DRT with Local Contexts1

In this note, we reconstruct some results of the DRT analysis of presupposition projection within the theory of local contexts of Schlenker 2009. The latter offered a way to annotate every sentence with variables that denote the various local context sets that play a crucial role in Heim’s satisfaction theory (Heim 1983). In standard satisfaction theories, a presupposition must be entailed by its local context. Here we allow a presupposition to be indexed with other local contexts, and we propose – following van der Sandt 1992 and Zeevat 1992 – that presuppositions are preferably anaphoric to the highest possible context. The resulting analysis emulates some desirable results of DRT – notably its solution to the ‘Proviso Problem’ (Geurts 1999). But it arguably improves on DRT in some respects: it can generate genuine conditional presuppositions; and it yields more adequate results for some quantified examples. Several limitations of the theory – some of them quite severe – are also discussed. In earlier work, we proposed an algorithm that annotates every sentence with context variables on propositional and predicative expressions (Schlenker 2009). These variables denote the ‘context sets’ that play a crucial role in Heim’s dynamic theory of presupposition projection (Heim 1983). Modulo certain assumptions, the resulting theory is equivalent to Heim’s, but it does without dynamic lexical entries: the value of the context variables can be predicted once the syntax and the classical semantics of a sentence have been specified (in Heim’s framework, by contrast, dynamic lexical entries could be stipulated at will, which made the analysis insufficiently explanatory). In this earlier work, we followed Heim’s satisfaction theory in claiming that a presupposition must be entailed by its local context. But since in our analysis context variables can be explicitly represented in Logical Forms, we can also explore a different analysis, much closer to the spirit of Discourse Representation Theory (DRT, van der Sandt 1992, Geurts 1999). We briefly sketch this theory and list some cases in which it improves on orthodox DRT, and others in which it inherits some of its difficulties, or must be refined to match its results. The present note attempts, like Zeevat 1992, to unify Heim’s theory and DRT. But the strategy we adopt is very different from Zeevat’s, in at least two respects: first, Zeevat assumed a rich dynamic semantics, whereas we start from a notion of local contexts which is entirely derivative on a classical semantics; second, Zeevat ‘semanticized’ DRT’s representational analysis by appealing to stacks of information states to keep track of the possible antecedents of presuppositions – whereas we directly encode the connection between a trigger and its antecedent in the syntax (we leave for future research a systematic comparison with Zeevat’s system). The definition of local contexts used in Schlenker 2009 is given in Appendix I. For present purposes, the reader may simply assume that our context variables denote the local contexts of Heim’s analysis. Typographically, a context variable appears as a superscript right before the expression whose local context it provides. Let us give three examples. (i) Take a sentence F uttered in a (global) context set C. In 0F, which is F decorated with the local context variable c0, the latter just denotes C. 1 Many thanks to Emmanuel Chemla, Bart Geurts and an anonymous referee for suggestions and criticisms on an earlier version. All errors are mine.