2016 Fiscal Year Final Research Report
The Categorical Unification of Foundations of Mathematics and of Quantum Physics, and its Applications to Categorical Duality in Machine Learning
| 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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| 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 |
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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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| Free Research Field |
数理科学・哲学
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