关键词: 概率测度, 概率真度, 相似度, 伪距离, 孤立点

Abstract: Using the infinite product of unevenly distributed probability space ，this paper introduces the theory of probability truth degree in £ukasiewicz 3-valued propositional logic.It is proved that the set of probability truth degree of all formulas has no isolated point in [0，1].The conceptions of probability similarity degree and pseudo-metric on two formulas are defined by means of the concept of probability truth degree of propositions.Moreover，the probability logic metric space is built.It is proved that this space has no isolated point.Then it can provide a possible framework for approximate reasoning theory.

Key words: probability measure, probability truth degree, similarity degree, pseudo-metric, isolated point