A Uniform Treatment of Pragmatic Inferences in Simple and Complex Utterances and Sequences of Utterances

Drawing appropriate defeasible inferences has been proven to be one of the most pervasive puzzles of natural language processing and a recurrent problem in pragmatics. This paper provides a theoretical framework, called stratified logic, that can accommodate defeasible pragmatic inferences. The framework yields an algorithm that computes the conversational, conventional, scalar, clausal, and normal state implicatures; and the presuppositions that are associated with utterances. The algorithm applies equally to simple and complex utterances and sequences of utterances. 1 Pragmatics and Defeasibility It is widely acknowledged that a full account of natural language utterances cannot be given in terms of only syntactic or semantic phenomena. For example, Hirschberg (1985) has shown that in order to understand a scalar implicature, one must analyze the conversants’ beliefs and intentions. To recognize normal state implicatures one must consider mutual beliefs and plans (Green, 1990). To understand conversational implicatures associated with indirect replies one must consider discourse expectations, discourse plans, and discourse relations (Green, 1992; Green and Carberry, 1994). Some presuppositions are inferrable when certain lexical constructs (factives, aspectuals, etc) or syntactic constructs (cleft and pseudo-cleft sentences) are used. Despite all the complexities that individualize the recognition stage for each of these inferences, all of them can be defeated by context, by knowledge, beliefs, or plans of the agents that constitute part of the context, or by other pragmatic rules. Defeasibility is a notion that is tricky to deal with, and scholars in logics and pragmatics have learned to circumvent it or live with it. The first observers of the phenomenon preferred to keep defeasibility outside the mathematical world. For Frege (1892), Russell (1905), and Quine (1949) “everything exists”; therefore, in their logical systems, it is impossible to formalize the cancellation of the presupposition that definite referents exist (Hirst, 1991; Marcu and Hirst, 1994). We can taxonomize previous approaches to defeasible pragmatic inferences into three categories (we omit here work on defeasibility related to linguistic phenomena such as discourse, anaphora, or speech acts). 1. Most linguistic approaches account for the defeasibility of pragmatic inferences by analyzing them in a context that consists of all or some of the previous utterances, including the current one. Context (Karttunen, 1974; Kay, 1992), procedural rules (Gazdar, 1979; Karttunen and Peters, 1979), lexical and syntactic structure (Weischedel, 1979), intentions (Hirschberg, 1985), or anaphoric constraints (Sandt, 1992; Zeevat, 1992) decide what presuppositions or implicatures are projected as pragmatic inferences for the utterance that is analyzed. The problem with these approaches is that they assign a dual life to pragmatic inferences: in the initial stage, as members of a simple or complex utterance, they are defeasible. However, after that utterance is analyzed, there is no possibility left of cancelling that inference. But it is natural to have implicatures and presuppositions that are inferred and cancelled as a sequence of utterances proceeds: research in conversation repairs (Hirst et al., 1994) abounds in such examples. We address this issue in more detail in section 3.3. 2. One way of accounting for cancellations that occur later in the analyzed text is simply to extend the boundaries within which pragmatic inferences are evaluated, i.e., to look ahead a few utterances. Green (1992) assumes that implicatures are connected to discourse entities and not to utterances, but her approach still does not allow cancellations across discourse units. 3. Another way of allowing pragmatic inferences to be cancelled is to assign them the status of defeasible information. Mercer (1987) formalizes presuppositions in a logical framework that handles defaults (Reiter, 1980), but this approach is not tractable and it treats natural disjunction as an exclusive-or and implication as logical equivalence. Computational approaches fail to account for the cancellation of pragmatic inferences: once presuppositions (Weischedel, 1979) or implicatures (Hirschberg, 1985; Green, 1992) are generated, they can never be cancelled. We are not aware of any formalism or computational approach that offers a unified explanation for the cancellability of pragmatic inferences in general, and of no approach that handles cancellations that occur in sequences of utterances. It is our aim to provide such an approach here. In doing this, we assume the existence, for each type of pragmatic inference, of a set of necessary conditions that must be true in order for that inference to be triggered. Once such a set of conditions is met, the corresponding inference is drawn, but it is assigned a defeasible status. It is the role of context and knowledge of the conversants to “decide” whether that inference will survive or not as a pragmatic inference of the structure. We put no boundaries upon the time when such a cancellation can occur, and we offer a unified explanation for pragmatic inferences that are inferable when simple utterances, complex utterances, or sequences of utterances are considered. We propose a new formalism, called “stratified logic”, that correctly handles the pragmatic inferences, and we start by giving a very brief introduction to the main ideas that underlie it. We give the main steps of the algorithm that is defined on the backbone of stratified logic. We then show how different classes of pragmatic inferences can be captured using this formalism, and how our algorithm computes the expected results for a representative class of pragmatic inferences. The results we report here are obtained using an implementation written in Common Lisp that uses Screamer (Siskind and McAllester, 1993), a macro package that provides nondeterministic constructs. 2 Stratified logic 6 6 * H H H H HY 6 6 * H H H H HY ⊥ ⊤