The Semantics and Pragmatics of Presupposition

In this paper, we offer a novel analysis of presuppositions, paving particular attention to the interaction between the knowledge resources that are required to interpret them. The analysis has two main features. First, we capture an analogy between presuppositions, anaphora and scope ambiguity (cf. van der Sandt 1992), by utilizing semantic underspecification (c£ Reyle 1993). Second, resolving this underspccification requires reasoning about how the presupposition is rhetorically connected to the discourse context. This has several consequences. First, since pragmatic information plays a role in computing the rhetorical relation, it also constrains the interpretation of presuppositions. Our account therefore provides a formal framework for analysing problematic data, which require pragmatic reasoning. Second, binding presuppositions to the context via rhetorical links replaces accommodating them, in the sense of adding them to the context (cf. Lewis 1979). The treatment of presupposition is thus generalized and integrated into the discourse update procedure. We formalize this approach in SDKT (Asher 1993; Lascarides & Asher 1993), and demonstrate that it provides a rich framework for interpreting presuppositions, where semantic 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 in which it is made. Consider, for instance, sentences (i) vs. (2), adapted from van der Sandt (1992); the presupposition triggered by Jack's son (that Jack has a 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 capture contextual effects such as these in an adequate manner. In particular, such a theory must account for why the presupposition in (1) projects from an embedded context, while the presupposition in (2) does not This is a special case 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, then what are the presuppositions of 5? Many recent accounts of presupposition that offer solutions to the Projection Problem have exploited the dynamics in dynamic semantics (e.g. Beaver 1996; Geurts 1996; Heim 1982; van der Sandt 1992). In these frameworks, assertional meaning is a relation between an input context (or information state) and an output context Presuppositions impose tests on the input context, which researchers have analysed in two ways: either the context must satisfy the presuppositions of the clause being interpreted (e.g. Beaver 1996; Heim 1982) or the presuppositions are anaphoric (e.g. van der Sandt 1992) and so must be bound to elements in the context But clauses carrying presuppositions can be felicitous even when the context fails these tests (e.g. (1)). A special purpose procedure known as accommodation is used to account for this (cf. Lewis 1979): if the context fails the presupposition test, then the presupposition is accommodated or added to it, provided various constraints are met (e.g. the result must be satisfiable). This combination of test and accommodation determines the projection of a presupposition. For example, in (1), the antecedent produces a context which fails the test imposed by the presupposition in the consequent (cither satisfaction or binding). So it is accommodated. Since it can be added to the context outside the scope of the conditional, it can project out from its embedding. In contrast, the antecedent in (2) ensures that the input context passes the presupposition test So the presupposition is not accommodated, the input context is not changed, and the presupposition is not projected out from the conditional. Despite these successes, this approach has trouble with some simple predictions. Compare the following two dialogues (3abc) and (3abd): (3) a. A: Did you hear about John? b. B: No, what?  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 between these two discourses and would find them both acceptable. But (3abd) is unacceptable. As it stands it lacks discourse coherence, while (3abc) does not; the presupposition of the car cannot be accommodated in (3abd). We will argue that the proper treatment of presuppositions in discourse, like a proper treatment of assertions, requires a notion of discourse coherence and must take into account the rhetorical function of both presupposed and asserted information. We will provide a formal account of presuppositions, which integrates constraints from compositional semantics and pragmatics in the required manner. Nicholas Asher and Alex Lascaridn 241 We will start by examining van der Sandt's theory of presupposition satisfaction, since he offers the most detailed proposal concerning accommodatioa We will highlight some difficulties, and offer a new proposal which attempts to overcome them. We will adopt van der Sandt's view that presuppositions are anaphoric, but give it some new twists. First, like other anaphoric expressions (e.g. anaphoric pronouns), presuppositions have an underspecified semantic content Interpreting them in context involves resolving the underspecification. The second distinctive feature is the way we resolve underspecification. We assume a formal model of discourse semantics known as SDRT (e.g. Asher 1993; Lascarides & Asher 1993). where semantic underspecification in a proposition is resolved by reasoning about the way that proposition rhetorically connects to the discourse context Thus, interpreting presuppositions becomes a part of discourse update in SDRT. This has three important consequences. The first concerns pragmatics. SDRT provides an explicit formal account of how semantic and pragmatic information interact when computing a rhetorical link between a proposition and its discourse context This interaction will define the interpretation of presuppositions, and thus provide a richer source of constraints on presuppositions than standard accounts. This account of presuppositions will exploit pragmatic information over and above the clausal implicatures of the kind used in Gazdar's (1979) theory of presuppositions. We'll argue in section 2 that going beyond these implicatures is necessary to account for some of the data. The second consequence of interpreting presuppositions is SDRT concerns accommodation. In all previous dynamic theories of presupposition, accommodation amounts to adding, but not relating, the presupposed content to some accessible part of the context This mechanism is peculiar to presuppositions; it does not feature in accounts of any other phenomena, including other anaphoric phenomena. In contrast, we model presuppositions entirely in terms of the SDRT discourse update procedure. We replace the notion that presuppositions are added to the discourse context with the notion that they are rhetorically linked to it Given that the theory of rhetorical structure in SDRT is used to model a wide range of linguistic phenomena when applied to assertions, it would be odd if presupposed information were to be entirely insensitive to rhetorical function. We will show that presupposed information is sensitive to rhetorical function and that the notion of accommodation should be replaced with a more constrained notion of discourse update. The third consequence concerns the compositional treatment of presupposition. Our approach affords that one could call a compositional treatment of presuppositions. The discourse semantics of SDRT is The Semantics and Pragmatics of Presupposition compositional upon discourse structure: the meaning of a discourse is a function of the meaning of its parts and how they are related to each other. In SDRT presuppositions, like assertions, generate underspecified but interpretable logical forms. The procedure for constructing the semantic representation of discourse takes these underspecified logical forms, resolves some of the underspecifications and relates them together by means of discourse relations representing their rhetorical function in the discourse. So presuppositions have a content that contributes to the content of the discourse as a whole. Indeed, presuppositions have no less a compositional treatment than assertions. Our discourse-based approach affords a wider perspective on presuppositions. Present dynamic accounts of presupposition have concentrated on phenomena like the Projection Problem. For us the Projection Problem amounts to an important special case, which applies to single sentence discourses, of the more general 'discourse' problem: how do presuppositions triggered by elements of a multi-sentence discourse affect its structure and content? We aim to tackle this question here. And we claim that a rich notion of discourse structure, which utilizes rhetorical relations, is needed. While we believe that our discourse based theory of presupposition is novel, we hasten to add that many authors on presupposition like Beaver (1996) and van der Sandt (1992) would agree with us that the treatment of presupposition must be integrated with a richer notion of discourse structure and discourse update than is available in standard dynamic semantics (e.g. Kamp & Reyle's DRT, Dynamic Predicate Logic or Update Semantics), because they believe that pragmatic information constrains the interpretation of presuppositions. We wish to extend their theories with this requisite notion of discourse structure. 2 VAN DER SANDT'S DYNAMIC A C C O U N T AND ITS PROBLEMS Van der Sandt (1992) views presuppositions as anaphors with semantic content 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 t