). There are threethat are relevant for our purposes. First, f« validates Defeasible ModusPonens (DMP): when the default laws whose antecedents are verified all haveconsequents that are consistent with the monotonic information and witheach other, then all the consequents are nonmonotonically inferred. Second,


\a validates Specificity: when conflicting default rules apply, the consequentof the most specific default rule (if there is one) is inferred. And finally, \& isrobust in that if F f̂ </>, then F U xp f« <f>, where tp is logically independentinformation.

The glue logic also contains (monotonic) axioms concerning the semanticeffects of rhetorical relations. For example, Axiom on Narration stipulatesthat any items that are connected with Narration must describe eventualitieswhere the first precedes the second (ea -< ep means ot's main eventualityprecedes /?s, and it's a gloss for a formula of the propositional gluelanguage). The Axiom on Background stipulates that the eventualitiesoverlap. And the Spatial Consequence of Narration is derived fromcertain commonplace assumptions about eventualities (Asher et al. 1996):if Narration(a, 0) holds and a and /3 share an actor x then the location ofx is the same at the end of the event ea as it is at the beginning of theevent ep:11

• Axiom on Narration: Narration(a, 0) —> ea -< ep• Axiom on Background: Background(a, 0) —> overlap(ea,ep)• Spatial Consequence of Narration:

(Narration(a, 0) A actor(x, a) A actor(x, /?))—•loc(x,source(ep)) = loc(x,goal(ea))

These rhetorical relations and their inferred semantic effects are used todefine the appropriate update function in SDRT.

As well as axioms for determining a rhetorical relation, we also need toencode constraints on where to attach, because in general more than oneattachment site is available in the SDRS T that's been built so far (e.g. if theprevious constituent a2 was attached to a, with Explanation, then both a,and a2 are available, and new information (3 could potentially bind to eitherone of these). We consider this issue in the particular case when theinformation to be attached is a presupposition. As many authors have noted,there is the intuition that presupposed information conventionally portraysgiven information in some sense (Clark 1977): assigning the presupposedinformation wide scope in SDRT may very well place it in an earlier p r t ofthe discourse context than the one containing the presupposition trigger.To reflect this, we will encode a default version of van der Sandt'spreference for global accommodation (cf. Mercer 1988). This is animportant distinction. In van der Sandt's account, the preference forglobal accommodation always wins, unless the constraints of informative-ness and consistency block it or the information can be bound at somelower site. In our theory, the exceptions to the default preference aren'tenumerable. Any conflicting monotonic rule or more specific default willoverride i t We'll see examples of such rules shortly, and also in section 5.2.


Furthermore, the default preference can be encoded declaratively in SDRT,

in contrast to van der Sandt where the way presuppositions are processedisn't part of the declarative definition of DRT Update.

The declarative rule, which captures a default preference for globalaccommodation, is given below. First some notation: If /? labels assertedcontent, then d{0) is the label for the corresponding presupposed contentSo Prefer Global Attachment says: if a is the most superordinate node in Tto which the presupposition d{0) can attach, then normally, it attachesthere:11

• Prefer Global AttachmentIf a is the most superordinate node in T, then normally: (r , a, d{0))

This default will ensure that global attachment occurs in (1) and (n).However, as we just mentioned, making this rule default allows otherconstraints on SDRT update to override it One particular rule that can dothis is a constraint called Maximize Discourse Coherence, which intuitivelycaptures the idea that people tend to interpret text in the way that makes'most sense'. We have argued elsewhere that such a rule is needed to explaindata where ambiguity resolution and bridging inferences are influenced bya complex interaction between semantics and pragmatics (e.g. Lascarides,Copestake & Briscoe 1996; Asher & Lascarides, in press). The rule we givebelow is a generalization of the rules in those papers. We assume thefollowing notational convention: @ ~% (3l means that Kpi is a DRS whichrepresents one way of resolving the underspecification in Kp.

As background to our rule, we assume that in some contexts, attachingwith one kind of rhetorical relation produces a 'closer connection' or *bettercoherence' than attaching with another kind (see Asher & Lascarides, inpress). To express this, we introduce a strict partial order on rhetoricalrelations, relative to the content of the context: Explanation yT Backgroundmeans that it would be preferable to interpret the new information that isto be attached as an explanation in r, rather than as backgroundinformation. Both alternatives may be coherent, but one is better thanthe other, and this is partly because of the content of r. But it will not dojust to look at the strength of the relation which attaches new information,perhaps resolved or not, to some site in r. We have to compare the strengthof all the discourse relations that are affected by the update. This means thatwe have to compare various updates—viz. those using different attachmentpoints or different resolutions of underspecified elements in the informa-tion 0 to be attached to the discourse context So we will introduce apredicate that says that a particular update is (coherence) maximal withrespect to the new information and the context, which, for a given SDRS T

and new information 0, we write as r, ^-maximal. The semantics of this


notion is given in terms of the above partial order on relations, andcomparing pairs of relations in any two updates under a partial, structuralisomorphism •d whose kernel on all updates is r.'3 We say that an update,Update(T, a,,/?,), is r, /3-maximal iff /? ~** /?, and for any updateL7Jp<iite(r)a1,/32) such that /?~»,/?2: (i) there is a relation R inUpdatelr^^P,) and ti(R) in Update(r, a2,/32) such that R XT •d(R)and (ii) for every relation R in Update(T,an /?,) and i?(R) inUpdate(r, a2,/?2), R yT ti(R)- Since ~>* resolves all underspecificationspresent in the SDRS (an idealization), maximal updates are well defined.

The rule below then captures the following: the underspecified elementsin Kp are normally resolved so as to maximize discourse coherence,regardless of which attachment site is the most superordinate one:

• Maximize Discourse Coherence:If (a) /?~\/?, ;and

(b) Update(T,a,0,) is r, /?-maximal; and(c) a ' is the most superordinate node in r

Then normally:(c) <r,a,/3,>

First, note that this rule has a more specific antecedent than Prefer GlobalAttachment. So it will override that rule, if it conflicts with it But whatcircumstances will produce conflict between these two rules? Suppose that/? labels a presupposition, and therefore there is a condition u = ?, whichencapsulates that the attachment point to which (3 should be rhetoricallylinked is underdetermined. Suppose furthermore that there is a (local)attachment site a; which yields a discourse relation R, between a; and j3,whereas the global attachment site ag results in the rhetorical relation R2

for linking /? to ag. Suppose furthermore that R, is maximal in the partialorder. Then Maximize Discourse Coherence favours resolving the under-specification in (3 so that u = ? resolves to u = a;, and R = ? resolves toR — R,. This means that the attachment point a; is preferred over theglobal site ag according to this rule. However, Prefer Global Attachmentapplies where a& replaces a. And so Prefer Global Attachment yields aconflicting default preference, that the presupposition (3 attach to ag ratherthan Qj. Given that Maximize Discourse Coherence is more specific, thelocal attachment will be chosen over the global one in these circumstances.

This interaction between Prefer Global Attachment and MaximizeDiscourse Coherence will explain why the presupposition that the problemhas been solved in (6) is bound locally, in spite of the default preference for'presupposition projection'.

(6) a. A: The Problem Solving Group is given a problem each day, and thegroup leader Mary has to assign it to someone in her group. John


is the best problem solver. But when he solves a problem, healways boasts about it This annoys Mary, and so if she thinks thatthe day's problem is an unsolved one, she gives it to him, to testhim. Otherwise, she gives it to someone else.

b. B: John's being very quiet just now. Did she give him today'sproblem?

c. A; Well, I'm not sure she did. Either John didn't solve the problem orelse Mary realized that the problem's been solved.

We shall give a detailed analysis of this in section 5.3. We'll also seehow Maximize Discourse Coherence accounts for the conditionalpresupposition in sentence (10) in section 5.2.


Arguably, the most important feature of SDRT update is that it models theway the content of a discourse is more than what's explicitly statedlinguistically. It does this as follows: if the DICE axioms yield a nonmono-tonic conclusion that the rhetorical relation between a and (3 is R, andinformation that's necessary for the coherence of R is not already in Ka orKp (e.g. Background(a, (3) is nonmonotically inferred, but ovtrlap(ea,ep) isnot in Ka or in Kp), then this content is added to the constituents in aconstrained manner through the SDRS update process. Hence the result of anupdating procedure can be not only the addition of a rhetorically connectedconstituent, but also the addition of semantic content to that constituent,that the grammar did not provide.

We're now in a position to define the update procedure in SDRT. Updatein DRT (glossed as UpdateDa:T) is used to define update in SDRT (glossed asUpdatelDn). UpdateDn uses set union:14

• DRT's Update Function:Update^K,,^) = [UKi U UKi][CKi U CKi]

When the discourse context is 'empty' (Le. when we are just starting adiscourse), UpdateSDn is just UpdateDKr But in general, UpdateiDn is muchmore complex. In particular, when the discourse context r is a non-emptySDRS, UpdatetDn requires an available attachment point a in r to beidentified, for attaching the new information (3 to with a rhetorical relation.In general, there is some indeterminacy in this choice of a in spite ofthe default preferences given in DICE, which constrain but may notfully determine which available site to attach new information to. Soto specify the update of old information with new, we need to specify threearguments: KT for the old information K^ (which is on the right frontier ofKT) for the attachment point, and Kp for the new information. We write


this as UpdaUSDKT(KT, Ka, Kp). Moreover, we do not perform set union onKQ and Kp. Rather, they are brought together by computing a rhetoricalrelation between a and (3 in DICE.

