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Study of multi-modal logics and its application to game theory

Research Project

Project/Area Number 16340022
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionShizuoka University

Principal Investigator

SUZUKI Nobu-yuki  Shizuoka University, Faculty of Science, Department of Mathematics, Professor, 理学部, 教授 (60216421)

Co-Investigator(Kenkyū-buntansha) ONO Hiroakira  Japan Advanced Institute of Science and Technology, School of Information Sciences, Professor, 情報科学研究科, 教授 (90055319)
KANEKO Mamoru  University of Tsukuba, Graduate School of Systems and Information Engineering, Professor, 大学院・システム情報工学研究科, 教授 (40114061)
YORIOKA Teruyuki  Lecturer, 理学部, 講師 (60432192)
Project Period (FY) 2004 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥6,700,000 (Direct Cost: ¥6,700,000)
Fiscal Year 2006: ¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 2005: ¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 2004: ¥2,000,000 (Direct Cost: ¥2,000,000)
Keywordsnon-classical logics / modal logic / epistemic logic / Kripke semantics / algebraic semantics / theory of games / set theory of reals / 限定合理性 / 多様相論理 / クリクキ意味論
Research Abstract

Among other multi-modal logics, we dealt mainly with multi-agent epistemic logics. We can describe inter-personal epistemic inference by making use of multi-agent epistemic logics, and hence we can apply them to game theory. As application, we tried mainly to analyze the game theoretical decision-making process. The idea of applying multi-modal epistemic logics enables us to get new perspectives on relations between epistemic logic and game theory. Many suggestions on future research were obtained.
We found that the restriction of inter-personal epistemic inference to "shallow depths" is an important aspect of bounded rationality.In this system IGEF, we can bescribe such restriction by making use of thought sequents. Our system enables us to 'isolate' inter-personal epistemic inference from other ability, and to consider bounded rationality as restrictions on the ability of inter-personal epistemic inference. Moreover, we succeeded to construct the extended Kripke-type semantics for such multi-modal epistemic logics.
The main and ralated results are the following.
1. Systems IGEF of multi-agent epistemic logics with the feature of the restriction of inter-personal epistemic inference to shallow depths are constructed. These systems enable us to describe contentwise cost of inter-personal epistemic inference in game theoretical situations.
2. The proof theory and Kripke-type model theory for such multi-modal epistemic logics are established.
3. Algebraic study of substructural logics.
4. Results on Martin's axiom on fragmnets of aleph-one dense sets.

Report

(4 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (27 results)

All 2007 2006 2005 2004 Other

All Journal Article (21 results) Book (6 results)

  • [Journal Article] Duality in comparative statics in rental housing markets with indivisibilitie2006

    • Author(s)
      M.Kaneko, Ito, Y.-I.Osawa
    • Journal Title

      Journal of Urban Economics 29

      Pages: 24-27

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Algebraization, parametrized local deduction theorem and interpolation for substructural logics over FL2006

    • Author(s)
      N.Galatos, H.Ono
    • Journal Title

      Studia Logica 83

      Pages: 279-308

    • NAID

      120000861748

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Glivenko theorems for substructural logics over FL2006

    • Author(s)
      N.Galatos, H.Ono
    • Journal Title

      Journal of Symbolic Logic Vol. 71, No. 4

      Pages: 1353-1384

    • NAID

      120001746778

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Duality in comparative statics in rental housing markets with indivisibilities2006

    • Author(s)
      M.Kaneko, Ito, Y.-I.Osawa
    • Journal Title

      Journal of Urban Economics 59

      Pages: 142-170

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Annual Research Report 2006 Final Research Report Summary
  • [Journal Article] Glivenko theorems for substructural logics over FL2006

    • Author(s)
      N.Galatos, H.Ono
    • Journal Title

      Journal of Symbolic Logic Vol.71, No.4

      Pages: 1353-1384

    • NAID

      120001746778

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Algebraization, parametrized local deduction theorem and interpolation for substructural logics over FL2006

    • Author(s)
      Nikolaos Galatos, Hiroakira Ono
    • Journal Title

      Studia Logica 83

      Pages: 279-308

    • NAID

      120000861748

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Glivenko theorems for substructural logics over FL2006

    • Author(s)
      Nikolaos Galatos, Hiroakira Ono
    • Journal Title

      Journal of Symbolic Logic 71, 4

      Pages: 1353-1384

    • NAID

      120001746778

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Contentwise Complexity of Inferences based on Epistemic Logics of Shallow Depths in Game Theoretical Situations2006

