2003 Fiscal Year Final Research Report Summary
Extended Kripke Semantics and its Application to Epistemic Logics and Game Theory
| Project/Area Number |
13640111
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Shizuoka University |
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Principal Investigator |
SUZUKI Nobu-yuki Shizuoka University, Faculty of Science, Associate Professor, 理学部, 助教授 (60216421)
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| Co-Investigator(Kenkyū-buntansha) |
KANEKO Mamoru University of Tsukuba, Institute of Policy and Planning Sciences, Professor, 社会工学系, 教授 (40114061)
ONO Hiroakira Japan Advanced Institute of Science and Technology, School of Information Science, Professor, 情報科学研究科, 教授 (90055319)
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| Project Period (FY) |
2001 – 2003
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| Keywords | Non-Classical Logics / Kripke Semantics / Epistemic Logics / Game Theory / Bounded Rationality |
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| Research Abstract |
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.
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