Abstract: Based on a new cognizing for Vague concepts, using random sets and probability theory, the concepts of expression of universe of discourse and its appropriate measure are introduced. Consequently, by introducing the concepts of same Vague predicate propositions and their probability-truth degree, a new non-classical logic, called probabilistic logic of same Vague predicate proposition, is presented, and the laws of the logic are provided. The laws of the logic show that it and classical logic have excellent consistency. This paper compares the advantages and shortages of both propositional Fuzzy logics and probabilistic logic of Vague propositions.

Key words: non-classical logic, probabilistic logic, same Vague predicate propositions, random sets, expression of universe of discourse

摘要： 基于对Vague（或Fuzzy）概念的一种新的认知，使用随机集和概率论，引入了论域表达式及其适当测度的概念。进一步地，通过引入同Vague谓词命题及其他们真的概率（简称概率真度）的概念，提出了一种新的非经典命题逻辑，称为同Vague谓词命题的概率逻辑，并提供了其逻辑规律。其逻辑规律表明它与经典逻辑具有优良的和谐性。比较了同Vague谓词命题的概率逻辑与模糊逻辑的长处与不足。

关键词: 非经典逻辑, 概率逻辑, 同Vague谓词命题, 随机集, 论域表达式