| 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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| 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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