Were we to ignore the effects of discourse structure on semantic content,and in particular on the resolution of underspecified conditions, we couldleave the matter here: a non-empty discourse context with an attachmentpoint a, Update^^KTjKajKp) would be a new SDHS KT>, which is justlike KT, except that it also includes: (a) the new information Kp; and (b)an attachment of /? to a with a rhetorical relation R that is computed viaDICE.

However, it is a central point of our theory that the choice of a rhetoricalrelation does affect semantic content, and the resolution of underspecifiedconditions. The update of a discourse context should therefore ensurethat the content of KT, Ka and Kp are modified, so that the coherenceconstraints on R are met (where R(a,j3) is inferred via DICE), andunderspecified conditions are resolved where appropriate. In fact, SDRT

Update is defined so that additional semantic content <p, that's inferrable inDICE from the discourse context and Kp, is added to Kp in the update. Inaddition, ip can be used to resolve underspecified conditions in Kp, Ka, andany Ka' such that a' is attached to a with a rhetorical relation.

A final complexity comes with the need to distinguish several cases. First,we need to specify how updates of a null context with new assertedinformation proceed (clause i below). This case is distinct from the others,because the information is added to the null context, rather than linkedto it with a rhetorical relation. We then need to specify updates of a non-null context with asserted information (clause 2), and with presupposedinformation (clause 3 below). These are different, because of the under-specified rhetorical conditions in presuppositions, which are absent fromasserted information.

We now define Updattlovx formally. As we have just seen, there are threecases: one when the discourse context is empty, one when assertedinformation like (17) is attached to a non-empty discourse context, andone when presupposed information (with underspecified rhetorical condi-tions) is attached to a non-empty discourse context Let \* be the(nonmonotonic) proof theoretic counterpart of the consequence relationfor the glue logic Let Predn be the label of the SDRS constituent in which nis declared, or (equivalently) in which a condition of the form TT : K occurs.And let a[/?/7] be the result of replacing 7 in a with (3. Then UpdateiDn isdefined as follows:

• SDRT'8 Update Function:

1. Updated, 0, [/?][/? : Kp]) = Update^®, [/?][/? : Kp])

Nicholas Ashcr and Alex Lascandes 267

2. For KT ^ 0, UpdateSDn(KT, Ka, [0][0 : Kp]) is the SDRS KT> such that(a) «T> a, 0), A*(«a)(a), »(Kp){0)) h (*(<*, /?) A y»); and(b) KT- = KT[K+/K/w(a)], where:(c) K+ = lVateD R T(K^ ( a ) ) [/?][/? : K0(V)tR(a,fi)]), and

Kp(f) = Kp together with those conditions specified by ip (wheretp is |~ provable) that are needed to satisfy the coherenceconstraints on R; where these conditions (p are also used inKp(<p) to resolve underspecified conditions in Kp (e.g. x = ?); and:

(d) Kpnj/a) is just Kprcjfa) except that it may contain specifications ofunderspecified conditions in Ka>, such that a' = a, or for somerhetorical relation R, R(a', a) or R(a, a') are conditions inKpnJ(a), if those specifications are \^> provable from (/i(Ka)(a),tx(Kp)(P)) znd R(a,0).

3. Fo r K T ^ < b , UpdateSOKt(Kr,Kcn\p]\/3:K0lRo = '!,u = ?i...]) isthe SDRS KT> such that(a) (<T,a,/3>,M(Ka)(c0,M(K/jX/3)) h (R(<*,0) A ¥>); and(b )K r -=K T [K + /Kp^ ( a ) ] , where:(c) K+ = UpdateUK^), [0\\fi : M v > ) , # o = ?,« = ? , . . . ] )

[Ro = R/i^, = ?][« = ct/u = ?], where Kp(ip) is specified asabove, and

(d) K'p^,,} is specified as above.

In words, clause 1 deals with the case when we start a new discourse. Itapplies only to the asserted information of a clause, for the new informationdoes not contain underspecified rhetorical conditions R = ? (in contrast toclause 3). It applies only to asserted content, because clause 1 simply addsthis to the SDRS for the discourse. Doing this with a presupposition wouldproduce an SDRS which contains the unresolved underspecified conditionsR = ? and u = ?, resulting in a representation that's not well-defined.Consequently, at the start of a discourse, one must attach the assertedinformation before one updates this with the presupposed information(using clause 3). However, when continuing a discourse rather than startingit, the relative order for attaching the asserted or the presupposed content ofa sentence is not specified. We'll say more on this shortly.

Clauses 2 and 3 deal with the case when we continue with a discourse(because KT is non-empty). Clause 2 deals with asserted information(because the SDRS /3 does not contain conditions of the form R = ? andM = ?), and clause 3 deals with presupposed information (because theseconditions are present in 0). Let us look at clause 2 first Clause 2 demandsthat you rhetorically connect 0 to a. Clause (2a) ensures that the rhetoricalrelation R that is chosen is the one that results from the DICE axioms. As canbe seen from clauses (2b) and (2c), R(a,0) gets added to the update,


specifically to the constituent that introduced the attachment point a as aspeech act discourse referent Furthermore, a in clause (2a) stands forinformation that follows from DICE when reasoning about how /?attaches to a. Thus ip will include information additional to thatgiven by the grammar, that follows from R's coherence constraints(e.g. if R is Background, ip includes overlap(ea, ep)). Clauses (2b) and (2c)guarantee that this additional semantic content that's inferred via DICE

also gets added, this time to the constituent Kp that was derived via thegrammar. Moreover, (2c) stipulates that ip replaces underspecifiedconditions in Kp with specified ones (in Kp(jp)), if it can (we shallsee many examples where this happens in section 5). Clauses (2c) and(2d) also ensure that information ip that is inferred in DICE resolves asmany underspecified conditions as it can in Kp^^y More precisely,underspecified conditions in the attachment Ka and things that arerhetorically linked to it can be resolved by (p.

Clauses (3a-d) stipulate that updating a discourse with a presuppositionis just like doing it with assertions (Le. clauses (2a-d)): that is, a conditionR(a, 0) is added; Kp gets modified with additional information ip; and Kp,Ka and Ka< (where a ' is attached to a) can have underspecified conditionsresolved by ip. But there's one more thing: the underspecified conditionsRo — ? and u = ? are replaced with RQ = R and u = a. In other words,the rhetorical anaphoric elements in the presupposition reflect therhetorical connection and attachment point that's given by DICE.

Note that UpdateiDm has been defined for attaching only one packet ofinformation to the discourse structure. But the grammar produces morethan one packet of information for each clause: there's one for the assertedcontent, and one for the presupposition. So defining how to update adiscourse with the content of a clause involves refining the definition ofSDRT update, to allow (perhaps) several attachments and their consequentmodifications to the content For the purposes of this paper, we shall assumethat updating the discourse with a clause is defined with respect to a set ofattachment points—one for the asserted information and one for eachdistinct presupposition. This more complex function is simply the result ofsequentially carrying out the procedure of UpdateSDKT as defined above,for the asserted information and each presupposition according to somesequence. In contrast to van der Sandt, we remain agnostic as to whetherupdating with presupposed information or asserted information is donefirst (except for the first clause in the discourse). The result of any sequenceof updates will be viewed as an admissible integration of the newinformation in the discourse.

Overall, the definition of SDRT update guarantees that the way apresupposition is interpreted in discourse is dependent on a complex

Nicholas Aiher and Alex Lascarides 269

mixture of compositional semantic and pragmatic information. This isbecause the DICE axioms that are used to infer R (in clause 3) are based onlinguistic and non-linguistic knowledge. Moreover, the interpretation ofpresuppositions is constrained by a richer notion of accessibility than thatgiven by DRT, since presuppositions can attach to what is SDRT-available, whichin general is a smaller set than what is DRT-accessible. We shall demonstrate inour analysis of examples that these two features overcome some of theproblems with traditional dynamic approaches to presuppositions. Further-more, the above axioms in the glue logic, which constrain which attachmentsite to use, will ensure that updating the context with a presupposition is ingeneral different from doing it with an assertion, in the manner we describedin section 3. In particular, these axioms will determine which attachment sitespresuppositions should attach to, and normally, they will be higher in thestructure than where the corresponding assertion attaches. In other words,presuppositions will tend to have wider scope than assertions.

The definition of Update models the resolution of ambiguity, because itconstrains the updated SDRS to be one where inferences in DICE resolveunderspecified conditions whenever possible (clauses (2c-d) and (3C-d)). Infact, clauses (2d) and (3d) mean that underspecified conditions can beresolved by the way certain other constituents update the discourse (e.g. Ka>can be resolved by the way Kp attaches to KQ, where £(0:', a) holds forsome R). This is what happens in (28):

(28) a. John took an engine from Avon to Dansville.b. He picked up the boxcar,c and took it to Broxburn.

