Quantified Announcements and Common Knowledge

Abstract

Public announcement logic (PAL) extends multi-agent epistemic logic with dynamic operators modelling the effects of public communication. Allowing quantification over public announcements lets us reason about the existence of an announcement to reach a certain epistemic goal. Two notable examples of logics of quantified announcements are arbitrary public announcement logic (APAL) and group announcement logic (GAL). The notion of common knowledge plays an important role in PAL, and in particular in characterisations of epistemic states that an agent or a group of agents might make come about by performing public announcements. In this paper, we study extensions of APAL and GAL with common knowledge, which has not been done before. We consider both conservative extensions where the semantics of the quantifiers is not changed, as well as extensions where the scope of quantification also includes common knowledge formulas. We compare the expressivity of these extensions relative to each other and other connected logics, and provide sound and complete axiomatisations.