二值命题逻辑中理论的发散性,相.pdf

504 Vol.50, No.4 20077 ACTA MATHEMATICA SINICA, Chinese Series Jul., 2007 : 0583-1431(2007)04-0841-10 : A Æ 710062 Æ 710049 E-mail: gjwang@snnu.edu.cn Æ 710062 (F (S), ρ) . Γ D (Γ) (F (S), ρ) , Γ Γ (F (S), ρ) . (F (S), ρ) , “”. ; ; MR(2000) 28A25, 28C15 O172.2, O174.12 Topological Description of Divergency and Consistency of Two-Valued Propositional Theories Guo Jun WANG Institute of Mathematics, Shaanxi Normal University, Xi’an 710061, P. R. China Research Center for Science, Xi’an Jiaotong University, Xi’an 710049, P. R. China E-mail: gjwang@snnu.edu.cn Yan Hong SHE Research Center for Science, Xi’an Jiaotong University, Xi’an 710049, P. R. China Abstract 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. Keywords logic metric space; theory; divergency degree MR(2000) Subject Classification 28A25, 28C15 Chinese Library Classification O172.2, O174.12 : 2006-03-13; : 2006-11-28 : 842 50 0 Æ, , ; .