真矛盾主義に基づく真理論及び数学の基礎の再検討

• Project/Area Number: 15J06850
• Research Category: Grant-in-Aid for JSPS Fellows
• Allocation Type: Single-year Grants
• Section: 国内
• Research Field: Philosophy/Ethics
• Research Institution: Kyoto University
• Principal Investigator: 大森 仁 京都大学, 文学研究科, 特別研究員(PD)
• Project Period (FY): 2015-04-24 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000); Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 真矛盾主義 / 矛盾許容型論理 / 命題の整合性 / 含意 / 否定 / 真理論 / 素朴集合論 / 論理的多元主義 / Belnap-Dunnの体系 / connexive logic / ポスト完全性 / 関数的完全性

Outline of Annual Research Achievements

哲学的課題に関しては、Goodshipの提案に命題の整合性を加えることで得られる見通しの検討を行い、真矛盾主義的な理論の展開において問題とされてきた種々の問題に対して明快な答えを提示することが明らかになった。

論理学的課題に関しては、二年目で得られた、命題の整合性に加えて、Graham PriestがIn Contradictionで提案したもののそれほど研究の進んでいない含意を含む体系の公理化について、これを論文としてまとめ、学術雑誌Logic Journal of the IGPLの命題の整合性を含む矛盾許容型論理に関する特別号に含まれることが決まっている。さらに、二年目に命題の整合性の研究に関連して、従来矛盾許容型論理の研究においてあまり着目されてこなかったHalldenの体系を命題の整合性を含む矛盾許容型論理として位置付けることに成功したが、これを発展させることでDamian Szmuc氏とともに更なる展開への足がかりを得た。

数学的課題に関しては、特に二年目で思いがけず得られた成果の精査を行った。具体的には、Belnap-Dunn の体系を出発点とした上で、命題の整合性のみを加えた体系に基づく真理論をJc Beallの提案する方法で展開することは不可能であることが明らかになったが、この成果を Zach Weber氏と共に他の真矛盾主義的な真理論に対するアプローチと比べる形で論文としてまとめ、受理された。また、二年目に構築した命題の整合性と含意とを含む論理体系に基づく真理論や素朴集合論の展開に関しては、特に含意の否定に関して、Priestの提案する方法とある含意の否定の捉え方とを合わせることは不可能であることが判明し、この点に関しては目下論文としてまとめているところである。

