Substructural logic with Galois connection
| Project/Area Number |
24500024
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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 |
Fundamental theory of informatics
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| Research Institution | Tokyo Denki University |
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Principal Investigator |
KONDO Michiro 東京電機大学, 情報環境学部, 教授 (40211916)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 部分構造論理 / 剰余束 / 決定可能性 / ガロア結合 / residauted lattices / Galois connection / 国際情報交換 |
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| Outline of Final Research Achievements |
In order to solve the open problem "Is the Intuitionistic tense logic decidable?", we generalized the problem to that of substructural logic with Galois connection and considered algebraic properties of residuated lattices with Galois connection. At first we proved the characterization theorem of residuated lattices with an operator representing the modal operator. Next we considered properties of residuated lattices with two operators as Galois connection and proved that the intuitionistic modal logic was decidable. Moreover we also verified that the intuitionistic tense logic was a fusion of intuitionistic modal logics. It follows from a well-known result that a fusion of decidable logics is also decidable that our results give a proof that the intuitionistic tense logic is decidable, which was the open problem since at least 1984.
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Report
(4 results)
Research Products
(19 results)
