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Extended Kripke Semantics and its Application to Epistemic Logics and Game Theory

扩展克里普克语义及其在认知逻辑和博弈论中的应用

基本信息

批准号：
13640111
负责人：
SUZUKI Nobu-yuki
金额：
$ 2.5万
依托单位：
Shizuoka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2003
项目状态：
已结题

项目摘要

We dealt mainly with multi-modal epistemic logics which can describe interpersonal epistemic inference. The idea of applying multi-modal epistemic logics to analysis of the "game theoretical decision-making process" described by game theory enables us to get new perspectives on relations between epistemic logic and game theory. Many suggestions on future research were obtained. We find that the restriction of inter-personal epistemic inference to "shallow depths" is an important facet of the bounded rationality. The bounded rationality is a concept interested in the recent literature of game theory. We succeeded to construct the extended Kripke-type semantics for such multi-modal epistemic logics. The main and ralated results are the following.1.The restriction of inter-personal epistemic inference to shallow depths is found to be an important facet of the bounded rationality. We showed that multi-modal epistenic logics provide a theoretical framework to this restriction. The proof theory and Kripke-type model theory for such multi-modal epistemic logics are established.2.Natural transformations in sheaf theory and functors in category theory are interpreted into extended Kripke semantics. By means of these techniques, Hellden-completeness in non-classical predicate logics is investigated and compared with the case in propositional logics.3.(in computer science) axiomatization and decidability of the logic of metric spaces.4.The set of all lattice-identities hold on the fuzzy subalgebra of an algebra coincides with the set of all lattice-identities hold on the ordinary subalgebra.5.The standard completeness proofs of some fuzzy logics are given.

我们主要研究可以描述人际认知推理的多模态认知逻辑。应用多模态认知逻辑来分析博弈论所描述的“博弈论决策过程”的想法，使我们能够对认知逻辑与博弈论之间的关系获得新的视角。获得了许多关于未来研究的建议。我们发现，将人际认知推理限制在“浅层深度”是有限理性的一个重要方面。有限理性是最近博弈论文献中感兴趣的一个概念。我们成功地为这种多模态认知逻辑构建了扩展的克里普克型语义。主要和相关结果如下：1.人际认知推理对浅层深度的限制被发现是有限理性的一个重要方面。我们表明，多模态认知逻辑为这种限制提供了理论框架。建立了这种多模态认识逻辑的证明理论和Kripke型模型理论。2.将层理论中的自然变换和范畴论中的函子解释为扩展的Kripke语义。通过这些技术，研究了非经典谓词逻辑中的Hellden完备性，并将其与命题逻辑中的情况进行了比较。3.（计算机科学中）度量空间逻辑的公理化和可判定性。4.代数的模糊子代数上所有格恒等式的集合与普通子代数上所有格恒等式的集合一致。5. 给出了一些模糊逻辑的标准完备性证明。