Quantum monadic algebras. (30th September 2022)

• Record Type: Journal Article
• Authors: Harding, J
• Is Part Of: Journal of physics. Volume 55:Number 39(2022)
• Publication Date: 2022-09-30
• Subjects: cylindric algebra -- monadic algebra -- quantum logic -- subfactor -- von Neumann algebra -- commuting square; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ac845b
• Languages: English
• ISSNs: 1751-8113

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.