论文标题
效应代数引起的逻辑
The logic induced by effect algebras
论文作者
论文摘要
效应代数形成量子力学逻辑的代数形式化。对于晶格效应代数E，我们研究了一种自然的含义，并证明E的含义还等于E。然后我们以质子样式提出了一个简单的公理系统，以便将晶格效应代数诱导的逻辑化。对于不需要晶格排序的代数效应代数，我们引入了某种含义，这些含义无处不在，但结果不必是单个元素。然后，我们研究效应含义代数，并证明这些代数与满足上升链条件的代数效应之间的对应关系。我们为不一定是晶格订购的效应代数提供了一种质感样式的公理系统，并证明它是有限效应代数引起的逻辑的代数语义。
Effect algebras form an algebraic formalization of the logic of quantum mechanics. For lattice effect algebras E we investigate a natural implication and prove that the implication reduct of E is term equivalent to E. Then we present a simple axiom system in Gentzen style in order to axiomatize the logic induced by lattice effect algebras. For effect algebras which need not be lattice-ordered we introduce a certain kind of implication which is everywhere defined but whose result need not be a single element. Then we study effect implication algebras and prove the correspondence between these algebras and effect algebras satisfying the Ascending Chain Condition. We present an axiom system in Gentzen style also for not necessarily lattice-ordered effect algebras and prove that it is an algebraic semantics for the logic induced by finite effect algebras.
