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The Categorical Unification of Foundations of Mathematics and of Quantum Physics, and its Applications to Categorical Duality in Machine Learning

Research Project

Project/Area Number 15H06313
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionKyoto University

Principal Investigator

Maruyama Yoshihiro  京都大学, 白眉センター, 特定助教 (20761290)

Project Period (FY) 2015-08-28 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords圏論的双対性 / 圏論的意味論 / 圏論的量子論 / 圏論的AI / 圏論的普遍論理 / 諸科学の圏論的基礎 / 圏論的統一科学 / 圏論の哲学 / 圏論的論理 / 量子基礎論 / 数学基礎論 / 非可換双対性 / 機械学習 / 再生核ヒルベルト空間 / 数理哲学 / スキーム論 / 非可換普遍代数 / 圏論的量子力学
Outline of Final Research Achievements

Our project is about the unification of mathematical and quantum foundations, and its applications to categorical duality in machine learning. Our result is nevertheless three-fold because "unification" has a double meaning. It is the unification of space conceptions in foundations of mathematics and of quantum theory (i.e., topos theory and categorial quantum theory); yet at the same time, it is the unification of (noncommutative) dualities in those two foundations. The first "unification" also implies the Lawverian unification of traditional quantum logic and categorical quantum mechanics. The remaining, third type of result is, of course, categorical duality in (the kernel method of) machine learning (or the duality of artificial intelligence). Overall, the project may be considered a stepping stone to what we call "categorical unified science" or "pluralistic unified science", which is the ultimate goal of "categorical logical positivism" as discussed in our recent Synthese paper.

Report

(3 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Annual Research Report
  • Research Products

    (11 results)

All 2017 2016 2015

All Journal Article (4 results) (of which Peer Reviewed: 3 results) Presentation (5 results) (of which Int'l Joint Research: 5 results) Book (2 results)

  • [Journal Article] Dynamics of Duality2017

    • Author(s)
      Y. Maruyama
    • Journal Title

      RIMS Kokyuroku

      Volume: xxx

    • Related Report
      2016 Annual Research Report
  • [Journal Article] Prior’s tonk, notions of logic, and levels of inconsistency: vindicating the pluralistic unity of science in the light of categorical logical positivism2016

    • Author(s)
      Y. Maruyama
    • Journal Title

      Synthese

      Volume: Logic and Philosophy of Prior Issue: 11 Pages: 3483-3495

    • DOI

      10.1007/s11229-015-0932-9

    • Related Report
      2016 Annual Research Report 2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Categorical Harmony and Paradoxes in Proof-Theoretic Semantics2016

    • Author(s)
      Y. Maruyama
    • Journal Title

      Advances in Proof-Theoretic Semantics

      Volume: 43 Pages: 95-114

    • DOI

      10.1007/978-3-319-22686-6_6

    • ISBN
      9783319226859, 9783319226866
    • Related Report
      2016 Annual Research Report 2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] AI, Quantum Information, and External Semantic Realism: Searle's Observer-Relativity and Chinese Room, Revisited2016

    • Author(s)
      Y. Maruyama
    • Journal Title

      Fundamental Issues of Artificial Intelligence

      Volume: 376 Pages: 115-127

    • DOI

      10.1007/978-3-319-26485-1_8

    • ISBN
      9783319264837, 9783319264851
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Presentation] Category Theory and Lightweight Ontology2017

    • Author(s)
      Y. Maruyama
    • Organizer
      Oxford OASIS Seminar
    • Place of Presentation
      University of Oxford, UK
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Machine and Causality2017

    • Author(s)
      Y. Maruyama
    • Organizer
      Oxford Quantum Foundations Discussion
    • Place of Presentation
      University of Oxford, UK
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Dynamics of Duality: How Duality Emerges, Changes, and Breaks2016

    • Author(s)
      Y. Maruyama
    • Organizer
      RIMS Workshop on Mathematical Logic and its Applications
    • Place of Presentation
      Kyoto University, Japan
    • Year and Date
      2016-09-26
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Harmony, the Curry-Howard Correspondence, and Higher Proof Theory2016

    • Author(s)
      Y. Maruyama
    • Organizer
      JSPS Core-to-Core Workshop on Mathematical Logic and its Applications
    • Place of Presentation
      Kyoto University, Japan
    • Year and Date
      2016-09-16
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Categorical Foundations of Big Data Analytics2016

    • Author(s)
      Y. Maruyama
    • Organizer
      International Conference on Category Theory
    • Place of Presentation
      Dalhousie University, Canada
    • Year and Date
      2016-08-08
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Book] Meaning and Duality: From Categorical Logic to Quantum Physics2017

    • Author(s)
      Y. Maruyama
    • Publisher
      University of Oxford
    • Related Report
      2016 Annual Research Report
  • [Book] 圏論の歩き方2015

    • Author(s)
      圏論の歩き方委員会(編)
    • Total Pages
      304
    • Publisher
      日本評論社
    • Related Report
      2015 Annual Research Report

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Published: 2015-08-26   Modified: 2018-03-22  

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