Active Logic and Heim's Rules for Updating Discourse Context

Discourse unfolds in time, giving rise to a cascade of belief changes in the listener. Yet this temporal evolution of discourse and belief is typically ignored in theoretical treatments of discourse. It has been claimed (see Soames Soames, 1989]) that Heim's Heim, 1983] theory of discourse context accounts for non-implicative discourse updating. We will present a new non-implicative discourse that cannot be accounted for with Heim's use of global or local accommodation and which appears to require attention to evolution of discourse. We use this example to motivate re-making Heim's update function, aimed toward a uniied approach to discourse|one in which Heim's rules for discourse updating can account for more of the problem cases for the theory of discourse context. These rules and the revised update function can then serve as principles that constrain the building of representations for discourse context (such as the Discourse Representation Structures, of Discourse Representation Theory, Kamp and Reyle, 1993]). We propose active logic as a convenient tool for executing the required inferences (as called for by our revised version of Heim's update function) as the discourse evolves through time. 1 Background on active logic and presupposition. is a family of formalisms developed for the purpose of modeling the reasoning process in a way that respects the passage of time as reasoning proceeds. That is, the reasoner may have beliefs (draw inferences) concerning what time it is (now), and these are updated during reasoning since what time it is changes during reasoning. Moreover, this update is itself reasoned, i.e., governed by the same inferential processes as the rest of the reasoning. These formalisms have been applied to a number of domains, from multi-agent interaction to deadline-coupled planning, from fully-decidable default reasoning to reasoning in the presence of contradictions, from correcting misidentiication errors to perceptual reference. Active-logic formalisms can have time-sensitive inference rules. The most obvious case of such a rule is the \clock-rule": from Now(t) the time is now t] infer Now(t+1) the time is now t+1] (and do not retain Now(t) as a belief). In such a logic, the update (or truth-maintenance) in which new information is integrated into the belief base, is not a separate process from the drawing of (defeasible) conclusions. Rather than proceeding from one nonmonotonic theory (with one set of axioms) to another nomonotonic theory (with an updated set of axioms) there is one evolving theory in which the evolution …