Journal of Frontiers of Computer Science and Technology ›› 2017, Vol. 11 ›› Issue (8): 1354-1360.DOI: 10.3778/j.issn.1673-9418.1701001

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Restudy on Randomization of Classical Logic System

MA Qiaoyun1+, WU Hongbo2   

  1. 1. College of Information Engineering, Xi’an University, Xi’an 710065, China
    2. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China
  • Online:2017-08-01 Published:2017-08-09

经典逻辑系统中的随机化再研究

马巧云1+,吴洪博2   

  1. 1. 西安文理学院 信息工程学院,西安 710065
    2. 陕西师范大学 数学与信息科学学院,西安 710062

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

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。

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