二值命题逻辑中理论的发散性、相容性及其拓扑刻画

Topological Description of Divergency and Consistency of Two-Valued Propositional Theories

在二值命题逻辑系统中基于逻辑度量空间(F(S),ρ)而建立起了逻辑理论的发散性、相容性和理论的拓扑性质之间的联系。证明了逻辑理论Г是全发散的当且仅当D(Г)在(F(S),ρ)中稠密,闭理论Г是相容的当且仅当Г在(F(S),ρ)中不含内点,证明了(F(S),ρ)是零维空间,并具有一种类似于樊畿性质的所谓“有限等球连通性”．

Let （F（S）, ρ） be the logic metric space of two-valued propositional logic. It is proved that a logic theory G is fully divergent iff D（G） is dense in （F（S）, ρ）., and G is consistent iff D（G） contains no interior point. Moreover, it is proved that （F（S）, ρ） is zero-dimensional and possesses a property similar to the Key Fan＇s property for describing connectedness of topological spaces.