The definite the boxcar in (28b) means that the DRS Kb, which appears in theSDRS that represents the presupposed content of (28b), contains the under-specified bridging relation B = ? to some underspecified antecedent objectv = ?. As in (14), Narration connects the asserted content of (28b), which welabel ba, to the content a of (28a). And as before, this imposes a spatio-temporal constraint, that the boxcar is in Dansville. Thanks to clause (3d),this additional information, that is added to K^ via updatetDKr, resolvesB = ? and v = ? in Kj to B = in and v = Dansville respectively. Thus inthis example, the resolution of content in the presupposition bp isdetermined by the way the asserted content ba attaches to the context a.We'll see the formal details of this example in section 5.3.

4.3 Some remarks about background

We proposed in section 3 that the principal relation that binds presupposi-tions to the context is Background. This captures the intuition that they

Z70 The Semantics and Pragmatics of Presupposition

provide given information. And the DICE rules predict that Background is theprincipal relation, because generally, the constituent in the context or thepresupposition itself is stative (c£ the rule Background).

Since Background plays such an important role in this theory, it is importantto define the constraints it places on the contents of the propositions it connects.This is because these constraints affect the interpretation of presuppositionsthrough UpdatetDWT. Ultimately, Background ensures that presuppositions areconstrained by more than informativeness and consistency.

We have already encountered the temporal constraint on Background,supplied by the Axiom on Background (Lascarides & Asher 1993; Asher et al.1996). There are three other constraints. First, all the so-called simplerhetorical relations (Asher 1993)—such as Background, Narration, Elaboration,Parallel and others—are veridicial: that is, the DRSS associated with the termsthey relate are true:

• Veridicality: If R is simple, then R(a,/3) —> (KaAKp)

This guarantees that the two propositions. There is a King of France and he isbald in the discourse (29), which features Background, are both true:

(29) There is a King of France. He is bald.

Second, both Background and Narration require a common topic This explainswhy discourses like (30) sound odd without any special prior context

(30) a. ??Max walked in. Mary dyed her hair black.b. ??Max smoked a cigarette. Mary had black hair.

The final constraint is designed to account for the behaviour of pronouns indiscourses that feature Background. Compare the text (31)—where (31b)connects to (3 ia) with Background—with (32), where the relation is Narration.

(31) a. A burglar broke into Mary's apartmentb. Mary was asleep.c. He stole the silver.

(32) a. A burglar broke into Mary's apartmentb. Mary discovered the break-in the next day.c. ??He stole the silver.

Asher et al (1996) use (31) vs. (32) to argue that if the discourse features acondition of the form Background(a,(3), then objects introduced in a areavailable for pronominal reference in the proposition 7 that comes after (3.This is not the case for Narration(a,P). But Background is a coordinatingrelation, and therefore a itself is not available. So why are its objectspossible antecedent's to 7's pronouns?

This pronominal behaviour is captured in SDRT via the different kinds oftopics that are constructed for Narrations and Backgrounds (Asher et al


1996). We concentrate here on the topics for Backgrounds. WhenBackground{Truiv1) is inferred, this induces a structural modification to theSDRS. It creates what is known as a Foreground-Background Pair, which contains(i) a constituent ni in which the information of both the backgroundconstituent TT2 and the foreground TT, is 'repeated' (7r3 is the topic and itscontent amounts to UpdateDn(Kni,K^)), (ii) the SDRS which contains theconstituents TT, , n2 and the condition Background^,, n2) forms a constituent,which gets labelled (with, say, 7r4), and (iii) a link between iri and TT4 isintroduced, known as FBP (standing for Foreground-Background Pair): Le.FBP(iri, 7r4) is introduced into the SDRS. Thus whenever an SDRS contains theconditions given in (33), it also contains those given in (34):

(33)

(34)

7 r 3 ) 7 r 4

TT3: V

TT4:

T*JiK""K'7r,,7r2

Background^,, )

Intuitively, the topic n} ensures that the 'main story line' content in KVi is stillaccessible. FBP is a subordinating relation. And so the available constituents towhich future representations of clauses can attach are: 7r3, TT4 and 7r2. Sincethere are referents in the topic ni which denote objects that were introducedin 7r, (since TT3 'repeats' the content of n,), this makes these objects available forfuture anaphoric reference. This predicts, correctly, that the burglar isavailable for anaphoric reference in (31). In contrast, Narrations like thatgiven in (32) do not have this topic structure. Moreover, the constituent TT,which represents the first sentence is not an available attachment site. So thepronoun he in (32c) cannot refer to the burglar, as required.

To handle examples like (30b), we impose the constraint on FBPformation that an FBP can be constructed only if the backgroundingconstituent sets the stage for the foregrounded constituent That is, there mustbe some thematic link between the two constituents that can either bedetermined already from the discourse context or from world knowledge. So


in (30b), we cannot form an FBP because neither the context nor conventionalknowledge have made clear any link between Mary's hair being black andMax's smoking a cigarette. Though we would like to have more to sayabout thematic continuity, at present we must leave the matter here.

We shall see in section 5.3 that the FBP topic structure plays animportant role in constraining the interpretation of presuppositions.However, in many cases, it is not essential to the analysis. So on occasion,we will omit it for the sake of simplicity.

5 THE PRAGMATICS OF PRESUPPOSITIONS

We now analyse some examples of how discourse is updated withpresuppositions. We will start with simple sentences (Le. sentences withoutscope bearing elements), and then move on to complex sentences andmulti-sentence discourse.

5.1 Presuppositions in simple sentences

Consider (15) again.

(15) The King of France is bald.

We must build the SDRS conditions from the grammar, and then use SDRT

update to build the final representation of the sentence. We will give aninformal synopsis first We saw in section 4.1 that the grammar willproduce two SDRSS for (15): one representing the presupposed content thatthere is a King of France, and the other representing the asserted contentthat he is bald. Since this is the first sentence in the discourse, the SDRS forthe whole sentence must be updated with the asserted content first (byadding it to the empty set), since the presupposed content demands a(rhetorical) anaphoric link. Now the presupposed content must be attachedto this asserted content with a rhetorical relation, DICE is used to computethis. The presupposed content is stative, and so the rule Background givenin section 4.2 will mean that the presupposed content is attached withBackground. That is, the SDRS for (15) will amount to: that there is a King ofFrance is Background to his being bald.

Background's topic structure is thus invoked in the analysis of (15), just asit is in any SDRS containing Background. This topic structure does not have acrucial effect here, largely because (15) is a simple sentence and does notfeature the kind of discourse phenomena that are central to our concerns inthis paper. However, we spell out the topic structure in this simple example,for the sake of completeness. In future analyses, in order to simplify matters,


we may omit the topic structure, unless it plays an important role inproducing the right semantic effects.

Let us now go into more detail First, we construct the two SDRSS that thegrammar produces for the presupposed content and the asserted contentThe former includes a bridging relation B between the object denoted bythe King of France and some (anaphoric) antecedent, that must be resolved.As argued in Asher & Lascarides (in press), the definite the King of France is aspecial case, where the grammar itself ensures that France and of serve to fillthe underspecified antecedent object and bridging relation respectively.'5

Therefore, the presupposed content of (15) that is produced by thegrammar is the SDRS p below, its asserted content is a:

(is) a: bald(e,x)

holds(e,t)

tC n

P-

n2,R,v

T T 2 :

v = 1

x,u,e',t'

king(x)

of(e',x,u)

France{u)

holds(e',t')

>

Now the task is to create an SDRS from these two constituents, using thedefinition of SDRT Update. (15) is the first clause in a discourse. So by clause1 of the Update definition, the SDRS when the assertion a is processed is justa itself We must then update this with p. According to clause 3 of SDRT

Update, this involves using DICE to compute a rhetorical relation between7r2 and an available propositional discourse referent In this case, there's onlyone: TT,. Both TT, and TT2'S main eventualities are states, and thereforeBackground applies. So by Defeasible Modus Ponens, BackgrounJ(iT1,iT1) isinferred. That is, that there is a King of France is background to his beingbald. And according to clause 3 of the definition of SDRT Update, theunderspecified conditions R = ? and v = ? need to be replaced withR = Background and v = n, in the updated SDRS.

The condition Background^MTT2) imposes coherence constraints,described in section 4.3. First, by Axiom on Background, overlap(e,J)holds. So, by clause 3 of the SDRT Update definition, this condition mustbe added to Kn2: that is, to the DRS that is labelled ir2 inp above. Second, theabove topic structure is created, since the thematic link constraint is


satisfied by the backgrounding constituent is giving a property of thesubject of the assertion. So the final representation of (15) is (isa):

(15a)

e,t,n,x,u,e',t'

bald(e, x) holds(e, t) t C «, overlap(e, e')

king(x) of(e',x,u) France(u) holds(e',t')

T T 4 :

7 T , :

e,t,n

bald(e,x)

holds(e,t)

( C «

T T 2 :

A(v,*')jR = Background

fan^(x)

#>,«)France(u)

holds{e',t')

overlap(e, e')

The SDRS (15a) entails that there is a King of France, because the axiomVeridicality applies to Background (and to FBP). Moreover, the King ofFrance could be referred to with a pronoun in a subsequent sentence to (15),even though there being a King of France is background information. Thisis because TT3 and n2 are available constituents.

