关键词: 经典命题逻辑系统, D-随机真度, D-随机相似度, D-随机伪距离

Abstract: 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 probability 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 representation of D-randomized similarity degree and D-randomized pseudo-metric among formulas.

Key words:  classical propositional logic system, D-randomized truth degree, D-randomized similarity degree, D-randomized pseudo-metric