2021 Fiscal Year Final Research Report
Understanding constructivity from the perspective of intermediate predicate logics
| Project/Area Number |
16K05252
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Shizuoka University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2022-03-31
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| Keywords | 構成性 / 非古典論理 / 述語論理 / disjunction property / existence property |
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| Outline of Final Research Achievements |
Constructivity is one of the important subjects of mathematical logic and a fundamental concept in intuitionistic logic and constructive mathematics. The disjunction and existence properties, which characteristically express the constructivity, have been studied almost independently in intermediate predicate logic and intuitionistic (constructive) mathematics. However, a crucial overlap between them has been found. The idea of this research is to advance research using this observation as leverage.
One academically significant achievement is the following:
With researchers in constructive mathematics and intuitionistic arithmetic, we have developed a method to construct a Kripke model of intuitionistic arithmetic from a given Kripke model for intermediate propositional logic, using the Arithmetical Completeness Theorem.
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| Free Research Field |
数学（数理論理学・非古典論理）
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| Academic Significance and Societal Importance of the Research Achievements |
構成性(特にDPとEP)は、数理論理学の由緒正しい主題である。これを本研究の観点で研究することは、中間述語論理と構成的数学という、密接な関連が意識されていなかった2分野を結びつけ、さらに新しい発展をもたらす。また、構成的数学で議論されてきた概念が、中間述語論理でも意味を持ち、計算機科学との関連が知られている。その意味では、さらに分野融合的な研究に発展する可能性もあり、将来的な波及効果が期待できる。
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