This is a much more complex than the analysis given by van der Sandt(1992). Van der Sandt represents (is) as (isb), and this is identical to hisanalysis of (35):

x,u,e,t,e',t',n

king-of-France(x)

bald(e,x)

holds(e,t)

t Cn

Nicholas Asher and Alex Lascarides 27$

(3 5) A King of France is bald.

In fact, it is also (almost) identical to the topic 7r3 in our representation. Sowe make the same predictions about which antecedents are available forfuture pronominal reference, in continuations of the discourse (15).16 Ouranalysis of (35) is (15b). This is different from the representation (15a) for(15). The difference arises because definites introduce anaphoric elements,including, for instance, the underspecified rhetorical relation R, which mustbe resolved by UpdaUiater Indefinites are not anaphoric in this way.

More importantly, however, our analysis of definites in discourse is moreconstrained than van der Sandt's. Van der Sandt imposes constraints such asinformativeness, consistency, and accessibility. We strengthen these withpragmatics. To illustrate this, consider (36):

(36) ??A woman lives in that house. The man is bald.

According to our theory, the undenpecified bridging relation B and therhetorical relation R that is triggered by the content of the definite in (3 6) mustbe resolved through SDRT Update. ButB cannot be resolved in this case, becausereasoning about the rhetorical link fails to produce a plausible connectionbetween the man and an antecedent object (the woman or the house) (see Asher& Lascarides, in press, for details). In contrast, van der Sandt does not explainwhy (36) is odd; since there is no antecedent man to bind thepresupposition to, one attempts to accommodate it, and since the resultis consistent and informative, the accommodation is successful. So (36) ispredicted on van der Sandt's account to be acceptable, when it is not

$.2 Presuppositions in conditional sentences

Conditional sentences such as (1) and (2) give rise to choices about whereto attach presupposed content, because the Condition relation, that isintroduced by if, is a subordinating relation.


Like van der Sandt, the presupposed content in the consequent can attach inthe global position (Le. to the conditional as a whole), the intermediateposition (Le. to the antecedent) or the local position (Le. to the assertedcontent of the consequent). Our glue logic must therefore yield inferencesabout which attachment site is chosea

Recall Beaver's (1996) idea that the interpretation of presuppositions isinfluenced by which reading is most plausible. One could imagine invokinghere a general Gricean constraint of the form: make all of your attachmentsor presupposed and asserted information so as to make the speaker's


contribution as plausible as possible. We think, however, that the choicebetween attachment points that is governed by plausibility is specificallylinked to conditional contexts and is a matter of discourse coherence. Weclaim that there is a linguistic convention about the strength of a DefeasibleConsequence (or conditional) relation vis a vis a higher attachment withBackground that is affected by plausibility. And it is just such a conventionalcomparison between the strength of discourse relations and attachmentsthat Maximize Discourse Coherence can exploit Indeed, the theory predictsdifferences between (10) and (11), because for (10) Maximize DiscourseCoherence conflicts with the default Prefer Global Attachment and willtherefore override it, whereas in (11) there is no conflict


(11) If David wrote the article, then the knowledge that David is acomputer program running on a PC will confound the editors.

SDRT alone has little to say about plausibility itself In general, this is amatter of extra-linguistic knowledge, and even the task of comparing theplausibility of one scenario over another requires reasoning with arbitrarydomain knowledge. Defining a logic of plausibility would therefore take ustoo far from our main concerns here. So, we'll simply assume that we havesome partial, qualitative or modal notion of comparative plausibility inDICE; PL(a) y PL((3) means a is more plausible than /3.'7

Let us now look at conditional contexts in more detail. Given anattachment of d(C) to B in the context A > B, where > is some standardconditional operator, we would expect A > (B A d(C)) to be equivalent toA > B and A > d(C). This equivalence holds in many conditional logics(for instance, Stalnaker's conditional logic, Lewis's (1973) counterfactuallogics, or the normality conditional of Asher & Morreau 1991 whichunderlies DICE).

One consequence of this is that the attachment of the presuppositiond(C) to the consequent B of a conditional whose antecedent is ^4, isequivalent to attaching A > d(C) to the constituent in which theconditional A > B occurs. So local attachments in this case are equivalentto conditional presuppositions. But since these conditional presuppositionsseem to be preferred in at least some cases, this would go against the vander Sandt proposal of accommodating presuppositions globally wheneverpossible.

Our approach to these conditional presuppositions will be to treat themas cases of binding with Def-Consequence. If we assume that > is theoperator version of the relation Def-Consequence, then such attachments inconditional contexts amount to attaching the presupposed information with

Nicholas Aiher and Alex Lascaiides 277

Def-Consequence. We will suppose in addition that this Defeasible Con-sequence relation can be demonstrated by a deduction, and that theinformation at the attachment point plays an essential role in the derivationof the presupposed information, in the sense that one could not make thederivation without it

In some cases, it is clear that commonly supposed background knowledgeis enough to link presupposition with an appropriate premise via DefeasibleConsequence. For example, consider the pair (37) (due to M. Krifka, p.c):

(37) a. If David is going diving, hell bring his wetsuitb. If David is going diving, he'll bring his dog.

(37a) generates the conditional presupposition:

(38) If David goes diving, then he has a wetsuit

On the other hand (37b) does not It generates the simple presupposition:

(39) David has a dog.

In (37a), general world knowledge allows us to derive defeasibly the factthat David has a wetsuit from the fact that David goes diving. But from thefact that David goes diving we can't derive that he has a dog. Given apreference for binding with Def-Consequence, we will predict this bindingfor (37a) but not for (37b).

Conditional presuppositions need not be generated only from theconsequents of conditionals, however. We can attach presuppositionsgenerated in the antecedent of a conditional to that antecedent with Def-Consequence as well, as in (40a) due to Beaver (p.c):

(40) a. If David is a shepherd and has a good rapport with his dog, he'll geta job on the farm,

b. David is a shepherd and he has a good rapport with his dog.

Once again it appears plausible that we can already defeasibly deriveDavid's having a dog from the fact that he is a shepherd. Note, however,that it is the conditional that licenses this conditional presuppositioa Theconditional presupposition vanishes when there is no conditional in contextas in (40b). Further, the presupposition changes depending on the modalcontext For example in (41) we only get the counterfactual presuppositionthat were David a shepherd, he would have a dog:

(41) If David were a shepherd and had a good rapport with his dog, hewould get a job on the farm.

We claim that conditional or counterfactual presuppositions surface onlyin conditional or counterfactual contexts. In (40a) the presupposition is


attached with Def-Consequence, but because the premises are taken to beasserted as true the defeasible consequence is itself drawn and assumed tohold in the context In cases where the attachment point (and essentialpremise) falls under a modal or conditional context, the defeasible contextcannot be drawn, and the presupposition that is bound by DefeasibleConsequence inherits the modal force of its attachment point Thisinheritance is predicted if we think of the discourse function of theseantecedents of conditionals as conditional or counterfactual assumptionsand we take these conditionals to be closed under the consequence relation'8

• Closure of Conditionals under Consequence: Suppose Def-Cons(a, 0)and Ka => K-y hold, where =>• represents either a normal orcounterfactual conditional Then: Ka =

Let's turn now to the analysis (10) and (11). While (10) generates aconditional presupposition, it is not plausible to claim that general worldknowledge and the discourse context make available the relevant premisesfor deriving the presupposition from the antecedent Such a conclusionwould follow if the context supported particular facts about David, likethe fact that he's not a good logician. But the interesting and puzzlingfact is that the conditional presupposition seems present even when thecontext doesn't support such facts. We claim that people add thesedistinct facts ip as implicatures in order to bind the presupposition withDefeasible Consequence, as long as the assumption of rj) is more plausiblethan the original presupposition. We'll say that one update of r with (3 isstrictly preferred to another when of the pair it is r, /3-maximal, whichwas defined in § 4.2.

• Preference for Binding:Suppose1. Update(r,a,d((3)) links a and d{0) with Def-Consequence, assuming

some extra information xp distinct from KQ^ that is attached to r viaBackground and

2. Update(T,a,,d(P)) links a, and d{0) with Background but notDef-Consequence

Then:Update(T,a,d(f3)) is strictly preferred to Update(T,a,,d(0))

(normally if) and only ifPL(/i(lfy)(*)) is greater than PL(fi(Km)(x)))

Note of course that V could simply be a tautology, in which case theupdate with Def-Consequence will be strictly preferred to the update withBackground without restriction.

This statement on preference of updates will play an important role in

Nicholas Ajher and Alex Lascarides 279

determining whether the presupposition should be locally or globallybound in conditional sentences such as (1), (2), (10) and (11).

Note that the above axiom on its own does not guarantee that a uniqueattachment site is chosen, even for conditional sentences. Heim (1983, 1992)and van der Sandt (1992) note that presuppositions have a conventionalproperty: they project out from embeddings to have the widest scopepossible. In fact, in certain cases, this tendency to project actually seems towin over what's plausible. Consider sentence (11), for example. According tocommon sense, it is more plausible that sentence (42) is true than (43):

(42) If David wrote the article and he's a computer program, then theknowledge that David is a computer program will confound the editors.

