Abstract: By means of randomization, the concept of random truth degree and random uncertainty degree of formulas in [n]-valued propositional logical system are introduced. It is proved that the uncertainty degree of conclusion is less than or equal to the sum of the product of uncertainty degree of every premise and its essentialness degree in formal inference. The MP，HS rules are proved by the generalization of fundamental theorem of probability logic.

Key words: random truth degree, random uncertainty degree, random pseudo-metric, random logic metric space

摘要： 利用赋值集的随机化方法，在[n]值命题逻辑系统中提出了公式的随机不可靠度概念，证明了一个有效推理结论的随机不可靠度不大于各前提的随机不可靠度与其必要度的乘积之和。通过推广的概率逻辑学基本定理，证明了随机逻辑度量空间中MP规则和HS规则成立。

关键词: 随机真度, 随机不可靠度, 随机伪距离, 随机逻辑度量空间