New development of Kripke semantics by combining with graph theory

点击翻译按钮获取中文摘要

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.