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Lukasiewicz模糊命题逻辑中极大相容理论的结构和拓扑刻画 被引量:3

Structural and topological characterizations of maximally consistent theories in Lukasiewicz fuzzy propositional logic
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摘要 通过研究Lukasiewicz模糊命题逻辑系统中极大相容理论的基本性质,证明了每个极大相容理论都是某赋值的核,反过来,每个赋值的核也都是一个极大相容理论.利用Lukasiewicz蕴涵算子的连续性在全体极大相容理论之集上引入了一种Fuzzy拓扑,证明了该Fuzzy拓扑空间是零维的、良紧的,但不是覆盖式紧的,其分明截拓扑空间是覆盖式紧的、可度量化的. By means of investigating basic properties of maximally consistent theories in Lukasiewicz fuzzy propositional logic,it is proved that each maximally consistent theory is the kernel of some valuation and vice versa,and consequently a structural characterization of maximally consistent theories in this logic is obtained.By virtue of the continuity of Lukasiewicz implication operator,a fuzzy topology as well as its cut topology on the set of all maximally consistent theories is introduced.It is proved that this fuzzy topological space is zero-dimensional and nice-compact,but not covering-compact,and its cut space is covering-compact and metrizable.
作者 周红军
出处 《陕西师范大学学报(自然科学版)》 CAS CSCD 北大核心 2011年第1期1-4,共4页 Journal of Shaanxi Normal University:Natural Science Edition
基金 国家自然科学基金资助项目(61005046) 陕西省自然科学基础研究计划项目(2010JQ8020)
关键词 Lukasiewicz模糊命题逻辑 极大相容理论 满足性定理 紧致性定理 Lukasiewicz fuzzy propositional logic maximally consistent theory satisfiability theorem compactness theorem
作者简介 周红军,男,讲师,博士,研究方向为模糊逻辑.E-mail:hjzhou@snnu.edu.cn.
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