Journal of Frontiers of Computer Science and Technology ›› 2020, Vol. 14 ›› Issue (11): 1975-1980.DOI: 10.3778/j.issn.1673-9418.2002004

Previous Articles    

Jaccard Distance of Logical Formulas and Its Application

YU Peng   

  1. School of Arts and Sciences, Shaanxi University of Science and Technology, Xi??an 710021, China
  • Online:2020-11-01 Published:2020-11-09

逻辑公式间的Jaccard距离及其应用

于鹏   

  1. 陕西科技大学 文理学院,西安 710021

Abstract:

Quantifying the related concepts of propositional logic is a new method of propositional logic research. It is differe.nt from the syntax and semantics method and is a powerful tool for studying the structure of propositional sets. By using the Jaccard similarity coefficient, this paper introduces the concepts of Jaccard similarity degree, Jaccard pseudo-metric and Jaccard similarity degree representation method of the truth degree of a formulae in quantitative logic, and constructs a new kind of quantitative model of logic system L. This paper investigates the basic properties of Jaccard logic metric space[(F(S),ρJ),]which is induced by Jaccard pseudo-metric. This paper gets the following results: firstly, contradictory is the only isolated point in logic metric space[(F(S),ρJ);]secondly, every non-empty sphere in [(F(S),ρJ)]is an inconsistency theory.

Key words: Jaccard similarity coefficient, approximate reasoning, quantitative logic, logic metric space

摘要:

对命题逻辑的相关概念进行量化处理,是命题逻辑研究的一种新方法,是一种有别于语构与语义的研究方法,是研究命题集结构的一个有力工具。通过运用向量间的Jaccard相似系数,在经典逻辑系统L中给出了公式间的Jaccard相似度、Jaccard距离等概念,给出了计量逻辑学中公式真度的Jaccard相似度表示形式,建立了一种新的量化模型。讨论了由Jaccard距离导出的逻辑度量空间[(F(S),ρJ)]的一些性质。得到结论:矛盾式是逻辑度量空间[(F(S),ρJ)]中唯一的孤立点;逻辑度量空间[(F(S),ρJ)]中的非空开球是不相容理论。

关键词: Jaccard相似系数, 近似推理, 计量逻辑学, 逻辑度量空间