2013 Fiscal Year Final Research Report

New development of Kripke semantics by combining with graph theory

Research Project

Project/Area Number	23500028
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Multi-year Fund
Section	一般
Research Field	Fundamental theory of informatics
Research Institution	Osaka University of Economics and Law
Principal Investigator	MIYAZAKI Yutaka 大阪経済法科大学, 公私立大学の部局等, 准教授 (40374607)
Project Period (FY)	2011 – 2013
Keywords	数理論理学 / Hybris Logic / Modal Logic / Graph Theory / WQO theory
Research Abstract	I started this research on basis of the observation "Kripke frame is a graph", and I aimed at restructuring the frame-theoretic approch to semantical study of modal logics by introducing the knowledge and techniques in graph theory. As the results after three-year investigation, I found the following facts. (1) We have to utilize graph theory for the class of infinite graphs, not ordinary graph theory, (2) The "minor relation" in Graph Minor Theorem may destroy the order of two modal logics which are determined by two Kripke frames. Therefore this relation is not suitable for analizing the lattice structure which is made of some class of modal logics, and (3) There are at least two methods for extending the usual modal language to characterize the logic determined by the class of all undirected graphs.

(6 results)