Interpreting Presuppositions Using Active Logic: From Contexts to Utterances

Presuppositionis a pervasive feature of human language. It involves many interesting interactions between the utterances of a discourse and the contextof the discourse. In this paper we focus on issues of logical form connected with the interaction of presupposition and discourse context, and illustrate our theory with some implementational work using the active logicframework. After reviewing some of the major issues in presupposition theory we turn to a largely successful unified approach of Heim. We show how the main principles of this theory can be implemented in active logic. But we also find two serious difficulties. These consist in (a) a straightforward counterexample and (b) a type of discourse that we call a garden-path discourse. We maintain that both the counterexample and the garden-path type of discourse can be handled by our active-logic version of Heim's theory. This requires us to reformulate and extend Heim's theorey. Although this work is largely theoretical, both Heim's theory and ours have important things to say about the incremental processing of the utterances that make up discourse. And we present our theory as a specification of a processing device that takes logical form of a sentence along with current discourse context as input and delivers an updated discourse context as output. As an experiment, we have implemented portions of this device.