LUO Qing-jun1,2, WANG Guo-jun1*
(1 College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China;2 College of Statistics, Xi′an University of Finance and Economics, Xi′an 710100, Shaanxi, China)
Abstract:
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, zero-dimensional 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 2n pairwise disjoint areas by n maximal consistent theories, and the diameter of each area is equal to 1 in the logic metric space.
KeyWords:
propositional logic; uniformity; uniform topology; maximal consistent theory
