论文标题
组合逻辑的逻辑
Logic of Combinatory Logic
论文作者
论文摘要
我们开发了一个经典的命题逻辑，用于有关组合逻辑的推理。我们定义其语法，公理系统和语义。语法和公理系统是根据经典命题逻辑提出的，并以类型的组合项为基本命题，以及基于与原始组合剂相对的特殊元素扩展的应用结构的语义。事实证明，未构图的组合逻辑的方程理论和所提出的公理系统都是合理的和完整的W.R.T.给定的语义。此外，我们证明组合逻辑是合理的，完整的W.R.T.给定的语义。
We develop a classical propositional logic for reasoning about combinatory logic. We define its syntax, axiomatic system and semantics. The syntax and axiomatic system are presented based on classical propositional logic, with typed combinatory terms as basic propositions, along with the semantics based on applicative structures extended with special elements corresponding to primitive combinators. Both the equational theory of untyped combinatory logic and the proposed axiomatic system are proved to be sound and complete w.r.t. the given semantics. In addition, we prove that combinatory logic is sound and complete w.r.t. the given semantics.
