命题逻辑系统L_(n)^(*)中理论的p-随机发散度的分布研究  

Distribution of p-Randomized Divergence Degree of Theory in Propositional Logic System L_(n)^(*)

作　　者：惠小静[1] 南琼 许倩 HUI Xiaojing;NAN Qiong;XU Qian(College of Mathematics and Computer Science,Yan'an University,Yan'an 716000)

机构地区：[1]延安大学数学与计算机科学学院,延安716000

出　　处：《系统科学与数学》2023年第9期2310-2318,共9页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(12261090)资助课题。

摘　　要：在命题逻辑系统L_(n)^(*)中提出了p-随机真度,p-随机相似度,p-随机伪距离的概念,建立了p-随机逻辑度量空间(F(S),ρp).在p-随机逻辑度量空间(F(S),ρp)中提出了理论的p-随机发散度的概念,指出理论的p-随机发散度是和随机n值分布序列p=(p1,p2,…)的具体取值是密切相关的.证明了全体原子公式集S的p-随机发散度随着n值分布序列p的不同取值可以充满(0,1]实数区间.In the propositional logic system L_(n)^(*),the concepts of p-randomized truth degree,p-randomized similarity degree and p-randomized pseudo-distance are proposed.p-randomized logical metric space(F(S),Pp)is established,and the concept of p-randomized divergence degree is proposed in the p-randomized logical metric space(F(S),Pp).It is pointed out that the p-randomized divergence degree of the theory and the values of randomized n-point distribution are closely related.It is proven that the p-randomized divergence degree of the set of atomic formulas with different values of n-point distribution sequence can be full of the real number interval(0,1].

关 键 词：p-随机真度 p-随机伪距离 p-随机逻辑度量空间 p-随机发散度 

分 类 号：O141[理学—数学]