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

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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.