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2013 Fiscal Year Final Research Report

New development of Kripke semantics by combining with graph theory

Research Project

  • PDF
Project/Area Number 23500028
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Fundamental theory of informatics
Research InstitutionOsaka 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.

  • Research Products

    (6 results)

All 2014 2013 2012 2011

All Presentation (6 results)

  • [Presentation] Graph theory and modal logic2014

    • Author(s)
      Yutaka Miyazaki
    • Organizer
      Application of Algebra in Logic and Computer Science XVIII
    • Place of Presentation
      in Zakopane, Poland
    • Year and Date
      2014-05-13
  • [Presentation] Graph theory and modal logic2013

    • Author(s)
      Yutaka Miyazaki
    • Organizer
      BLAST2013
    • Place of Presentation
      in Chapman University, California, US
    • Year and Date
      2013-08-06
  • [Presentation] WQO theory in Modal Logic2013

    • Author(s)
      Yutaka Miyazaki
    • Organizer
      Application of Algebra in Logic and Computer Science XVII
    • Place of Presentation
      in Zakopane, Poland
    • Year and Date
      2013-05-06
  • [Presentation] Unification problems in Not-weakly-transitive modal logics2012

    • Author(s)
      Yutaka Miyazaki
    • Organizer
      Application of Algebra in Logic and Computer Science XVI
    • Place of Presentation
      in Zakopane, Poland
    • Year and Date
      2012-02-28
  • [Presentation] Unification problems in Non-weakly-transitive modal logics2012

    • Author(s)
      Yutaka Miyazaki
    • Organizer
      Asian Workshop on Philosophical Logic
    • Place of Presentation
      in Jaist Ishikawa, Japan
    • Year and Date
      2012-02-16
  • [Presentation] Some properties of orthomodular lattices2011

    • Author(s)
      Yutaka Miyazaki
    • Organizer
      Summer School in General Algebra and Ordered Sets
    • Place of Presentation
      in Svratka, Czech Republic
    • Year and Date
      2011-09-05

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Published: 2015-07-16  

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