2016 Fiscal Year Final Research Report
Reconstruction of algebraic semantics for non-classical predicate logics
| Project/Area Number |
24540120
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Shizuoka University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2017-03-31
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| Keywords | 非古典論理 / 代数的意味論 / 述語論理 / クリプキ意味論 |
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| Outline of Final Research Achievements |
Algebraic semantics for classical logic was given by an algebraic system called Boolean algebra (named after G. Boole in 19th century). It is known that the completion of Boolean algebra can capture classical predicate logic. However, it has been hard to extend this method to non-classical predicate logics.
In this research, we reconstructed algebraic semantics for some non-classical predicate logics by making use of the notion of adjoints in category theory, not by completion; and we presented its applications.
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| Free Research Field |
数学（数理論理学・非古典論理）
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