(43) David is a computer program, and if he wrote the article, then theknowledge that David is a computer program running on a PC willconfound the editors.

(42) is the reading one gets of (11) if the presupposition attaches in theintermediate position. (43) is the result of global attachment, and corres-ponds to the intuitive interpretation of (11) (since it entails David is acomputer program). So global attachment seems to be favoured here, eventhough the result is the less plausible scenario. These examples show that, incontrast to Beaver (1996), a preference for attaching presuppositions that isbased solely on plausibility cannot be right

It is important to stress that (42) being dispreferred is not a counter-example to the Preference for Binding constraint That axiom togetherwith Maximize Discourse Coherence only rules out a conditional attach-ment, unless it is most plausible. But the presupposition in (42) is notattached with a conditional or Def-Consequence, and so the constraint doesnot apply. There seems to be some tension between deriving a plausiblereading, and the conventional property of presuppositions that they projectto the widest scope. The constraint Preference for Binding and the axiomsof Maximize Discourse Coherence and Prefer Global Attachment reflectthis tension. Prefer Global Attachment will determine that globalattachment occurs in (1) and (11). But Preference for Binding withMaximize Discourse Coherence will override this default to produce localattachment in (10).

With these constraints on conditional attachments in place, let us analyse(1) and (2). Let (i)'s antecedent that baldness is hereditary be represented bya (so Kff| supplies the information that baldness is hereditary):


The consequent (that Jack's son is bald), contains a presupposition, and so itis represented by two constituents ba and bf given below (as before, we haveglossed over the presupposition triggered by the proper name Jack, bymaking the simplifying assumption that Jack is represented by theconstant j}.

(*.) bald(c,x)

holds(e, t)

tC n

(K)T T 3 :

XJson(x)

The SDHS after updating with the first clause is simply a itself. Moreover,because of the cue word if, the grammar produces a Condition relationbetween the speech act discourse referent n, in a and another discoursereferent, which must be equal to or include within its scope the assertedinformation ba of the consequent We will label the result—which includesthe Condition relation, a and ba—with the speech act discourse referent 7r4.

Now SDRS Update must be used to attach the rest of the discourseinformation, namely bf, which is labeled ny Condition is a subordinatingrelation, and so there are three available attachment sites for ny Condition isa subordinating relation, and so there are three available attachment sitesfor TTy either (a) iri binds 'globally', to the speech act discourse referent 7r4;or (b) 7r3 binds in the 'intermediate' position, to 7T,; or (c) TT3 attaches in the'local' position, to 7;2. One must check which of these choices produces acoherent result, and then choose among these coherent alternatives, usingthe axioms we specified earlier.

Attaching ni to TT, is not possible: Background applies, butBackground^,,7T3) cannot be inferred, because a decent topic cannot beconstructed; there is no thematic link between background and foreground,just as there is no thematic link in the incoherent (44).

(44) Baldness is hereditary. Jack has a son.


Neither can we infer Def-Consequence{^\, 7r3), for the auxilliary informationneeded to make the derivation is surely less plausible than the presupposi-tion itself Thus, Preference for Binding does not apply. 7r3 can attach to TT4 orTT2 coherently, both with Background (since Background applies in each case).We claimed earlier that the local attachment corresponds to the reading: Ifbaldness is hereditary, then Jack has a son and he is bald. We can nowexplain why. The Condition relation holds between 7r, and the topic that'sintroduced by the Background relation between TT2 and 7r3, and this topiccontains a 'repeat' of the content given in ba and bp. Thus part of themeaning of this SDRS is that if baldness is hereditary, then Jack has a son.

However, the default Prefer Global Attachment applies and so byDefeasible Modus Ponens, global binding is chosen in this case. The finalanalysis is given in (1') below (in simplified form, since we have notincluded the FBP structure that's introduced by Background):

7T4,7T3

T T 4 :

7r,,7r2

Condition(n,, 7r2)

Background (nA, TT3)

Now consider the analysis of (2). As before, the grammar produces aconstituent a which contains the information in the antecedent clause,which we label TT, again. And it induces a Condition relation between thisand (at least) the asserted information in the consequent So just as with(1), there are three available attachment points for binding TT3 in thepresupposed information bp: n4, TT,, and ir2.

In (1), TT3 could not attach to TT, with a rhetorical relation. But now thesituation is different, because the content of n, is different As we suggestedin section 3, if the content of the new information is a defeasibleconsequence of the content of the proposition to which it is to be attached,then normally, the rhetorical relation Def-Consequence is inferred. This isencapsulated in Defeasible Consequence:

• Defeasible Consequence:«r ,a , /?> A ((A*(«r)(r)

Def-Consequence(a, 0)

The constraints on Def-Consequence are compatible with those onBackground, and so it is possible for both Def-Consequence and Background


to fire, yielding the result that both Def-Consequence(a, 0) andBackground(a, 0) hold. Note also that <f> > (f> is valid for any proposition<f>. So Defeasible Consequence will apply whenever one attempts to attacha presupposition to a constituent of the same content So Preference forBinding holds without restriction, since no extra information is needed toestablish i t Our constraints Preference for Binding and Maximize DiscourseCoherence force us in the analysis of (2) to bind TT3 to 7r, (Le. to bind thepresupposition to the antecedent of the conditional) with Def-Consequence.We therefore infer a binding to the (intermediate) attachment site withBackground and Def-Consequence, even though the presupposition couldcoherently bind at the global level with Background. Thus MaximizeDiscourse Coherence and Preference for Binding capture in a more generalway van der Sandt's principle that binding is preferred over accommoda-tion. And for (2), these axioms predict, correctly, that the presuppositiondoes not project out from the conditional.

In general, whether a presupposition projects from an embedding or notdepends on several things. First, it depends on pragmatic and semanticcontent of the prior discourse and the presupposition, because this is used toreason about which available attachment sites the presupposition cancoherently bind to, and which rhetorical relation to use. Second, theprojection depends on the relative plausibility of the various choices ofattachment (that are coherent). Third, it depends on the relative strength ofthe rhetorical connections provided by various choices of attachment.Finally, it depends on the default which favours attaching presuppositionshigh up in the SDHS structure. Some general results concerning projectionfollow from this. Some of these are given below (for single sentences in thenull context):

1. Projection does not occur in a sentence of the form, if A then B, when thepresupposition triggered by B is a default consequence of A.

2. Projection does occur in a sentence of the form. If A then B, when thepresupposition triggered by B is logically independent of that given byA and plausibilities reflect logical independence in the way thatprobabilities do (note that it can always attach coherently withBackground to the global site, because B will contain sufficient contentthat's similar to its presuppositions so that the topic required byBackground can be constructed).

3. In a sentence of the form A and not B, the presuppositions triggered by Bwill project from the embedding so long as they can coherently attach toA with a rhetorical relation.

To say more in general is tricky, because projection is determined by acomplex interaction between semantic and pragmatic knowledge resources.

Nicholas Asher and Alex Laicarides 283

Furthermore, we view these solutions to the Projection Problem as a sideissue; we are more concerned with addressing the problem of interpretingpresuppositions in multi-sentence discourse.

We now consider the analyses of (10) and (11). Van der Sandt's analysiswas inadequate, because it failed to distinguish their presupposed contents.In our theory, the constraint Preference for Binding accounts for this variation.Consider (10) first The pre-supposition trigger knowledge that <j> generates aprepositional presupposition <f> that must be attached to the context Wewill defeasibly infer <f> if we assume that David is not a good logician. Butthis assumption about one individual seems more plausible than the generalassertion that no good logician was involved.'9 So local binding (to dieasserted information in the consequent) is inferred for (10) via Preference forBinding and Maximize Discourse Coherence in the now familiar way. Incontrast, the information needed to establish an inference from the fact thatDavid wrote the article to the fact that he's a computer program is no moreplausible than David's being a computer program tout court. So the truthfunctional 'only if' part of Conditional Presuppositions forces one toeschew the conditional attachment and to bind the presupposition in (11)non-locally (Le. as Background to the antecedent, or to the whole conditionalstatement). Prefer Global Attachment leads us to infer global attachment,because of the default preference for it Note that global attachment occurseven though the intermediate attachment describes a more plausiblescenario, as we explained earlier. Our theory predicts this, becauseplausibility is a deciding factor only in quite specific circumstances. Thusthe axioms which constrain the update of discourse with presuppositionspredict the difference between (10) and (11).

It is interesting to compare this approach to conditional presuppositionsto that offered by satisfaction theorists (e.g. Beaver 1997). Satisfactionaccounts always generate conditional presuppositions in contexts such as(10). But such conditional presuppositions do not always occur (cf (11)). Sothey have tried to provide accounts for how the unconditional presupposi-tions arise from the conditional ones. Geurts (1996) argues convincinglythat these attempts are flawed. This approach is different the conditionalpresuppositions occur only when Def-Consequence can be inferred.

In section 2, we observed examples where intermediate accommodationis predicted in standard theories of presupposition (e.g. van der Sandt 1992),even though intuitively it should be blocked;

(7) ?? I don't know whether the Pope has measles. But every Catholicrealizes the Pope has measles.

