Abstract: The present paper introduces the notion of probabilistic truth degree of formulas in the unified framework of n-valued S-MTL logic by means of Borel probability measures on the space of all valuations endowed with the usual product topology. The integral expression of truth degree of formulas is given, similarity degree and pseudo metric between formulas are introduced based on the probabilistic truth degree of formulas, this makes it possible to construct a kind of model behaved both randomly and globally for approximate reasoning in the unified framework of n-valued S-MTL logic.

Key words: quantitative logic, Borel probability measure, pseudo metric, approximate reasoning

摘要： 在n值[S-MTL]逻辑系统的统一框架下，通过视全体赋值之集为通常乘积拓扑空间，给出了命题的Borel概率真度定义。通过构造公式所诱导的阶梯函数给出了公式真度的积分表达式，进而利用命题的Borel概率真度在该逻辑系统中引入公式间的相似度及其伪距离，使得在n值[S-MTL]逻辑系统的统一框架下搭建起融随机性和整体性于一体的近似推理模型成为可能。

关键词: 计量逻辑学, Borel概率测度, 伪距离, 近似推理