经典逻辑中的模糊命题(Ⅰ)
Fuzzy proposition in classical logic(Ⅰ)
袁学海1
作者信息
- 1. 大连理工大学数学科学学院,辽宁大连 116024
- 折叠
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"模糊命题十二值真值指派"的模糊逻辑.
Abstract
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 varia-bles.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 intro-duced,which is formally fuzzy,and classical propositions are special cases of fuzzy propositions.Sec-ondly,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 in-troducing 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Key words
proposition/fuzzy propositions/true value assignment/tautology/fuzzy logic引用本文复制引用
基金项目
国家自然科学基金资助项目(12071056)
出版年
2024
NETL
NSTL
万方数据