We now examine these examples in more detail. First, note that intermediateaccommodation isn't always blocked:


(45) Nobody regrets leaving school.(46) Everybody takes their children to school.(47) Most people in the neighbourhood take their children to school.

These cases apparently all involve information in the presupposition thatserves to resolve the underspecified elements like the B relation of section4.1 (example 24) generated by the treatment of the generalized quantifiers.Further, it is just these resolutions that will allow us to infer an appropriaterhetorical link between the presupposition generated in the nuclear scopeof the quantification and the restrictor. This predicts that intermediateattachment is allowed in (45-47). The presupposed material in these casesdescribe a property of the 'quantified' discourse referent For instance in(46), the presupposed material is that x has children, where x is thediscourse referent introduced by everybody. So we can set B to the lias'relation, and so relate x to y where y is a discourse referent representing achild of x, and at the same time establish the relevant thematic linkbetween presupposed information arising from the nuclear scope andasserted information in the restrictor so as to establish a coherentBackground relation (and FBP which we omit below for simplicity). Sothe representation of (46) is (46'):

(46') a,:

7 T , :

Background(n, w)

u = 7T,

T T 2 :take-to-xhool(x, y)


In the cases where intermediate accommodation is blocked, the presup-posed information is not of the right type to be identified with thecontextually specified element in the restrictor of the quantifier. Morespecifically, it is not a property of the discourse referent that's beingquantified over. So it doesn't give rise to an appropriate instantiation for thebridging relation B, and thus doesn't provide the appropriate diematiccontinuity for Background. So some and perhaps all of the underspecifiedconditions in the restrictor fail to receive a resolution. Consider for instance(7). The presupposed material that the Pope has measles is not a property ofevery Catholic More precisely, it does not involve the variable introducedby every Catholic. So the presupposed information cannot help resolve thebridging relation B or its other term. And we cannot get a thematic link soas to validate a Background relation between the presupposition and therestrictor; so the presupposition fails to bind to the intermediate position. Aswe explained in section 2, the presupposition should not bind globallybecause of Moore's paradox. Assuming that die constraints on rhetoricalrelations capture this constraint on assertability, global attachment will beblocked in SDRT. In fact, local attachment will also be blocked in this way,note that (48), which is the reading given by local attachment, is alsounassemble:

(48) I don't know whether the Pope has measles. But for every person, ifhe's a Catholic, then the Pope has measles and he realizes the Pope hasmeasles.

So SDRT predicts that (7) is odd.

5.3 Multi-sentence discourse

In this section, we examine presuppositions in multi-sentence discourse.Consider (49):

(49) a. John failed at school years ago.b. He now regrets that

The pronoun that in (49b) introduces a propositional anaphoric discoursereferent One must resolve this to an available discourse referent of thesame type. This gives only one choice: the proposition expressed by (49a).So, the pronoun that is identified with the content of (49a), regardless ofhow the constituents attach together with rhetorical relations. Therefore,the representation of (49a) is a, and the representation (49b) is ba for dieasserted content and bp for the presupposed content (in slighdy simplifiedform):


7r,: fail(j,X)

school(x)

(*.)

7T,

I T , :

(*,)

KVR,V

7r3:

R =

v = l

J,x

fail(j,x)

school(x)

?

' R(y,irs)

We now attempt to update a with bp. Defeasible Consequence applies toft, and TT3. And the temporal and topical constraints on Background aremet, since TT, and TT3 specify the same content So, Updateim yieldsBackgroundfa^iT}) and Def-Consequence(TT, , 7r3) via DICE, and the condi-tion R = ? and v = ? in 6̂ are replaced with R = Background A Def -Consequence and v = TT,.

Furthermore, a topic 7r is built on top of this SDRS n' which contains a, bp

and the Background relation. The content in the topic n is a repeat of thecontent a and ba, which is just a. And FBP(ir, n') holds. This topic structureis important in this case, because it means that the asserted content ba canattach to the content of a, which is 'repeated' in TT—for note that a itself isblocked from attachment by the Background relation with the presupposi-tion. Intuitively, we want the asserted content of (49b) to be connerted tothe content (49a), because there is a causal relation between the action offailing in school and regretting i t The topic n lets us do this. In fact, sincethe presupposed content in this case is exactly that of (49a), attaching TT2 to


the presupposition iri would have been adequate. But this would not be thecase in the slightly modified example, given in (50):

(50) a. John failed at school years ago.b. He now regrets that awful mistake.

Suppose Background did not produce a topic that 'repeated' the contentof (50a) and the presupposition (that there is an awful mistake). Then theregret would have to attach to the awful mistake with a rhetorical relation.So the regret would be caused by the awful mistake, rather than the actionof failing in school and the fact that this was a mistake. By repeating all thecontent in the topic, new elements can attach to both the foreground andbackground information as required.

In (49), therefore, in order to capture this intuition that the regret iscaused by the action described in (49a), we attach vr2 to the topic TT withResult. Therefore, the final representation of (49) is (49'):

(49) a. John failed in school,b. He now regrets that.

(49')

7T, 7T , 7T2

->do

uhool(x)

T T 2 :

FBP(TT, it')

/regret

f

school( *) JResult(ir, 7r2)

T T ' :7 T , : fail(j\x)

school(x)

7r 3 :

; . *

fail(j,x)

school(x)

Background(nt, TT3)

Def-Consequence(nl, •KJ )

(49) is analogous to van der Sandt's binding of presupposed content Inthis case the presupposed information is a defeasible consequence ofthe constituent it attaches to, and it attaches with Background and


Def-Consequence. In contrast, (51) is an example where the presuppositionwould traditionally be accommodated:

(51) a. The US bombing of Baghdad during the Gulf War was muchmore indiscriminate and brutal than the American public was ledto believe.

b. But military commanders will not acknowledge that theircampaign resulted in massive civilian casualties.

(51b)—which we label TTJ—contains the presupposition trigger acknow-ledge, which introduces the presupposition d{itb) that their campaignresulted in massive civilian casualties. The cue phrase but indicates thatthe asserted content (that the military commanders will not acknow-ledge d(ni,)) must attach with Contrast to the discourse context (51a)—which we label na. This Contrast imposes coherence constraints: the twopropositions 7rfl and 717, must have contrasting themes (Asher 1993). Inparticular, the truth of one should lead to an expectation of thenegation of the other. We must check this is the case. We must alsocompute a rhetorical attachment between #(717,) and an availableattachment site. Suppose we attempt to attach dfa) to ira (Le., attach'globally'). Then given that world knowledge supports a defeasibleconsequence relation between na and d(ni,), they are connected withBackground and Defeasible Consequence via Defeasible Modus Ponens onthe rules Background and Defeasible Consequence. If d(ny) attaches thisway, then the coherence constraints on Contrast between TTJ and the(modified) discourse context—which contains na, d(ni,) and a Backgroundbetween them—are verified: there is a contrasting theme between dfa)(which is in the discourse context) and not acknowledge that d(ni,). Thealternative to this is to attach d(ny) 'locally' instead of 'globally': Le. to TTJitself. But this will not produce as strong a contrasting theme. Therefore,the default preference for global attachment wins out by MaximizeDiscourse Coherence, and ensures that d(ni,) attaches to na rather than7TJ,, because this produces the better discourse.

Consider now an example which involves bridging as well aspresupposition satisfaction:

(28) a. John took an engine from Avon to Dansville.b. He picked up the boxcarc and took it to Broxburn.

(28a) is represented as a, while the asserted and presupposed components of(28b) are ba and bp:

Nicholas Ashcr and Alex Lascarides 289

(K)

it,:engtne(Ei) jrom(e,,a)

Avon(a) to(fM<f)

DansvtlU{d) holdsie,,!,)

t, ~< n

*i

TT2:

e>,t2,n

pick-up(e2j,y)

holds(e2112)

t2 ~< n

TT3:

« = '

B = ? B(e,,r,«)M = ? holsd(ei,ti)

boxcar(y)

r3)

According to UpdateSDn, we should check whether there is sufficientinformation in IT, , irz and n} that we can attach them together with rhetoricalrelations, which lead to the underspecified elements in ni being resolved.Suppose we were to try and attach n} to 7r, (or TT2) first 7r3 cannot attach to TT,(or 7T2) with any relation—in particular Narration or Background—because thereis insufficient information in n} to trigger the relevant DICE axioms.

So let us ignore 7r3 for now, and try to attach TT2 to n,, to see if this producespossible resolutions of underspecified elements in ni." And indeed, it does, n,and n2 both describe events, and so Defeasible Modus Ponens on the axiomNarration yields NarTation(n,, n2). We must then accommodate contentarising from Narration's coherence constraints. First, en< occurs before eVl:that is, the taking of the engine from Avon to Dansville occurs before y(which is the boxcar according to Kni) is picked up. Second, by modus


ponens on Spatial Consequence on Narration, the actor John is in the sameplace at the end of taking the engine to Dansville as when he starts to pickup y. By the prepositional phrase in (28a), this is Dansville. And by thelexical semantic content of the phrase picking up, this event starts in thesame location as it finishes, and the object y that's picked up is also at thislocation. Therefore, y is in Dansville.

