| 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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| 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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