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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Schematic Validity in Dynamic Epistemic Logic: Decidability
verfasst von : Wesley H. Holliday, Tomohiro Hoshi, Thomas F. Icard III
Erschienen in: Logic, Rationality, and Interaction
Verlag: Springer Berlin Heidelberg
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Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitution. The classic example is Public Announcement Logic (
PAL
), an extension of epistemic logic based on the idea of information acquisition as elimination of possibilities. In this paper, we address the open question of whether the set of
schematic validities
of
PAL
, the set of formulas all of whose substitution instances are valid, is decidable. We obtain positive answers for multi-agent
PAL
, as well as its extension with relativized common knowledge,
PAL-RC
. The conceptual significance of substitution failure is also discussed.