Thus, the coherence constraints on Narration provide a particular way ofresolving some of the underspecified conditions in the presupposed informa-tion—viz. B resolves to in, and u to d or Dansville. So the definition oWpdatemrr

ensures that B and u are resolved this way. So the content of bp now containssufficient information for us to compute a rhetorical relation between it and thediscourse context since B has resolved to in, e3 is a state. Moreover, attaching n2

to 7T, with Narration has made only n2 available for attachment ThereforeDefeasible Modus Ponens on Background yields Background(7T2,7r3). Thetemporal constraint on Background means that en2 and e^t overlap (Le. pickingup the boxcar and the boxcar being in Dansville temporally overlap). This isas required. Moreover, a topic is computed by creating a new constituent nwith all the content of ba and bf repeated in it, and this is related via FBP to theSDRS IT', which contains ba, bp and the condition Background(ir2,7r3). Becausethis new topic n gets built over the SDRS IT', the original constituent TT, that wasattached with Narration moves up to be attached to TT (for details, see Asher1993 and Asher et al. 1996). The final result is given in (28'):

(28')

n, IT,,

j,Ei,a,d,e,,t

John(j)

engine(Ei)

Avon(a)

Dansville(d)

f, -< n

, »

take(e,,j,Ei)

from(e,,a)to(e,,d)

holds(e,,t,)

Narration(ir,,n)

IT:

y . e a . f i . e j . t j , "

puk-up{e1,j,y)

hoUs(e,,t,)

boxcar{y)

in(evy,d)

t, -< n

hahb(evtj)

FBP(n, n')

I T ' :

7 T , :

holds(el,t1) t, -< n

boxcar(y)

B = in

u — d

B(evy,u)

hoUs(e},ti)

R = Background


Note that we predicted in this analysis that the presupposition is locallyaccommodated to TT2: TT2 must be attached first because ni is notinformative enough, and since the rhetorical relation is Narration, n, isblocked from future attachments. This predicts correctly that the engine in(28a) cannot be an antecedent to a pronoun in a continuation of (28): e.g.?John drove it quickly. However, John drove the engine quickly is a much moreacceptable continuation. And our theory reflects this: the engine requires abridging relation, and computing the bridging relation is possible, byadding to n2 (and hence to the topic TT) the content that the original enginein (28a) (to which 7r2 is linked) is used to pick up the boxcar.

Let us now return to an example which was problematic for van derSandt's account

(4) Either John didn't solve the problem or else Mary realizes that theproblem has been solved.

The presupposition that the problem has been solved cannot bind anywherecoherently, because unresolved bridging relations would remain, which aretriggered by the definite the problem. So sentence (4) is predicted to be odd inthis null context.

However, in the appropriate discourse context, (4) is coherent:

(6) a. A: The Problem Solving Group is given a problem each day, andthe group leader Mary has to assign it to someone in her group.John is the best problem solver. But when he solves a problem,he always boasts about it This annoys Mary, and so if shethinks that the day's problem is an unsolved one, she gives it tohim, to test him. Otherwise, she gives it to another member ofher group.

b. B: John's being very quiet just now. Did she give him today's problem?c A: Well, I'm not sure she did. Either John didn't solve the problem

or else Mary realized that the problem's been solved.

The overall structure of this example is that (6b) is a response to (6a),perhaps some sort of Commentary, while (6c) is a response to the question in(6b) (we'll ignore the internal structure of (6b) here). The disjunction in (6c)offers two, contrasting Explanations to the response Ym not sure. Theexplanations explain why John is behaving quietly (Le. why (6b) is a fact).

How do the presuppositions fit into this structure? A sets up arelationship between Mary and John in (6a); Mary gives problems thatshe believes are unsolved to John, and problems that she believes are solvedto the others. (6b) refers to a problem (today's problem), to which thepresuppositions triggered by the definite the problem in (6c) can bind. Notethat (6b) is available to these for binding, because (6c) is a response to (6b).


So the bridging relation and antecedent are resolved to identity and today'sproblem respectively.

The second sentence in (6c) triggers two further presuppositions. Johndidn't solve the problem presupposes he got the problem, and Mary realized thatthe problem's been solved presupposes that the problem has been solved. Notethat given the content of (6a), this second disjunct also implies, at leastdefeasibly, that John did not get the problem.

Let us look at the binding possibilities for these presuppositions. BindingJohn got the problem locally with Background allows the coherence constraintson Contrast to be satisfied: the first disjunct now implies that John got theproblem, and the second implies that he did not It also ensures that thesecond sentence in (6c) does provide two contrasting Explanations to theanswer in the first sentence of (6c): either (i) John did get the problembecause Mary believed it was unsolved, but he could not solve it, or (ii) hedid not get die problem because Mary believed the problem already had asolution (note diat realize entails believes). In effect both (i) and (ii) allow usto compute answers to B's question as to whether Mary gave John theproblem: (i) implies that he got the problem (and presumably that she gaveit to him); (ii) implies that she did not They both also offer contrastingexplanations for what happened yesterday, and their disjunction explainswhy A is not sure about how to answer B's question.

Now consider what happens if we attempt to bind the presuppositionthat John got the problem globally. In that case, the explanation for the firstsentence to (6c) becomes: John got the problem, and either he did not solveit, or Mary realizes that the problem has been solved. This utteranceimplicates that John got the problem, but from someone other than Mary,because the second disjunct implies that Mary didn't give the problem toJohn. This utterance would form a coherent explanation for John's quietbehavior only if it is interpreted as follows: John got the problem fromsomeone other than Mary, and either he did not solve it, or he did, butbecause Mary realized the problem had been solved and so John did not getthe problem from her, he didn't boast that he has solved it Thus, there aremore assumptions required to support this explanation than for the localbinding case. Intuitively, the explanation for the local binding case isstronger than this one. But then our principle of Maximize DiscourseCoherence predicts that the presupposition ofjohn didn't solve the problem isbound locally.

Now consider the presupposition that the problem has been solved.According to the discourse structure, the problem's been solved could bindlocally to Mary realizes that the problem's been solved, to the first sentence Tmnot sure she did in (6c), or to the question to which (6c) is a response, namelythe utterance (6b). In this case again, the constraints on discourse relations


and discourse update in SDRT determine a preferred attachment site, andonce again Maximize Discourse Coherence plays a crucial role. The Contrastbetween options (i) and (ii) is strengthened if the presupposition of realizebinds locally to Mary realizes the problem's been solved with Background, ratherthan being bound globally. To see this, consider the interpretation of thediscourse under local binding, vs. that given by global binding. The local'interpretation is: Either (i) John got the problem because Mary believes itwas unsolved, but John didn't solve it, or (ii) John didn't get the problembecause the problem has been solved and Mary realized this. The 'global'interpretation is: the problem has been solved, and either (i) John got theproblem because Mary thought it had not been solved, and he failed tosolve it, or (ii) John did not get the problem because Mary realized that theproblem has been solved.

In the local case, Contrast relates two propositions where onecontains the content that John did not solve the problem and theother contains the content that the problem has been solved. Butthe 'global' case does not relate two propositions with this content.Rather, the Contrast in the global case is supported only by the contrast thatis there for the local case too, between John getting the problem and notgetting it So, the Contrast relation is better in the local case than in theglobal one. Therefore, Maximize Discourse Coherence yields the predictionthat the presupposition is bound locally in this discourse, rather thanglobally.

In contrast to van der Sandt (1992) and to Gazdar (1979), we havepredicted local attachment in (6), because of SDRT'S constraints on discourserelations and discourse update. The context in (6) does not implicate thatthe problem has been solved; nor does it implicate that it has not been. Andtherefore one cannot determine that the presupposition should be boundlocally in these theories in virtue of the conversational implicaturessupported by the context, at least in any straightforward interpretation ofGazdar's views. Given what A said in (6a), A and B would know the answerto the question as to whether John got today's problem, if they knew ifMary believed it was solved. This context implicates that A and B do notknow if Mary believes the problems been solved. However, as we explainedearlier, the context does not implicate whether or not A and B themselvesbelieve that the problem has been solved. And so these implications on theirown do not determine whether the presupposition should be boundglobally or locally. Hence, the coherence constraints on Contrast, and thepreference for interpreting discourse in a way that strengthens rhetoricalconnections, both play a crucial role in interpreting the presuppositions inthis example. This demonstrates that constraints imposed by discoursestructure are in general stronger than informativeness and consistency,


and indeed go beyond constraints provided by conversational implicaturealone.

