The Epistemics of Presupposition Projection (Abstract)

Accounts of presupposition and presupposition projection almost invariably go back to Karttunen [4, 5] and Stalnaker [9, 10]. These authors proposed an explanation for the fact that the presupposition of a conjunction A ∧ B consists of the presupposition of A conjoined with the implication assA → presB. When a speaker utters this conjunction, she may take it for granted that A after she has uttered this first conjunct. So even if A is not presupposed initially, it will be presupposed by the time she gets to assert B, for now the context has shifted to encompass A. This idea has been worked out by various authors who have tried to make the idea of shifting context precise, most notably Heim [3], and presupposition projection has been a major topic in dynamic semantics of natural language ever since, although there have been dissenting voices, witness the recent attack by Schlenker [7]. Recent advances in the logic of announcements and knowledge — the logic of public announcements of Plaza [6], the action style dynamics of Baltag cs [1], and the axiomatisation of a very general logic of communication and change by Van Benthem cs [2] — 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 partipants (or, more subtly, knowledge that the speaker believes to have in common with the audience). Indeed, it is obvious that the machinery is available for a dynamic epistemic account of presupposition, but as far as we know we are the first to actually carry out such a task. We will show that the core of proposition projection facts follows from the way in which announcements are composed in dynamic epistemic logic. Asserting A and next asserting B boils down to the same thing as making a single assertion ‘A holds, and, after I assert A, B will hold’. In dynamic epistemic logic with announcements this is made precise by the following equivalence: