广义MP问题的α-三Ⅰ解的形式化理论

Formalized theory of α-triple Ⅰ solutions for problems of generalized modus ponens

研究了二值命题逻辑中模糊推理的全蕴涵α-三Ⅰ算法的形式化问题.提出了(F(S),)中的极小α公式的概念,当α∈{k/2n|k=0,1,…,2n,n=1,2,…}时得到如下结果:(1)全体极小α(α{0,1})公式构成(F(S),)中的反链;(2)当α=1时,全体极小α公式之集是相容的;当α≠1时,全体极小α公式之集是不相容的.证明了广义MP问题的形式化α-三Ⅰ解的存在性定理.

The aim of to study the formalized theory of α-triple Ⅰ methods for fuzzy reasoning in classical propositional logic.The concept of minimal α formula in（F（S）,） is introduced and the following results are proved when α belongs to k/2n｜k=0,1,…,2n,n=1,2,…：（1） All the minimal α（α{0,1}） formulas constitute an antichain in（F（S）,）;（2） The set of all the minimal α formulas is consistent when α equals 1;otherwise,it is inconsistent.The existence theorem of formalized α-triple Ⅰ solution for problems of generalized modus ponens is also proved.