Journal of Symbolic Logic

Common Knowledge Logic and Game Logic

Mamoru Kaneko

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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.

Article information

Source
J. Symbolic Logic, Volume 64, Issue 2 (1999), 685-700.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745802

Mathematical Reviews number (MathSciNet)
MR1777779

Zentralblatt MATH identifier
0929.03023

JSTOR
links.jstor.org

Keywords
Game Logic Common Knowledge Logic Fixed-Point and Iterative Definitions of Common Knowledge Nash Equilibrium

Citation

Kaneko, Mamoru. Common Knowledge Logic and Game Logic. J. Symbolic Logic 64 (1999), no. 2, 685--700. https://projecteuclid.org/euclid.jsl/1183745802


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