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Game Logic and its Applications II

Abstract

This paper provides a Genzten style formulation of the game logic framework GLm (0 ≤ m ≤ ω), and proves the cut-elimination theorem for GLm. As its application, we prove the term existence theorem for GLω used in Part I.

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References

  1. GENTZEN, G., 1935, ‘Untersuchungen über das logische Schliessen’, Mathematische Zeitschrift 39, 176-210, 405–431. English translation, ‘Investigations into Logical Deduction’, The Collected Papers of Gerhard Gentzen, 1969.

    Google Scholar 

  2. HARROP, R., 1956, ‘On Disjunctions and Existential Statements in Intuitionistic Systems of Logic’, Math. Annalen 132, 247-361.

    Google Scholar 

  3. HARROP, R., 1960, ‘Concerning Formulas of the Types A → B V C, A → (Ex)B(x) in Intuitionistic Formal System’, J. Symbolic Logic 25, 247-361.

    Google Scholar 

  4. KANEKO, M. and T. NAGASHIMA, 1996, ‘Game Logic and its Applications I’, To appear in Studia Logica 57.

  5. OHNISHI, M., and K. MATSUMOTO, 1957, ‘Gentzen Method in Modal Calculi. I’, Osaka Math. J. 9, 113-130.

    Google Scholar 

  6. OHNISHI, M., and K. MATSUMOTO, 1959, ‘Gentzen Method in Modal Calculi. II’, Osaka Math. J. 11, 115-120.

    Google Scholar 

  7. VAN DALEN, D., 1986), ‘INTUITIONISTIC LOGIC’, Handbook of Philosophical Logic (III), eds. D. Gabbay and F. Guenthner, Reidel, 225-339.

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Kaneko, M., Nagashima, T. Game Logic and its Applications II. Studia Logica 58, 273–303 (1997). https://doi.org/10.1023/A:1004975724824

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  • DOI: https://doi.org/10.1023/A:1004975724824

  • infinitary predicate KD4
  • common knowledge
  • Nash equilibrium
  • undecidability on playability