中文摘要：

给出了（F（S）,ρ）中公式的一种逻辑等价分解,利用这种逻辑等价分解讨论公式的真度、伪距离和相似度的计算问题,并且引入了（F（S′）,ρ）中公式的限制逻辑等价概念,建立了一种等价关系.作为限制逻辑等价关系的应用,得到了（F（S）,ρ）中基于真度的τ（A→X）=α型逻辑方程的解集,利用限制逻辑等价关系进行的一种相等＂直径＂的子集划分结果,为二值命题逻辑系统的逻辑推理和程度化的进一步研究提供了方法.

英文摘要：

A kind of logical equivalence decomposition of the formula in is presented and applied to discuss the calculating issues of the truth degree,pseudo metric and similarity degree of the formula.With the introduction of restricted logic equivalence,an equivalence relation is established and applied to obtain the subset＇s partition of the solution set of logical equation based on the truth degree by the equal ＇diameter＇ method,which provides useful methods for further research of the logical reasoning and grading in two-valued propositional logic system.