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Common knowledge logic and game logic

Published online by Cambridge University Press:  12 March 2014

Mamoru Kaneko
Mamoru Kaneko*
Affiliation:
Institute of Policy and Planning Sciences, University of Tsukuba, Ibaraki 305, Japan E-mail: [email protected]
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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.

Keywords

Game LogicCommon Knowledge LogicFixed-Point and Iterative Definitions of Common KnowledgeNash Equilibrium
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 2 , June 1999 , pp. 685 - 700
Copyright
Copyright © Association for Symbolic Logic 1999

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References

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