Common knowledge logic and game logic

Journal of Symbolic Logic 64 (2):685-700 (1999)
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Abstract

We show the faithful embedding of common knowledge logic CKL into game logic GL, that is, CKL is embedded into GL and GL is a conservative extension of the fragment obtained by this embedding. Then many results in GL are available in CKL, and vice versa. For example, an epistemic consideration of Nash equilibrium for a game with pure strategies in GL is carried over to CKL. Another important application is to obtain a Gentzen-style sequent calculus formulation of CKL and its cut-elimination. The faithful embedding theorem is proved for the KD4-type propositional CKL and GL, but it holds for some variants of them.

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Citations of this work

About cut elimination for logics of common knowledge.Luca Alberucci & Gerhard Jäger - 2005 - Annals of Pure and Applied Logic 133 (1):73-99.
Strong Completeness Theorems for Weak Logics of Common Belief.Lismont Luc & Mongin Philippe - 2003 - Journal of Philosophical Logic 32 (2):115-137.

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References found in this work

Game logic and its applications I.Mamoru Kaneko & Takashi Nagashima - 1996 - Studia Logica 57 (2-3):325 - 354.
Languages with Expressions of Infinite Length.William P. Hanf - 1964 - Journal of Symbolic Logic 33 (3):477-478.

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