David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of Symbolic Logic 64 (2):685-700 (1999)
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 Logic Common Knowledge Logic Fixed-Point and Iterative Definitions of Common Knowledge Nash Equilibrium|
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Luca Alberucci & Gerhard Jäger (2005). About Cut Elimination for Logics of Common Knowledge. Annals of Pure and Applied Logic 133 (1):73-99.
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