| Project/Area Number |
15H06313
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2015-08-28 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| 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)
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| 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 |
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| 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.
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