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1 results

  • Common knowledge logic and game logic

  • Mamoru Kaneko
  • Journal:
    The Journal of Symbolic Logic / Volume 64 / Issue 2 / June 1999
    Published online by Cambridge University Press:
    12 March 2014, pp. 685-700
    Print publication:
    June 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.