Probability Measures and Projections on Quantum Logics

被引：0
|
作者：
Nanasiova, Olga [1 ]
Cernanova, Viera [2 ]
Valaskova, Lubica [3 ]
机构：
[1] Slovak Univ Technol Bratislava, Inst Comp Sci & Math, Ilkovicova 3, Bratislava 81219, Slovakia
[2] Trnava Univ, Fac Educ, Dept Math & Comp Sci, Priemyselna 4, Trnava 91843, Slovakia
[3] Slovak Univ Technol Bratislava, Dept Math & Descript Geometry, Radlinskeho 11, Bratislava 81005, Slovakia
来源：
INFORMATION TECHNOLOGY, SYSTEMS RESEARCH, AND COMPUTATIONAL PHYSICS | 2020年 / 945卷
关键词：
Logical connectives; Orthomodular lattice; Quantum logic; Probability measure; State; CONJUNCTION;
D O I：
10.1007/978-3-030-18058-4_25
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
The present paper is devoted to modelling of a probability measure of logical connectives on a quantum logic (QL), via a G-map, which is a special map on it. We follow the work in which the probability of logical conjunction, disjunction and symmetric difference and their negations for non-compatible propositions are studied. We study such a G-map on quantum logics, which is a probability measure of a projection and show, that unlike classical (Boolean) logic, probability measure of projections on a quantum logic are not necessarilly pure projections. We compare properties of a G-map on QLs with properties of a probability measure related to logical connectives on a Boolean algebra.
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页码：321 / 330
页数：10
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