Schematic validity in dynamic epistemic logic: decidability

Authors:
Wesley H. Holliday;Tomohiro Hoshi;Thomas F. Icard, III
Affiliations:
Logical Dynamics Lab, Center for the Study of Language and Information, Stanford, CA and Department of Philosophy, Stanford University;Logical Dynamics Lab, Center for the Study of Language and Information, Stanford, CA and Logical Dynamics Lab, Center for the Study of Language and Information, Stanford, CA and Department of Phil ...;Logical Dynamics Lab, Center for the Study of Language and Information, Stanford, CA and Logical Dynamics Lab, Center for the Study of Language and Information, Stanford, CA and Department of Phil ...
Venue:
LORI'11 Proceedings of the Third international conference on Logic, rationality, and interaction
Year:
2011

Citing 5
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Abstract

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.