论文标题
量子元代数
Quantum monadic algebras
论文作者
论文摘要
我们引入量子元和量子圆柱代数。这些是对HALMOS的Monadic代数的量子设置以及Henkin，Monk和Tarski的圆柱代数的适应，这些代数用于古典和直觉谓词逻辑的代数处理中。量子设置中的主要示例来自von Neumann代数和子因子。在这里，我们开发了这些量子元素和圆柱代数的基本特性，并将它们与量子谓词逻辑相关联。
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.
