经典逻辑系统中的随机化再研究

摘要

给出了经典命题逻辑系统中n元命题公式基于随机数列和随机映射的向量表示形式,利用命题公式的基于随机数列的向量表示形式给出公式的D-随机真度、公式间的D-随机相似度和D-随机伪距离的等价表示形式.说明了一个具体的n元经典命题公式的D-随机真度最多只有22n种情况.利用命题公式间的D-随机相似度和D-随机伪距离的等价表示形式,给出了关于命题公式的D-随机真度、命题公式间的D-随机相似度和D-随机伪距离的一些性质的新的证明.%This paper gives the vector representation of n-ary formula in classical propositional logic system based on random sequence and random mapping, defines the D-randomized truth degree of formulas and D-randomized similarity degree and D-randomized pseudo-metric among formulas based on the vector representation of formula, and explains that the definitions of truth degree and D-randomized pseudo-metric are equivalent to the original prob-ability definition. Then, this paper proves that the D-randomized truth degree of n-ary formula is not more than 22n cases. Finally, some simple properties of pseudo-metric among formulas are obtained based on the equivalent repre-sentation of D-randomized similarity degree and D-randomized pseudo-metric among formulas.