Abstract: Based on conditional probability, using the randomization method of valuation set, the concept of conditional randomized truth degree of formulas is introduced in the  Lukasiewicz n-valued propositional logic. The MP rule and HS rule of conditional randomized truth degrees are proved. The concepts of conditional randomized similarity and conditional pseudo-metric between formulas are introduced and conditional randomized logic metric space is built. Several properties of conditional pseudo-metric are deduced and it is proved that the logical operations are continuous on conditional randomized logic metric space. The theory of approximate reasoning under certain information is given out.

Key words: conditional randomized truth degree, conditional randomized similarity, conditional randomized logic metric space, approximate reasoning

摘要： 基于条件概率的思想，利用赋值集的随机化方法，在Lukasiewicz n值命题逻辑系统中引入公式的条件随机真度，证明了条件随机真度的MP规则和HS规则。引入公式间的条件随机相似度和条件伪距离，建立了条件随机逻辑度量空间，推导出条件伪距离的若干性质，证明了条件随机逻辑度量空间中逻辑运算的连续性，初步研究了给定条件下的近似推理理论。

关键词: 条件随机真度, 条件随机相似度, 条件随机逻辑度量空间, 近似推理