论文标题
通过拓扑类别统一模态逻辑
Unification of Modal Logic via Topological Categories
论文作者
论文摘要
在本文中，我们通过拓扑类别的框架在文献中提供了对模态逻辑的不同类型语义的统一描述。以分类逻辑的方式，我们一方面建立了模态逻辑的各种句法扩展之间的确切对应关系，包括模态依赖性，群体代理结构和逻辑动力学和拓扑类别中的语义结构。该框架为我们提供了在模态逻辑的所有不同类型的语义中解释这些句法扩展的统一处理，它加深了我们对模态逻辑抽象结构的概念理解。
In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of categorical logic, we establish an exact correspondence between various syntactic extensions of modal logic on one hand, including modal dependence, group agent structures, and logical dynamic, and semantic structures in topological categories on the other hand. This framework provides us a uniform treatment of interpreting these syntactic extensions in all different types of semantics of modal logic, and it deepens our conceptual understanding of the abstract structure of modal logic.
