Game logic and its applications I
Game logic and its applications I
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游戏逻辑及其应用Ⅰ
DOI：
10.1007/bf00370838
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发表时间：
1996
期刊：
影响因子：
0.7
通讯作者：
T. Nagashima
中科院分区：
文献类型：
--
作者：
M. Kaneko;T. Nagashima
本文为博弈论问题的研究提供了一个逻辑框架。我们采用经典谓词逻辑的无限扩展作为框架的基础逻辑。无限扩展的原因是显式地表达公共知识概念。根据知识算子上公理的选择，存在逻辑的层次结构。极限情况是模态命题逻辑KD 4的一个无限谓词扩展，在应用中具有特殊的意义。在第一部分中，我们开发了基本框架，并展示了一些应用：纳什均衡的认识公理化和游戏可玩性的形式不可判定性。为了证明形式上的不可判定性，我们使用了一个项存在定理，这将在第二部分中证明。
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.