A categorical generalization of models for modal logics

• 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
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥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)
• Keywords: Heyting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.

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 (2007)
  • Author(s): Yoshihito Tanaka
  • Journal Title: Proceedings of the 506^<th> MLG meeting
• [Journal Article] Continuous homomorphisms of Heyting algebras (2006)
  • Author(s): Yoshihito Tanaka
  • Journal Title: Proceeding of the 40th MLG meeting Pages: 26-29
• [Journal Article] An infinitary extension of Jankov' s theorem
  • Author(s): Yoshihito Tanaka
  • Journal Title: Studia Logica (受理済)
• [Presentation] Extensions of Canonical Formulas for Heyting Algebras and Intuitionistic Frames (2008)
  • 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
• [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
• [Presentation] An extension of canonical formulas (2007)
  • 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
• [Presentation] An extension of canonical formulas (2007)
  • Author(s): Yoshihito Tanaka
  • Organizer: The 41th MLG meeting
  • Place of Presentation: KKR城崎玄武
• [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
• [Remarks] Nobu-Yuki Suzuki and Yoshihito Tanaka, Proceedings of the 42nd MLG meeting, 2008
• [Remarks]
  • URL: http://www.ip.kyusan-u.ac.jp/J/ms/event/mlg08/notice.html