States on non-commutative residuated lattices
| Project/Area Number |
15K00024
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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 |
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, システムデザイン工学部, 教授 (40211916)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | residuated lattice / state / state 剰余束 / state 演算子 / 非可換剰余束 / derivation / 特徴付け定理 |
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| Outline of Final Research Achievements |
In this research programme, I consider some properties of states on non-commutative residuated lattices and prove that for any non-commutative residuated lattice L, if there exists a state s on L, then the quotient structure L/ker(s) by a kernel ker(s) of the state s is a (commutative) MV-algebra. Therefore, it follows from this result that the measurement problems in quantum logics reduce to those of MV-algebras. After that, I aslo consider algebraic properties of residuated lattices L with state operators $\sigma$ which are not outer languages like mappings but inner ones like modal operators. These structures (L,$\sigma$) are called $\sigma$-residuated lattices. I got some results about algebraic properties of $\sigma$-residuated lattices and published a paper in a journal.
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Report
(4 results)
Research Products
(19 results)