    • Author(s)
      M.Kaneko, N.-Y.Suzuki
    • Journal Title

      Proceedings of the 39th MLG meeting at Gamagori, Japan 2005

      Pages: 24-27

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Algebraization, parameterized local deduction theorem and interpolation for substructural logics over FL2006

    • Author(s)
      N.Galatos, H.Ono
    • Journal Title

      Studia Logica 83(to appear)

      Pages: 1-32

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Duality in comparative statics in rental housing markets with indivisibilities2006

    • Author(s)
      M.Kaneko, T.Ito, Y.Osawa
    • Journal Title

      Journal of Urban Economics 59

      Pages: 142-170

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Contentwise Complexity of Inferences based on Epistemic Logics of Shallow Depths in Game Theoretical Situations2005

    • Author(s)
      M.Kaneko, N.-Y.Suzuki
    • Journal Title

      Proceedings of the 39th MLG meeting at Gamagori, Japan

      Pages: 24-27

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Contentwise Complexity of Inferences based on Epistemic Logics of Shallow Depths in Game Theoretical Situations2005

    • Author(s)
      M.Kaneko, N.-Y.Suzuki
    • Journal Title

      Proceedings of the 39th MLG meeting at Gamagori, Japan 2005,

      Pages: 24-27

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Utility theories in cooperative games2004

    • Author(s)
      M.Kaneko, M.H.Wooders
    • Journal Title

      Handbook of Utility Theory Vol. II. Chapter 19 Vol. II

      Pages: 1065-1098

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Algebraic aspects of cut elimination2004

    • Author(s)
      F.Belardinelli, P.Jipsen, H.Ono
    • Journal Title

      Studia Logica Vol. 77, No. 2

      Pages: 209-240

    • NAID

      120000861747

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Algebraic aspects of cut elimination2004

    • Author(s)
      F.Belardinelli, P.Jipsen, H.Ono
    • Journal Title

      Studia Logica Vol.77, No.2

      Pages: 209-240

    • NAID

      120000861747

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Algebraic aspects of cut elimination2004

    • Author(s)
      Francesco Belardinelli, Peter Jipsen, Hiroakira Ono
    • Journal Title

      Studia Logica 77・2

      Pages: 209-240

    • NAID

      120000861747

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Contentwise complexity of inferences in epistemic logic2004

    • Author(s)
      Mamoru Kaneko, Nobu-Yuki Suzuki
    • Journal Title

      Proceedings of the 38th MLG meeting

      Pages: 47-49

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Some Weak fragments of Martin's Axiom related to the rectangle refining property

    • Author(s)
      T.Yorioka
    • Journal Title

      Archive for Mathematical Logic (掲載決定)

    • NAID

      120000796353

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Utility theories in cooperative games

    • Author(s)
      M.Kaneko, M.H.Wooders
    • Journal Title

      Handbook of Utility Theory Vol.II (Kluwer Academic Press) Chapter 19 (2004)

      Pages: 1065-1098

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Some Weak fragments of Martin's Axiom related to the rectangle refining property

    • Author(s)
      T, Yorioka
    • Journal Title

      Archive for Mathematical Logic (to appear)

    • NAID

      120000796353

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Some Weak fragments of Martin's Axiom related to the rectangle refining property

    • Author(s)
      Teruyuki Yorioka
    • Journal Title

      Archive for Mathematical Logic (掲載決定)

    • NAID

      120000796353

    • Related Report
      2006 Annual Research Report
  • [Book] -地界で考えるー社会正義2007

    • Author(s)
      金子 守
    • Total Pages
      300
    • Publisher
      勁草書房(2007年5月刊行予定)
    • Related Report
      2006 Annual Research Report
  • [Book] ゲーム理家の酔夢譚:詩の饗宴2006

    • Author(s)
      金子 守
    • Total Pages
      204
    • Publisher
      勁草書房
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Book] ゲーム論家の酔夢潭 : 詩の饗宴2006

    • Author(s)
      金子 守
    • Total Pages
      204
    • Publisher
      勁草書房
    • Related Report
      2006 Annual Research Report
  • [Book] ゲーム論家の酔夢譚:詩の饗宴2006

    • Author(s)
      金子 守
    • Publisher
      勁草書房
    • Related Report
      2005 Annual Research Report
  • [Book] Game Theory and Mutual Misunderstanding2005

    • Author(s)
      M.Kaneko
    • Total Pages
      247
    • Publisher
      Springer
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Book] Game Theory and Mutual Misunderstanding2004

    • Author(s)
      Mamoru Kaneko
    • Total Pages
      257
    • Publisher
      Springer Verlag
    • Related Report
      2004 Annual Research Report

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Published: 2004-04-01   Modified: 2016-04-21  

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