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Semantic theory of finite lattice-valued propositional logic

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Abstract

Based on the methodology of Pavelka’s fuzzy propositional logic, in this paper, by combining L-fuzzy set and classical two-value propositional logic theory, a kind of graded semantic theory in lattice-valued propositional logic based on finite lattice implication algebras is established. The notions of L-tautology and L-contradiction are introduced, and several theorems about the relations among different kinds of L-tautologies are given. From the viewpoint of uncertainty reasoning, the notion of satisfiability with certain level for a set of formulas is also defined. On this basis, the semantic consequence operation concerning a set of formulas is proposed, and the properties of semantic consequence operation and the consistency of fuzzy information are discussed.

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Authors and Affiliations

  1. School of Maths, Southwest Jiaotong University, Chengdu, 610031, China

    XiaoDong Pan

  2. Intelligent Control Development Center, Southwest Jiaotong University, Chengdu, 610031, China

    XiaoDong Pan & Yang Xu

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  1. XiaoDong Pan
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  2. Yang Xu
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Correspondence to XiaoDong Pan.

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Pan, X., Xu, Y. Semantic theory of finite lattice-valued propositional logic. Sci. China Inf. Sci. 53, 2022–2031 (2010). https://doi.org/10.1007/s11432-010-4059-9

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