逻辑公式的模糊度  

Fuzzy Degree of Logical Formula

作　　者：于鹏[1] 

机构地区：[1]陕西科技大学理学院,西安710021

出　　处：《计算机科学与探索》2015年第5期635-640,共6页Journal of Frontiers of Computer Science and Technology

基　　金：陕西省自然科学基金No.2011JQ1015;陕西省统计科研计划项目No.2014LX05~~

摘　　要：从判断一个命题正确与否的难易程度入手,在经典的二值逻辑系统中,利用一个命题公式赋值为1与赋值为0的个数,引入了一个反映命题公式清晰程度的量——模糊度。给出了模糊度的相关性质,指出了模糊度与计量逻辑学中真度定义之间的联系与区别,得到如下结论:(1)在一个推理中过程中,随着前提模糊度的降低,结论的模糊度也随之降低;(2)具有相同模糊度的命题公式构成的命题集是一个不相容命题集;(3)两个距离相近的命题公式,其模糊度也十分接近。From the view whether it is easy to judge a formula correctly or not, this paper proposes the concept of fuzzy degree of a given formula in classical two-valued logic, which uses the numbers of a propositional logic assign-ment 1 and 0. This paper gives the related properties of fuzzy degree, and points out the connections and differences between fuzzy degree and the definition of truth degree in quantitative logic. The following conclusions are got：（1） In a reasoning process, with the lower of the fuzzy degree of premise, the fuzzy degree of conclusion is also lower;（2） The set which constitutes of the same fuzzy degree proposition formulas is inconsistent; （3） If the distance of two formulas is closer, the fuzzy degree of two formulas is closer.

关 键 词：计量逻辑学 模糊度 近似推理 真度 

分 类 号：O235[理学—运筹学与控制论]