Abstract: The research for logic metric is an important part of approximate reasoning.Firstly，based on the method of probability measure，this paper introduces the concept of probability truth degrees and its general expression in unevenly probability space.Secondly，it obtaines the similarity degree between two formulas on a residuated lattice in terms of L-fuzzy similarity.And the character properties are discussed in four types of n-valued logic systems based on the left-continuous t-norms.Lastly，a pseudo-distance is introduced by means of probability truth degree.Then it can provide a kind of inference frame for the approximate reasoning theory.

Key words: probability measure, probability truth degree, residuated lattice, similarity degree, pseudo-distance

摘要： 逻辑度量研究是近似推理理论的一个重要组成部分。首先在四种常见n值逻辑系统中，利用概率测度的方法，引入了逻辑公式概率真度的概念及其表达式，讨论了其基本性质；然后在剩余格上定义了公式间的相似度，给出了四种n值逻辑系统中公式间相似度的统一表达式，研究了相似度的若干特征性质；最后引入了公式间的伪距离，为近似推理理论提供了依据。

关键词: 概率测度, 概率真度, 剩余格, 相似度, 伪距离