论文标题
通过时空的含义
Implication via Spacetime
论文作者
论文摘要
在本文中，我们打算以最通用的形式研究含义，从而推广不同类别的含义，包括Heyting的含义，依从性含义和弱的严格含义。遵循直觉逻辑的拓扑解释，我们将引入非交互性空间，以提供对直觉命题的更具动态和主观的解释。这些时空的组合是表现良好的含义的自然来源，我们将表明它们的时空含义代表了任何其他合理的抽象含义。然后，为了为抽象的含义提供忠实的表现良好的语法，我们将为非共同空间开发一个逻辑系统，我们将介绍拓扑和kripke语义。这些逻辑通过将它们作为其特殊片段来统一了次级结构和次要主义逻辑。
In this paper we intend to study implications in their most general form, generalizing different classes of implications including the Heyting implication, sub-structural implications and weak strict implications. Following the topological interpretation of the intuitionistic logic, we will introduce non-commutative spacetimes to provide a more dynamic and subjective interpretation of an intuitionistic proposition. These combinations of space and time are natural sources for well-behaved implications and we will show that their spatio-temporal implications represent any other reasonable abstract implication. Then to provide a faithful well-behaved syntax for abstract implications, we will develop a logical system for the non-commutative spacetimes for which we will present both topological and Kripke semantics. These logics unify sub-structural and sub-intuionistic logics by embracing them as their special fragments.
