经典命题逻辑中的一致结构与一致拓扑  

Uniformities and uniform topologies in classical propositional logic

作　　者：罗清君[1,2] 王国俊[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062 [2]西安财经学院统计学院,陕西西安710100

出　　处：《陕西师范大学学报（自然科学版）》2013年第3期7-12,共6页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10771129;11171200)

摘　　要：为描述经典命题逻辑中全体公式之集F(S)的拓扑结构,基于理论Γ在F(S)上诱导的同余关系构建一致结构与一致拓扑.证明了所得的一致拓扑是第二可数的、零维的、没有孤立点的完全正则拓扑,且逻辑连接词■与→关于导出的一致拓扑是连续的.得出了n个极大相容理论恰好将F(S)划分成2n个两两不交的非空区域,且每个区域在逻辑度量空间中的直径均为1.Based on the congruence induced by Γ theory in the set F（S） of all formulae in classical propositional logic, the uniformities and uniform topologies on F（S） are established to describe its topological structure. It is proved that the uniform topologies are the second countable, zerodimensional and complete regular topologies without isolated points. It can be proved that the logic connections and → are continuous with respect to the uniform topology. Meanwhile, it is concluded that F（S） is divided into 2^n pairwise disjoint areas by n maximal consistent theories, and the diameter of each area is equal to 1 in the logic metric space.

关 键 词：命题逻辑 一致结构 一致拓扑 极大相容理论 

分 类 号：O141.1[理学—数学]