A categorical generalization of models for modal logics

2008 Fiscal Year Final Research Report

• Project/Area Number: 18740062
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kyushu Sangyo University
• Principal Investigator: TANAKA Yoshihito Kyushu Sangyo University, 経済学部, 教授 (70320132)
• Project Period (FY): 2006 – 2008
• Keywords: Heyting代数 / Kripkeモデル / 非古典論理

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.

Research Products

• [Journal Article] Extensions of canonical formulas for Heyting algebras and intuitionistic frames (2008)
  • Author(s): Yoshihito Tanaka
  • Journal Title: Proceedings of the 42nd MLG meeting Pages: 25-28
• [Journal Article] An infinitary extension of Jankov's theorem (2007)
  • Author(s): Yoshihito Tanaka
  • Journal Title: Studia Logica 71-1 Pages: 57-86
  • Peer Reviewed
• [Journal Article] Continuous homomorphisms of Heyting algebras (2006)
  • Author(s): Yoshihito Tanaka
  • Journal Title: Proceeding of the 40th MLG meeting Pages: pp.26-29
• [Presentation] Extensions of canonical formulas for Heyting algebras and intuitionistic frames (2008)
  • Author(s): Yoshihito Tanaka
  • Organizer: The 42nd MLG meeting
  • Place of Presentation: 九州産業大学
  • Year and Date: 20081100
• [Presentation] An extension of canonical formulas (2007)
  • Author(s): Yoshihito Tanaka
  • Organizer: The 41th MLG meeting
  • Place of Presentation: KKR城崎玄武
  • Year and Date: 20071200
• [Presentation] Continuous homomorphisms of Heyting algebras (2006)
  • Author(s): Yoshihito Tanaka
  • Organizer: The 40th MLG meeting
  • Place of Presentation: ゆふいん七色の風
  • Year and Date: 20061200
• [Remarks] Nobu-Yuki Suzuki and Yoshihito Tanaka, Proceedings of the 42nd MLG meeting, 2008