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中文摘要：
将模糊命题逻辑中的∑-a-重言式理论与计量逻辑学中的真度理论相结合，在模糊命题逻辑系统Ln^＊中引入了公式集相对于有限理论的∑r-模糊真度理论，讨论了其中的主要性质。并利用真度关系：τr（A）＋τr（A→B）≤1＋τr（B）在模糊命题逻辑系统Ln^＊中的公式集F（S）上引入相对于有限理论的 Г-伪距离概念，从而为在模糊命题逻辑系统Ln^＊中建立相对于有限理论的近似推理框架奠定了基础。
英文摘要：
Having combination the theory of .∑-a-tautologies of fuzzy propositional logic and the theory of truth degree in metrology of logic, which have been introduced by proffesor G. J. Wang, we have introduced the theory of ∑r-fuzzy truth degrees relent to finite theoryof formulas of F（S） in the propositional logic system Ln^＊. By employing the relation of theory of ∑r-fuzzy truth degree： τr（A）＋τr（A→B）≤1＋τr（B）, we have proposed the concept of Г-pesdo-metric on F （S） relent to finite theory of the propositional logic system Ln^＊. The results gained in the paper have complemented and enhanced the original theories of metrology of logic, and the work proposes a new idea and a new frame for study of fuzzy reasoning.
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