Quantum monadic algebras

被引：1
|
作者：
Harding, J. [1 ]
机构：
[1] New Mexico State Univ, Las Cruces, NM 88003 USA
来源：
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2022年 / 55卷 / 39期
关键词：
cylindric algebra; monadic algebra; quantum logic; subfactor; von Neumann algebra; commuting square; COMMUTING SQUARES; SUBFACTORS; REPRESENTATION; CATEGORIES; LATTICES; ENTROPY;
D O I：
10.1088/1751-8121/ac845b
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We introduce quantum monadic and quantum cylindric algebras. These are adaptations to the quantum setting of the monadic algebras of Halmos, and cylindric algebras of Henkin, Monk and Tarski, that are used in algebraic treatments of classical and intuitionistic predicate logic. Primary examples in the quantum setting come from von Neumann algebras and subfactors. Here we develop the basic properties of these quantum monadic and cylindric algebras and relate them to quantum predicate logic.
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页数：27
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