Research Progress Status

29年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

29年度が最終年度であるため、記入しない。

Research Products

• [Int'l Joint Research] ブエノスアイレス大学(アルゼンチン)
• [Int'l Joint Research] オタゴ大学(ニュージーランド)
• [Int'l Joint Research] コンスタンツ大学(ドイツ)
• [Journal Article] From Logics of Formal Inconsistency to Logics of Formal Classicality (2018)
  • Author(s): Hitoshi Omori
  • Journal Title: Logic Journal of the IGPL Volume: 印刷中
  • Peer Reviewed
• [Journal Article] A note on Goddard and Routley's significance logics (2018)
  • Author(s): Damian Szmuc, Hitoshi Omori
  • Journal Title: The Australasian Journal of Logic Volume: 印刷中
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Just true? On the metatheory for paraconsistent truth (2018)
  • Author(s): Hitoshi Omori, Zach Weber
  • Journal Title: Logique et Analyse Volume: 印刷中
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Conjunction and Disjunction in Infectious Logics (2017)
  • Author(s): Omori Hitoshi、Szmuc Damian
  • Journal Title: Logic, Rationality, and Interaction. LORI 2017 Volume: － Pages: 268-283
  • DOI: 10.1007/978-3-662-55665-8_19
  • ISBN: 9783662556641, 9783662556658
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] An Extended First-Order Belnap-Dunn Logic with Classical Negation (2017)
  • Author(s): Norihiro Kamide、Hitoshi Omori
  • Journal Title: Logic, Rationality, and Interaction. LORI 2017. Lecture Notes in Computer Science, vol 10455 Volume: - Pages: 79-93
  • DOI: 10.1007/978-3-662-55665-8_6
  • ISBN: 9783662556641, 9783662556658
  • Peer Reviewed
• [Journal Article] There is more to negation than modality (2016)
  • Author(s): Michael De and Hitoshi Omori
  • Journal Title: Journal of Philosophical Logic Volume: - Issue: 2 Pages: 281-299
  • DOI: 10.1007/s10992-017-9427-0
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] A note on Francez' half-connexive formula (2016)
  • Author(s): Omori, H.
  • Journal Title: IfCoLog Journal of Logics and their Applications Volume: 3
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Hallden's Logic of Nonsense and its expansions in view of Logics of Formal Inconsistency (2016)
  • Author(s): Omori, H.
  • Journal Title: Proceedings of DEXA2016 Volume: --
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Classical and Empirical Negation in Subintuitionistic Logic (2016)
  • Author(s): De, M. & Omori, H.
  • Journal Title: Advances in Modal Logic, Vol 11 Volume: --
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] A Note on Wansing's expansion of Nelson's logic (2016)
  • Author(s): Omori, H.
  • Journal Title: Reports on Mathematical Logic Volume: 51
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] An axiomatization of Wansing's expansion of Nelson's logic (2015)
  • Author(s): Hitoshi Omori
  • Journal Title: Reports on Mathematical Logic Volume: 50 Pages: 41-51
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Presentation] Logical consequence and methodological consequence (2017)
  • Author(s): Omori, H.
  • Organizer: Relativisms Global Research Network Workshop 1
  • Place of Presentation: Seoul (Korea)
  • Year and Date: 2017-02-17
  • Int'l Joint Research / Invited
• [Presentation] Infectious Logicsの周辺 (2017)
  • Author(s): 大森仁
  • Organizer: 第52回MLG数理論理学研究集会
• [Presentation] Classical and Empirical Negation in Nonclassical Logics (2017)
  • Author(s): Hitoshi Omori, Michael De
  • Organizer: Negation and Negativity in Natural Language
  • Int'l Joint Research
• [Presentation] From Dunn to Avron: towards a systematic overview of paraconsistent logics (2017)
  • Author(s): Hitoshi Omori
  • Organizer: ISRALOG17
  • Int'l Joint Research
• [Presentation] Sette, Jaskowski, and beyond (2017)
  • Author(s): Omori, H.
  • Organizer: Prague Seminar on Paraconsistent Logic
  • Place of Presentation: Prague (Czech Republic)
  • Int'l Joint Research / Invited
• [Presentation] Towards a unification of paraconsistent logics (2016)
  • Author(s): Omori, H.
  • Organizer: V Workshop on Philosophical Logic
  • Place of Presentation: Buenos Aires (Argentina)
  • Year and Date: 2016-11-23
  • Int'l Joint Research / Invited
• [Presentation] Towards a unification of paraconsistent logics (2016)
  • Author(s): 大森仁
  • Organizer: 第51回MLG数理論理学研究集会
  • Place of Presentation: 四季の湯強羅静雲荘（神奈川県箱根町）
  • Year and Date: 2016-10-27
  • Int'l Joint Research
• [Presentation] Towards a unification of paraconsistent logics (2016)
