概率逻辑伪度量空间及其性质  

Probability Logic Pseudo-metric Space and Its Properties

作　　者：惠小静[1] 王国俊[2] 崔志明[1] 

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000 [2]陕西师范大学数学研究所

出　　处：《模糊系统与数学》2007年第5期1-7,共7页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金重点资助项目(10331010)

摘　　要：论证有限多个公式的概率分布与生成它的原子公式集的概率分布之间的关系,然后把计量逻辑学与概率逻辑学相结合,提出了概率真度、概率逻辑伪度量空间(F(n),ρP);指出当取均匀概率分布时,概率真度就转化为计量逻辑学中的真度,同时两公式间的概率逻辑伪距离Pρ就转化为计量逻辑学中的伪距离ρ.从而在有限理论中建立了一种更具一般性的概率逻辑伪度量空间理论。The relationship between the probability distribution of finite formulas and the probability distribution of atomic formulas generating them is discussed, and the concepts of probability truth degree and probability logic pseudo-metric space （F（n）, ρp） are proposed by combining quantitative logic and probability logic. It is proved that when the probability distribution is even, the value of probability truth degree is equal to the value of truth degree and the value of probability logic pseudometric ρp is equal to the value of pseudo-metric ρ in quantitative logic. Thus a more general pseudo- metric is established in finite theories.

关 键 词：概率逻辑 概率分布 概率真度 伪度量空间 

分 类 号：O211[理学—概率论与数理统计]