New development of Kripke semantics by combining with graph theory

Kripke语义与图论结合的新发展

• 批准号: 23500028
• 负责人: MIYAZAKI Yutaka
• 金额: $ 3.24万
• 依托单位: Osaka University of Economics and Law
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23500028/
• 关键词: 数理論理学; Hybris Logic; Modal Logic; Graph Theory; WQO theory; Hybrid Logic; Hybrid logic; Modal logic; Graph theory; Unification Problem

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.

本文从“Kripke框架是一个图”的观点出发，试图通过引入图论的知识和技术，重构模态逻辑语义研究的框架理论方法。经过三年的调查，我发现了以下事实。(1)图次定理中的“次关系”可能破坏由两个Kripke框架所决定的两个模态逻辑的序。（3）至少有两种方法可以扩展通常的模态语言来刻画由所有无向图类所决定的逻辑。

项目成果

Unification problems in Not-weakly-transitive modal logics

非弱传递模态逻辑中的统一问题

• 发表时间: 2012
• 作者: Umair F. Siddiqi;Yoichi Shiraishi and Sadiq M. Sait;Yosuke Sato and Shutaro Inoue;星加大輝;Shuichi Oikawa;Yutaka Miyazaki
• 通讯作者: Yutaka Miyazaki

WQO theory in Modal Logic

模态逻辑中的WQO理论

• 发表时间: 2013
• 作者: 甫水佳奈子;脇田建;佐々木晃;江藤宏;Yutaka Miyazaki
• 通讯作者: Yutaka Miyazaki

Some properties of orthomodular lattices

正交模格的一些性质

• 发表时间: 2011
• 作者: Taku Kuribayashi;Yasuhito Asano;Masatoshi Yoshikawa;Yutaka Miyazaki
• 通讯作者: Yutaka Miyazaki

Graph theory and modal logic

图论和模态逻辑

• 发表时间: 2014
• 作者: F.M. Toyama;W. van Dijk;Y. Nogami;Eiji Miyano;Yutaka Miyazaki
• 通讯作者: Yutaka Miyazaki

Unification problems in Non-weakly-transitive modal logics

非弱传递模态逻辑中的统一问题

• 发表时间: 2012
• 作者: Naoto Ogawa;Shuichi Oikawa;Yutaka Miyazaki
• 通讯作者: Yutaka Miyazaki