Negations and Meets in Topos Quantum Theory
Negations and Meets in Topos Quantum Theory
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DOI：
10.1007/s10701-021-00529-7
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发表时间：
2021-11
影响因子：
1.5
通讯作者：
Y. Kitajima
中科院分区：
文献类型：
--
作者：
Y. Kitajima
Daseinisation是从普通量子理论中的正交模格到拓扑量子理论中的Heyting代数的映射。虽然分配性在正交模格中并不总是成立，但在Heyting代数中是成立的。我们调查的条件下，否定和满足被保存的daseinisation，和的条件下，任何元素的海廷代数通过daseinisation转换对应于一个元素在原来的正交模格。我们表明，这些条件是等价的，而且，不仅在非分配的正交模格的情况下，而且在布尔代数包含超过四个元素的情况下，从正交模格通过daseinisation变换的海廷代数将包含一个元素，不对应于任何元素的原始正交模格。
The daseinisation is a mapping from an orthomodular lattice in ordinary quantum theory into a Heyting algebra in topos quantum theory. While distributivity does not always hold in orthomodular lattices, it does in Heyting algebras. We investigate the conditions under which negations and meets are preserved by daseinisation, and the condition that any element in the Heyting algebra transformed through daseinisation corresponds to an element in the original orthomodular lattice. We show that these conditions are equivalent, and that, not only in the case of non-distributive orthomodular lattices but also in the case of Boolean algebras containing more than four elements, the Heyting algebra transformed from the orthomodular lattice through daseinisation will contain an element that does not correspond to any element of the original orthomodular lattice.