Satisfiability of Quantified Boolean Announcements

Abstract

Dynamic epistemic logics consider formal representations of agents' knowledge, and how the knowledge of agents changes in response to informative events, such as public announcements. Quantifying over informative events allows us to ask whether it is possible to achieve some state of knowledge, and has important applications in synthesising secure communication protocols. However, quantifying over quite simple informative events, public announcements, is not computable: such an arbitrary public announcement logic, APAL, has an undecidable satisfiability problem. Here we consider even simpler informative events called Boolean announcements, where announcements are restricted to be a Boolean combination of atomic propositions. The logic is called Boolean arbitrary public announcement logic, BAPAL. A companion paper provides a complete finitary axiomatization, and related expressivity results, for BAPAL. In this work the satisfiability problem for BAPAL is shown to decidable, and also that BAPAL does not have the finite model property.