The Epistemics of Presupposition Projection

Pragmatic accounts of presupposition projection go back to work of Karttunen and Stalnaker, who proposed that presuppositions are requirements on the common ground and that their projection behaviour should follow from the way this common ground is updated in a discourse. This idea has been worked out by various authors who made the idea of shifting context precise, most notably Heim 1983, and presupposition projection has been a major topic in dynamic semantics of natural language ever since, although there have been dissenting voices, see e.g. Schlenker 2007. Recent advances in the logic of announcements and knowledge — the logic of public announcements of Plaza 1989, the action style dynamics of Baltag et al. 1999, and the axiomatisation of a very general logic of communication and change in van Benthem et al. 2006 — make it possible to have another go at formalizing the intuitions of Karttunen and Stalnaker. This task is taken up in this paper. Context is represented (not as a set of propositions but) as a multimodal Kripke model, utterances are (public) announcements, sequencing is uttering one announcement after another, context shift is epistemic updating, common ground is common knowledge between discourse participants (or, more subtly, knowledge that the speaker believes to have in common with the audience), and basic presuppositions are checks on common knowledge. We will show that the core of presupposition projection facts then follows from the way in which announcements are composed in dynamic epistemic logic.