Abstract
Abstract
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.
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
Reference71 articles.
1. An introduction to Type II1 factors;Anantharaman,2010
2. An angle between intermediate subfactors and its rigidity;Bakshi;Trans. Am. Math. Soc.,2019
3. Functional monadic Heyting algebras;Bezhanishvili;Algebra Universalis,2002
4. The logic of quantum mechanics;Birkhoff;Ann. Math.,1936
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