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A proof-theoretical investigation on diagrammatic reasoning

Research Project

Project/Area Number 22820053
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Philosophy/Ethics
Research InstitutionKeio University

Principal Investigator

TAKEMURA Ryo  慶應義塾大学, 文学部, 講師 (70583665)

Project Period (FY) 2010 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥2,964,000 (Direct Cost: ¥2,280,000、Indirect Cost: ¥684,000)
Fiscal Year 2011: ¥1,443,000 (Direct Cost: ¥1,110,000、Indirect Cost: ¥333,000)
Fiscal Year 2010: ¥1,521,000 (Direct Cost: ¥1,170,000、Indirect Cost: ¥351,000)
Keywords論理学 / 証明論 / 図形推論
Research Abstract

Recently, logical reasoning based on diagrammatic or graphical representations has been investigated by researchers from various areas. For the study of diagrammatic reasoning, it is important to combine methods and analyses of traditional symbolic logic and cognitive science. In such studies, researches so far have concentrated on semantic studies on the static nature of diagrams, i. e., the nature at the level of representation. And there are few proof-theoretical investigations on the dynamic nature of diagrams, i. e., the nature at the level of proofs or at the level of manipulation of diagrams.
In this study, I introduced a proof-theoretical framework to investigate the dynamic nature of diagrammatic representations, in particular of Euler and Venn diagrams. Then, I formalized, by applying one of the basic proof-theoretical techniques of logic translation, the notion of "free ride" in my proof-theoretical framework. Free ride is one of the most basic properties of diagrams that is mainly discussed in the literature of cognitive science as an account of inferential efficacy of diagrams. Then, based on the formalization of free ride, I investigated a proof-theoretical characterization of the structure of Euler diagrammatic proofs and that of Venn diagrammatic proofs, compared with the usual natural deduction proofs of the traditional symbolic logic.

Report

(3 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • Research Products

    (25 results)

All 2012 2011 2010 Other

All Journal Article (12 results) (of which Peer Reviewed: 9 results) Presentation (10 results) Remarks (3 results)

  • [Journal Article] Proof theory for reasoning with Euler diagrams : a Logic Translation and Normalization2012

    • Author(s)
      Ryo Takemura
    • Journal Title

      Studia Logica

      Volume: Volume 101 Issue: 1 Pages: 157-191

    • DOI

      10.1007/s11225-012-9370-6

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A Diagrammatic Inference System with Euler Circles2012

    • Author(s)
      Koji Mineshima, Mitsuhiro Okada, and Ryo Takemura
    • Journal Title

      Language and Information

      Volume: 21 Issue: 3 Pages: 365-391

    • DOI

      10.1007/s10849-012-9160-6

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] オイラー図・ヴェン図推論の翻訳とFree rides2011

    • Author(s)
      竹村亮
    • Journal Title

      JSAI2011論文集(Web版)

    • NAID

      130007423184

    • URL

      https://kaigi.org/jsai/webprogram/2011/paper-238.html

    • Related Report
      2011 Final Research Report
  • [Journal Article] オイラー図・ヴェン図推論の翻訳とFree rides2011

    • Author(s)
      竹村亮
    • Journal Title

      2011年度人工知能学会全国大会(第25回)JSAI2011論文集

      Volume: (Web版)

    • NAID

      130007423184

    • Related Report
      2011 Annual Research Report
  • [Journal Article] A Diagrammatic Reasoning System with Euler Circles2011

    • Author(s)
      Koji Mineshima, Mitsuhiro Okada, Ryo Takemura
    • Journal Title

      Journal of Logic, Language and Information

      Volume: (近刊)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Two Types of Diagrammatic Inference Systems : Natural Deduction Style and Resolution Style2010

    • Author(s)
      Koji Mineshima, Mitsuhiro Okada, and Ryo Takemura
    • Journal Title

      Diagrammatic Representation and Inference

      Volume: 6170 Pages: 99-114

    • DOI

      10.1007/978-3-642-14600-8_12

    • ISBN
      9783642145995, 9783642146008
    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] The efficacy of Euler and Venn diagrams in deductive reasoning : empirical findings2010

    • Author(s)
      Yuri Sato, Koji Mineshima, and Ryo Takemura
    • Journal Title

      Diagrammatic Representation and Inference

      Volume: 6170 Pages: 6-22

    • DOI

      10.1007/978-3-642-14600-8_6

    • ISBN
      9783642145995, 9783642146008
    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Constructing internal diagrammatic proofs from external logic diagrams2010

    • Author(s)
      Yuri Sato, Koji Mineshima, and Ryo Takemura
    • Journal Title

      The annual meeting of the Cognitive Science Society(CogSci 2010)

      Pages: 2668-2673

    • URL

      http://palm.mindmodeling.org/cogsci2010/papers/0640/index.html

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] オイラー図・ヴェン図を用いた図形推論の証明論的分析2010

    • Author(s)
      竹村亮, 峯島宏次, 佐藤有理, 岡田光弘
    • Journal Title

      JSAI2010論文集(Web版)

