逻辑公式间的Jaccard距离及其应用

doi:10.3778/j.issn.1673-9418.2002004

摘要/Abstract

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

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

于鹏. 逻辑公式间的Jaccard距离及其应用[J]. 计算机科学与探索, 2020, 14(11): 1975-1980.

YU Peng. Jaccard Distance of Logical Formulas and Its Application[J]. Journal of Frontiers of Computer Science and Technology, 2020, 14(11): 1975-1980.

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