
TL;DR
This paper introduces quantum monadic and cylindric algebras, adapting classical algebraic logic structures to the quantum setting using von Neumann algebras, and explores their properties and relation to quantum predicate logic.
Contribution
It presents the first development of quantum analogs of monadic and cylindric algebras, extending algebraic logic into quantum theory.
Findings
Defined quantum monadic and cylindric algebras
Established their basic properties
Connected these algebras to quantum predicate logic
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.
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Taxonomy
TopicsAdvanced Algebra and Logic · Logic, programming, and type systems · Logic, Reasoning, and Knowledge