    • NAID

      130007425448

    • URL

      https://kaigi.org/jsai/webprogram/2010/paper-389.html

    • Related Report
      2011 Final Research Report
  • [Journal Article] Two Types of Diagrammatic Inference Systems : Natural Deduction Style and Resolution Style2010

    • Author(s)
      Koji Mineshima, Mitsuhiro Okada, Ryo Takemura
    • Journal Title

      Diagrammatic Representation and Inference : 6th International Conference, Diagrams 2010

      Volume: 6170 Pages: 99-114

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The efficacy of Euler and Venn diagrams in deductive reasoning : empirical findings2010

    • Author(s)
      Yuri Sato, Koji Mineshima, Ryo Takemura
    • Journal Title

      Diagrammatic Representation and Inference : 6th International Conference, Diagrams 2010

      Volume: 6170 Pages: 6-22

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Constructing internal diagrammatic proofs from external logic diagrams2010

    • Author(s)
      Yuri Sato, Koji Mineshima, Ryo Takemura
    • Journal Title

      The annual meeting of the Cognitive Science Society (CogSci 2010)

      Pages: 2668-2673

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] オイラー図・ヴェン図推論の翻訳とFree rides2011

    • Author(s)
      竹村亮
    • Organizer
      2011年度人工知能学会全国大会(第25回)
    • Place of Presentation
      アイーナいわて県民情報交流センター(岩手県)
    • Year and Date
      2011-06-01
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] Proof theory for reasoning with Euler diagrams2011

    • Author(s)
      Ryo Takemura
    • Organizer
      Proof theory and philosophy
    • Place of Presentation
      Keio University, Tokyo
    • Year and Date
      2011-02-26
    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Presentation] オイラー図推論の証明論的分析:自然演繹への翻訳と正規形証明2011

    • Author(s)
      竹村亮
    • Organizer
      2010年度MLG数理論理学研究集会(第45回)
    • Place of Presentation
      KKR湯沢ゆきぐに,新潟
    • Year and Date
      2011-01-07
    • Related Report
      2011 Final Research Report
  • [Presentation] オイラー図推論の証明論的分析:自然演繹への翻訳と正規形証明2011

    • Author(s)
      竹村亮
    • Organizer
      2010年度MLG 数理論理学研究集会(第45回)
    • Place of Presentation
      KKR湯沢ゆきぐに,新潟
    • Year and Date
      2011-01-07
    • Related Report
      2010 Annual Research Report
  • [Presentation] オイラー図推論の証明論的分析: Free ride propertyと正規形証明2010

    • Author(s)
      竹村亮
    • Organizer
      日本科学哲学会第43回(2010年)大会
    • Place of Presentation
      大阪市立大学,大阪
    • Year and Date
      2010-11-27
    • Related Report
      2011 Final Research Report
  • [Presentation] オイラー図推論の証明論的分析:Free ride propertyと正規形証明2010

    • Author(s)
      竹村亮
    • Organizer
      日本科学哲学会第43回(2010年)大会
    • Place of Presentation
      大阪市立大学,大阪
    • Year and Date
      2010-11-27
    • Related Report
      2010 Annual Research Report
  • [Presentation] Two Types of Diagrammatic Inference Systems : Natural Deduction Style and Resolution Style2010

    • Author(s)
      Koji Mineshima, Mitsuhiro Okada, and Ryo Takemura
    • Organizer
      Sixth International Conference on the Theory and Application of Diagrams(Diagrams 2010)
    • Place of Presentation
      Portland State University, Portland, Oregon, USA
    • Year and Date
      2010-08-10
    • Related Report
      2011 Final Research Report
  • [Presentation] Two Types of Diagrammatic Inference Systems : Natural Deduction Style and Resolution Style2010

    • Author(s)
      Koji Mineshima, Mitsuhiro Okada, Ryo Takemura
    • Organizer
      Sixth International Conference on the Theory and Application of Diagrams (Diagrams 2010)
    • Place of Presentation
      Portland State University, Portland, Oregon, USA
    • Year and Date
      2010-08-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] オイラー図・ヴェン図を用いた図形推論の証明論的分析2010

    • Author(s)
      竹村亮, 峯島宏次, 佐藤有理, 岡田光弘
    • Organizer
      2010年度人工知能学会全国大会(第24回)
    • Place of Presentation
      長崎ブリックホール,長崎
    • Year and Date
      2010-06-09
    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Presentation] Reasoning with Euler diagrams : a proof-theoretical approach2010

    • Author(s)
      Koji Mineshima, Mitsuhiro Okada, and Ryo Takemura
    • Organizer
      3rd World Congress and School on Universal Logic
    • Place of Presentation
      Estoril Eden, Lisbon, Portugal
    • Year and Date
      2010-04-25
    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Remarks]

    • URL

      http://abelard.flet.keio.ac.jp/person/takemura/index.html

    • Related Report
      2011 Final Research Report
  • [Remarks]

    • URL

      http://abelard.flet.keio.ac.jp/person/takemura/index.html

    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

      http://abelard.flet.keio.ac.jp/person/takemura/index.html

    • Related Report
      2010 Annual Research Report

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Published: 2010-08-27   Modified: 2016-04-21  

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