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A categorical generalization of models for modal logics

Research Project

Project/Area Number 18740062
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKyushu Sangyo University

Principal Investigator

TANAKA Yoshihito  Kyushu Sangyo University, 経済学部, 教授 (70320132)

Project Period (FY) 2006 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥3,070,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
KeywordsHeyting代数 / Kripkeモデル / 非古典論理 / canonical formula / 直観主義論理 / Kripkeフレーム / 双対性 / 数理論理 / 連続写像 / Canonical formula / Jankovの定理 / 無限論理 / 代数モデル / 様相論理
Research Abstract

Subdirectly irreducibleな有限Heyting代数におけるJankovの定理から,有限という条件を外し,ある一定の条件を満たすsudirectly irreducible Heyting代数への拡張を行った.また,有限Kripke frameにおけるcanonical formulaの理論を,一般のKripke frameに拡張した.

Report

(4 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (12 results)

All 2008 2007 2006 Other

All Journal Article (5 results) (of which Peer Reviewed: 1 results) Presentation (5 results) Remarks (2 results)

  • [Journal Article] Extensions of canonical formulas for Heyting algebras and intuitionistic frames2008

    • Author(s)
      Yoshihito Tanaka
    • Journal Title

      Proceedings of the 42nd MLG meeting

      Pages: 25-28

    • Related Report
      2008 Final Research Report
  • [Journal Article] An infinitary extension of Jankov's theorem2007

    • Author(s)
      Yoshihito Tanaka
    • Journal Title

      Studia Logica 71-1

      Pages: 57-86

    • Related Report
      2008 Final Research Report 2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Continuous homomorphisms of Heyting algebras2007

    • Author(s)
      Yoshihito Tanaka
    • Journal Title

      Proceedings of the 506^<th> MLG meeting

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Continuous homomorphisms of Heyting algebras2006

    • Author(s)
      Yoshihito Tanaka
    • Journal Title

      Proceeding of the 40th MLG meeting

      Pages: 26-29

    • Related Report
      2008 Final Research Report
  • [Journal Article] An infinitary extension of Jankov' s theorem

    • Author(s)
      Yoshihito Tanaka
    • Journal Title

      Studia Logica (受理済)

    • Related Report
      2006 Annual Research Report
  • [Presentation] Extensions of Canonical Formulas for Heyting Algebras and Intuitionistic Frames2008

    • Author(s)
      Yoshihito Tanaka
    • Organizer
      MLG数理論理学研究集会
    • Place of Presentation
      九州産業大学
    • Year and Date
      2008-11-08
    • Related Report
      2008 Annual Research Report
  • [Presentation] Extensions of canonical formulas for Heyting algebras and intuitionistic frames2008

    • Author(s)
      Yoshihito Tanaka
    • Organizer
      The 42nd MLG meeting
    • Place of Presentation
      九州産業大学
    • Related Report
      2008 Final Research Report
  • [Presentation] An extension of canonical formulas2007

    • Author(s)
      Yoshihito Tanaka
    • Organizer
      MLG数理論理学研究集会
    • Place of Presentation
      KKR城崎玄武
    • Year and Date
      2007-12-20
    • Related Report
      2007 Annual Research Report
  • [Presentation] An extension of canonical formulas2007

    • Author(s)
      Yoshihito Tanaka
    • Organizer
      The 41th MLG meeting
    • Place of Presentation
      KKR城崎玄武
    • Related Report
      2008 Final Research Report
  • [Presentation] Continuous homomorphisms of Heyting algebras2006

    • Author(s)
      Yoshihito Tanaka
    • Organizer
      The 40th MLG meeting
    • Place of Presentation
      ゆふいん七色の風
    • Related Report
      2008 Final Research Report
  • [Remarks] Nobu-Yuki Suzuki and Yoshihito Tanaka, Proceedings of the 42nd MLG meeting, 2008

    • Related Report
      2008 Final Research Report
  • [Remarks]

    • URL

      http://www.ip.kyusan-u.ac.jp/J/ms/event/mlg08/notice.html

    • Related Report
      2008 Annual Research Report

URL: 

Published: 2006-04-01   Modified: 2016-04-21  

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