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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.