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

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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



  1. 陕西科技大学 文理学院,西安 710021


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



关键词: Jaccard相似系数, 近似推理, 计量逻辑学, 逻辑度量空间