Logics of public communications

Synthese 158 (2):165 - 179 (2007)
Multi-modal versions of propositional logics S5 or S4—commonly accepted as logics of knowledge—are capable of describing static states of knowledge but they do not reflect how the knowledge changes after communications among agents. In the present paper (part of broader research on logics of knowledge and communications) we define extensions of the logic S5 which can deal with public communications. The logics have natural semantics. We prove some completeness, decidability and interpretability results and formulate a general method that solves certain kind of problems involving public communications—among them well known puzzles of Muddy Children and Mr. Sum & Mr. Product. As the paper gives a formal logical treatment of the operation of restriction of the universe of a Kripke model, it contributes also to investigations of semantics for modal logics.
Keywords Logics of knowledge  Communications  Kripke models  (applicable in) expert systems
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References found in this work BETA
Jaakko Hintikka (1962). Knowledge and Belief. Ithaca, N.Y.,Cornell University Press.

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Johan van Benthem (2007). Dynamic Logic for Belief Revision. Journal of Applied Non-Classical Logics 17 (2):129-155.

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