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Reverse public announcement operators on expanded models. (English) Zbl 1441.03016

Summary: Past public announcement operators have been defined in [T. Hoshi and A. Yap, Synthese 169, No. 2, 259–281 (2009; Zbl 1184.03009); A. Yap, in: Dynamic formal epistemology. Berlin: Springer. 33–50 (2011; Zbl 1260.03028)] 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version of \(\mathcal {M}\) that makes our operators potentially useful for studying non-standard interpretations of rescinded announcements in PAL.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 Y. Zhang and Y. Zhou [Artif. Intell. 173, No. 16–17, 1525–1537 (2009; Zbl 1187.03015)]. We show that the logic resulting from adding reverse announcements to PAL is sound and complete.

MSC:

03B42 Logics of knowledge and belief (including belief change)
03B45 Modal logic (including the logic of norms)
Full Text: DOI

References:

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