  • Author(s): Omori, H.
  • Organizer: Paradoxes, Logic and Philosophy
  • Place of Presentation: Beijing (China)
  • Year and Date: 2016-10-15
  • Int'l Joint Research
• [Presentation] Classical and Empirical Negation in Subintuitionistic Logic (2016)
  • Author(s): De, M. & Omori, H.
  • Organizer: Advances in Modal Logic 2016
  • Place of Presentation: Budapest (Hungary)
  • Year and Date: 2016-08-30
  • Int'l Joint Research
• [Presentation] Bhaviveka's Negations Viewed from a Contemporary Viewpoint (2016)
  • Author(s): Deguchi, Y. & Omori, H.
  • Organizer: CCPEA 2016
  • Place of Presentation: Seoul (Korea)
  • Year and Date: 2016-08-19
  • Int'l Joint Research
• [Presentation] Towards a unification of paraconsistent logics (2016)
  • Author(s): Omori, H.
  • Organizer: CCPEA 2016
  • Place of Presentation: Seoul (Korea)
  • Year and Date: 2016-08-19
  • Int'l Joint Research
• [Presentation] Towards a unification of paraconsistent logics (2016)
  • Author(s): Omori, H.
  • Organizer: Logic in Bochum 2
  • Place of Presentation: Raesfeld (Germany)
  • Year and Date: 2016-06-27
  • Int'l Joint Research / Invited
• [Presentation] 矛盾許容型論理の矛盾許容性再考 (2016)
  • Author(s): 大森仁
  • Organizer: 2016年度科学基礎論学会
  • Place of Presentation: 埼玉大学（埼玉県さいたま市）
  • Year and Date: 2016-06-18
• [Presentation] Towards a unification of paraconsistent logics (2016)
  • Author(s): 大森仁
  • Organizer: 論数哲2016
  • Place of Presentation: 御茶ノ水大学（東京都文京区）
  • Year and Date: 2016-05-06
  • Invited
• [Presentation] Remarks on Many-valued Approach to Modality (2016)
  • Author(s): Hitoshi Omori
  • Organizer: MLG 数理論理学研究集会（第50回）
  • Place of Presentation: 大原の里（京都府・京都市）
  • Year and Date: 2016-01-08
• [Presentation] From Logics of Formal Inconsistencies to Logics of Formal Classicality (2016)
  • Author(s): Omori, H.
  • Organizer: Applied Mathematical Logic Seminar
  • Place of Presentation: Prague (Czech Republic)
  • Int'l Joint Research / Invited
• [Presentation] Hallden's Logic of Nonsense and its expansions in view of Logics of Formal Inconsistency (2016)
  • Author(s): Omori, H.
  • Organizer: COIN2016
  • Place of Presentation: Porto (Portugal)
  • Int'l Joint Research
• [Presentation] Strengthening the Goodship Project (2015)
  • Author(s): Hitoshi Omori
  • Organizer: Pluralism, Language and Logic Workshop
  • Place of Presentation: ソウル（韓国）
  • Year and Date: 2015-09-11
  • Int'l Joint Research / Invited
• [Presentation] Strengthening the Goodship Project (2015)
  • Author(s): Hitoshi Omori
  • Organizer: Logic and Metaphysics Workshop
  • Place of Presentation: ニューヨーク（米国）
  • Year and Date: 2015-08-31
  • Int'l Joint Research / Invited
• [Presentation] Strengthening the Goodship Project (2015)
  • Author(s): Hitoshi Omori
  • Organizer: Workshop on Philosophy of Logic
  • Place of Presentation: ブエノスアイレス（アルゼンチン）
  • Year and Date: 2015-08-20
  • Int'l Joint Research / Invited
• [Presentation] From Logics of Formal Inconsistencies to Logics of Formal Classicality (2015)
  • Author(s): Hitoshi Omori
  • Organizer: TALKS
  • Place of Presentation: ブエノスアイレス（アルゼンチン）
  • Year and Date: 2015-08-18
  • Int'l Joint Research / Invited
• [Presentation] A Simple Connexive Extension of the Basic Relevant Logic BD (2015)
  • Author(s): Hitoshi Omori
  • Organizer: Fifth World Congress and School on Universal Logic
  • Place of Presentation: イスタンブール（トルコ）
  • Year and Date: 2015-06-25
  • Int'l Joint Research
• [Presentation] Remarks on many-valued approach to modality (2015)
  • Author(s): Hitoshi Omori
  • Organizer: Logic in Bochum 1
  • Place of Presentation: ボーフム（ドイツ）
  • Year and Date: 2015-06-22
  • Int'l Joint Research / Invited
• [Presentation] Remarks on gluons in One (2015)
  • Author(s): Hitoshi Omori
  • Organizer: one: Workshop with Graham Priest
  • Place of Presentation: ミュンスター（ドイツ）
  • Year and Date: 2015-06-21
  • Int'l Joint Research / Invited
• [Presentation] Remarks on many-valued approach to modality (2015)
  • Author(s): Hitoshi Omori
  • Organizer: Logica 2015
  • Place of Presentation: ヘニツェ（チェコ）
  • Year and Date: 2015-06-15
  • Int'l Joint Research
• [Presentation] A note on naive set theory in an expansion of LP (2015)
  • Author(s): Hitoshi Omori
  • Organizer: Prague seminar on Non-Classical Mathematics
  • Place of Presentation: プラハ（チェコ）
  • Year and Date: 2015-06-11
  • Int'l Joint Research
• [Remarks] Connexive logic
  • URL: https://sites.google.com/site/connexivelogic/