命题公式集F(S)的基于修正的Gdel算子的十八类分划

An eighteen-classification partition of propositional formula set F(S)based on revised Gdel operator

本文利用修正的Gdel蕴涵算子研究了命题公式集F(S)中公式确定集的特征,进而以确定集为工具得到F(S)的一个十八类分划,并证明了这种分划关于非运算是同余的.最后讨论了各类关于MP运算和HS运算的封闭性.

In this paper the characterization of formula's validation set are discussed by using revised Gdelimplication operator in the propositional formula set F(S).Using this concept eighteen classifications of F(S) is given and it is proved that this partition about negation is congruent.Moreover,it is discussed whether each classification in F(S) is closed under modus ponens and hypothetical syllogism.