Reverse Public Announcement Operators on Expanded Models

Abstract

Past public announcement operators have been defined in Hoshi and Yap (Synthese 169(2):259–281, 2009) and Yap (Dynamic logic montreal, 2007), to describe an agent’s knowledge before an announcement occurs. These operators rely on branching-time structures that do not mirror the traditional, relativization-based semantics of public announcement logic (PAL), and favor a historical reading of past announcements. In this paper, we introduce reverse public announcement operators that are interpreted on expanded models. Our model expansion adds accessibility links from an epistemic model $$\mathcal {M}$$ to a filtrated submodel of the canonical model for $$\mathbf K _g$$ . Here $$\mathbf K _g$$ is the minimal normal modal logic together with $$\mathbf S5 $$ axioms for the universal operator U. This yields a highly general pre-announcement version of $$\mathcal {M}$$ that makes our operators potentially useful for studying non-standard interpretations of rescinded announcements in PAL. Indeed, we find that our reverse announcement operators cannot be represented by product update, and that they have an intimate connection with the knowledge forgetting of Zhang and Zhou (Artif Intell J 173(16–17):1525–1537, 2009). We show that the logic resulting from adding reverse announcements to PAL is sound and complete.