经典逻辑中的模糊命题(Ⅰ)  

Fuzzy proposition in classical logic(Ⅰ)

作　　者：袁学海[1] YUAN Xuehai(School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]大连理工大学数学科学学院,辽宁大连116024

出　　处：《辽宁师范大学学报（自然科学版）》2024年第2期145-150,共6页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(12071056)。

摘　　要：经典逻辑对命题变元的真值指派为二值的,即为0或1.如果将命题公式中的命题变元的真值指派为[0,1]中的值,则形成了模糊命题,从而形成了模糊逻辑理论.在现有的模糊逻辑中,模糊命题在形式上并不“模糊”,只不过对命题变元做了“模糊”的指派.因此,这种模糊逻辑实际上是“经典命题公式+模糊真值指派”的模糊逻辑.首先在经典命题逻辑中引入了模糊命题的概念,这种模糊命题在形式上就是模糊的,而经典命题是模糊命题的特例.其次,通过对命题变元的二值指派,得到了模糊命题的真值.最后,研究了模糊命题的真值运算性质.研究发现:在经典逻辑系统中引入新的模糊命题的概念后,公式增加了,真值指派没有变,重言式没有减少.本研究可以看作是“模糊命题+二值真值指派”的模糊逻辑.Classical logic assigns the truth value of propositional variables to binary values,i.e.0 or 1.If the truth value of propositional variables in a propositional formula is assigned within the range of[0,1],it constitutes a fuzzy proposition and thus forms the theory of fuzzy logic.In existing fuzzy logic,fuzzy propositions are not“fuzzy”in form,but only“fuzzy”assignment to propositional variables.Therefore,this fuzzy logic is actually a fuzzy logic of“classical propositional formulas and fuzzy truth assignment”.Firstly,the concept of fuzzy proposition in classical propositional logic was introduced,which is formally fuzzy,and classical propositions are special cases of fuzzy propositions.Secondly,the truth value of fuzzy propositions was obtained by assigning binary propositional variables.Finally,the truth operation properties of fuzzy propositions were studied.It was found that after introducing the new concept of fuzzy propositions in classical logic systems,the formula increased,the truth assignment did not change,and the tautology did not decrease.This study can be regarded as a fuzzy logic of“fuzzy propositions and binary truth assignment”.

关 键 词：命题 模糊命题 真值指派 重言式 模糊逻辑 

分 类 号：O141.1[理学—数学]