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Journal of Logic, Language and Information

, Volume 27, Issue 3, pp 205–224 | Cite as

Reverse Public Announcement Operators on Expanded Models

  • Ryuichi Sebastian Haney
Article

Abstract

Past public announcement operators have been defined in Hoshi and Yap (Synthese 169(2):259–281, 2009) and Yap (Dynamic logic montréal, 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version of \(\mathcal {M}\) that makes our operators potentially useful for studying non-standard interpretations of rescinded announcements in PAL.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.

Keywords

Modal logic Epistemic logic Public announcement logic Dynamic epistemic logic 

Notes

Acknowledgements

I would like to thank Dr. Tomohiro Hoshi for his extensive guidance and commentary as I wrote this paper. I am grateful to him for introducing me to logic, and I was very lucky to have him as a mentor. I would also like to thank my reviewers for their comments on this paper, which helped to improve it significantly.

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of VirginiaCharlottesvilleUSA

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