5.4 Presuppositions, cognitive states and global accommodation

We have sketched already in section 5.1 how the constraints on Backgroundrules out many cases of infelicitous accommodation: die presupposition tobe accommodated and the global attachment site do not have the requisitethematic continuity. However, what appears as global accommodationsoften seem felicitous. Consider the following from Vallduvi (1990):

(52) a. A: I bought the President a tray for his Delft china setb. B: That wasn't a good idea. The president [hatesjf the Delft china

set (from Vallduvi 1990)

We claim that in (52) the presupposition introduced by the focussed phrasehates is bound by means of Background to a belief of the interpreter aboutthe speaker. That is, the presupposition binds the presuppositions to whatone reconstructs about the speaker's cognitive states. To reconstruct theElaboration or Explanation given by B's response to A, we need to introducea wide range of assumptions about what B thought was behind A'sutterance. Ordinary theories of focus linked with a theory of presupposition(eg. Rooth 1992) claim that some element of the alternative set for thefocussed expression is presupposed. But the standard view of the pre-suppositions of focus would in this case simply accommodate this element,when the presupposition is in fact bound to what B reconstructs about A'smental state from what A said.21

The possibility that presuppositions can bind via Background or evenDef-Consequence to an interpreter's beliefs to be sure puts some slop into ourdiscourse based account of presupposition. Nevertheless, in contrast to thestandard account, we predict that such so called global accommodationsobey more constraints than consistency and informativity. Our approachwould in principle distinguish between (53) and (54) (Asher & Lascarides, inpress):

(53) The present King of France docs not exist(54) (The man does not exist

In contrast to (15), Background cannot hold between the asserted andpresupposed content in (53), because the two states of the king existingand not existing cannot overlap. We claim that Background holds in (54)between the presupposed information and the cognitive state of the hearer,who is familiar with the concept, the King of France. But as (54) shows, this

Nicholas Asher and Alex Lascaxides 29$

strategy is not available in all cases. With (54) there simply isn't enoughcontent associated with the description to provide the necessary thematiccontinuity and to bind the presupposition to any particular concept viaBackground.

But even in cases where this strategy isn't available, it appears thatsometimes presuppositions can be introduced felicitously in informationthat is 'discourse structure initial' (Le. is simply added and not attached to anempty discourse context). Consider the first sentence from Austen's Senseand Sensibility.

The family of Dashwood had been long settled in Sussex. Their estate was large, and theirresidence was at Norland Park, in the center of their property, where for many generationsthey had lived in so respectable a manner as to engage the general good opinion of theirsurrounding acquaintance.

Austen knows that there is no Dashwood that the reader knows about, butshe fills in the scene during the course of the novel. There is presuppositionfailure but the reader does not really care. He expects the author to tell himmore later. Presupposition in such cases is not anaphoric but cataphoricupon what will come next. The licensing conditions for such cataphors is amatter for future research.

6 CONCLUSION

We have offered a new picture of presuppositions: we have modified vander Sandt's view that they are anaphoric by loosening the notion of binding,thereby foregoing the need for accommodation. We have demonstratedthat there are three main advantages to processing presuppositionsthrough binding them to the context with a rhetorical relation. First,accommodation by addition as in van der Sandt (1992) fails to accountfor the interaction that many have observed between the interpretation ofpresuppositions, domain knowledge and the content of the discoursecontext (e.g. Beaver 1996, 1997; Lascarides & Oberlander 1993). Incontrast, binding material together with rhetorical relations involvesreasoning about domain knowledge and semantic content, and so inessence, we have provided pragmatic constraints on presuppositionsatisfaction that is lacking in current dynamic accounts of presuppositions.Second, through taking rhetorical constraints into account, we model howthe semantic content itself of a presupposition is dependent on pragmaticinformation (e^. (10) vs. (11)), and we model how the level ofaccommodation (Le. global vs. intermediate vs. local) is also pragmaticallydetermined. The result is a more fine-grained analysis of presuppositions


than has been offered so far. Finally, and arguably most importantly, wehave reduced the problem of presupposition satisfaction to the problemof resolving scope ambiguities—a phenomenon that arises in many otherareas of linguistic study.

Acknowledgements

This work is sponsored by a granted funded by ESRC UK (grant number R000236052), andby the ESRC-funded Human Communication Research Centre, University of Edinburgh.We would like to thank David Beaver, Hans Kamp, Rob van der Sandt and an anonymousreviewer for helpful comments on previous drafts.

NICHOLAS ASHERDepartment of Philosophy

University of Texas at Austin

Austin, Texas 78712USA

e-maih [email protected]

ALEX LASCARIDESCentre for Cognitive Science and HCRCUniversity of Edinburgh2, Buccleuch Place

Edinburgh EH8 aLWScotland, UK

e-mail [email protected]

Received: 12.02.98Final version received: 08.02.99

NOTES

1 We are endebted to a reviewer from theJournal of Semantics for pointing this outto us.

2 We could make this notion of informa-tiveness more precise in a way proposedby Michael Morreau: any accommoda-tion of a presupposition <f> m a contextC of a sentence ip must not make rp in Clogically equivalent to \< I u c n thatX ]= (p but it's not the case that <j> |= x-

3 For more on too and Parallel, see Asher(1993) or Asher, Hardt & Busquets

4 In more complex examples, we mayform local SDSSS that are then attachedtogether.

5 The idea of handling presuppositionsatisfaction through computing how it

is rhetorically connected to the dis-course context was used in Lascarides& Oberlander (1993) to process thecontent of when-, before- and after-clauses. This approach is similar inspirit, but more general. We havereplaced their procedural approachwith a declarative one; we haveintegrated semantic and presupposi-tional information into the constructionof an SDES in a compositional way byusing underspecification; and finally, wecover a wider variety of presuppositiontriggers. Furthermore, Lascarides andOberlander ignored the way computinga rhetorical relation can lead to furtherinferences about semantic content, andso they did not model the way the

Nicholas Alter and Alex Lascarides 207

content of the presupposition itself isdetermined by context (e£. (10) vs (11)).

6 One could take an even more extremeposition, and suggest that presuppo-sitions are extra inferred knowledge,which strictly speaking doesn't comprisepart of the semantic content of the textat all. AJ Gazdar (1979) and Mercer(1985) have argued, they arc impli-catures of some kind. We reject thisextreme position. Treating presupposi-tions as part of the semantic contentallows one to record how it affects theinterpretation of other expressions inthe text, such as pronouns (van derSandt 1992).

7 We ignore here and below the con-troversial issue as to whether definitesintroduce a uniqueness requirement (cf.Russell 1905).

8 Indeed, the principal advantage of usingSDKT for investigating presuppositionover other theories of discourse structure(Hobbs et al. 1993; Grosz & Sidner 1986;Polanyi 198s; and others) is that SDRT hasalready explored extensively the inter-action between compositional semanticinformation extracted from the grammarand pragmatic information.

9 Since our main concern is modellingpresuppositions, we will ignore pro-blems of quantifier scope and concen-trate only on the different possible'scopes' of presupposed and assertedinformation.

10 Asher & Lascarides (in press), howeveT,ignored spatio-temporal conditions onwhen the bridging relation holds. Werectify this here by subsuming thebridging within our general treatmentof presuppositions. We demonstratethat resolving the rhetorical connectionbetween the presupposed content andthe discourse context introduces spatio-temporal constraints on that content,which in turn impose the spatio-temporal conditions on the bridgingrelation B in the required way.

11 This spatial constraint applies only to

Narration because, as we have notedelsewhere (Asher & Lascarides 1995), itdoes not apply for all discourse rela-tions. For example Contrast and Parallelhave different spatial constraints, asgiven in Asher & Lascarides (1995, inpress).

12 For simplicity, we have written this rulein words, although it can be encodedusing the modal connective >.

13 This kernel ensures that only the rela-tions in the context change, and not thestructure.

14 Note that this definition holds only forDRSS without conditions of the formx = ?. We gloss over the complicationsthat occur when we countenance suchconditions. They are not relevant forour purposes, since we resolve condi-tions such as these in different waysfrom those in DKT.

1$ This is a slightly simplistic analysis. Forexample, we have ignored die presup-positional content of proper names suchas France, and we have also ignored anyuniqueness conditions that might formpart of the content of Tne King of France.

16 Of course Russell's analysis of (15) isdifferent from ours and van der Sandt'sbecause of his uniqueness condition, butwe won't go into diat here.

17 There are many ways one could developthis notion. For instance, one couldtentatively identify the plausibility of aconditional plausibility of die conse-quent upon die antecedent If so, we'llalso want to assume diat propositionscan have a relative or conditional degreeof plausibility PL(/? I a), just as dicy canhave conditional probabilities (in factplausibility could be interpreted assubjective probability, though we willremain agnostic on diis issue). On dieodicr hand, one might explore a modalapproach to comparative plausibdity,PL(a) >- PL(P) iff there are some aworlds dut are closer to die expectedworlds (given die content of die dis-course so far) dian any P worlds are. But


again to pursue this discussion wouldlead us too far afield.

18 In general we would like to thank DavidBeaver for the examples that led us tothink about conditional presuppositionsgenerated from the antecedents ofconditionals.

19 Given this assumption, there is a logicaldependence between the statementsDavid wrote the article and no good logicianwrote the article. And so the general ruleswe've stated about projection, which

arise from Update^** and die plau-sibility axioms, predicts that the pre-supposition doesn't project from theembedding.

20 Note that clauses (2c-d) and (3C-d) inUpdate^j allow content ip, diat isinferred by attaching ir2 to ir,, toaffect the resolution of underspecifi-cation in n} to occur, because 7r3 willattach to w, or TT,.

21 For some details as to how this storyshould go, see Asher (1095).

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the semantics and pragmatics of presupposition...the semantics and pragmatics of presupposition...

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