Faculty of mathematics and computer science adam mickiewicz university matejki 48/49 60-769 poznan, Poland game logic and its applications I

Mamoru Kaneko, Takashi Nagashima, Mamoru Kaneko, Takashi Nagashima

Research output: Contribution to journalArticle

24 Citations (Scopus)


This paper provides a logic framework for investigations of game theoretical problems. We adopt an infinitary extension of classical predicate logic as the base logic of the framework. The reason for an infinitary extension is to express the common knowledge concept explicitly. Depending upon the choice of axioms on the knowledge operators, there is a hierarchy of logics. The limit case is an infinitary predicate extension of modal propositional logic KD4, and is of special interest in applications. In Part I, we develop the basic framework, and show some applications: an epistemic axiomatization of Nash equilibrium and formal undecidability on the playability of a game. To show the formal undecidability, we use a term existence theorem, which will be proved in Part II.

Original languageEnglish
Pages (from-to)325-354
Number of pages30
JournalStudia Logica
Issue number2-3
Publication statusPublished - 1996
Externally publishedYes



  • Common knowledge
  • Infinitary predicate kd4
  • Nash equilibrium
  • Undecidability on playability

ASJC Scopus subject areas

  • Logic

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