逻辑系统NMG的满足性和紧致性-软件学报.PDFVIP

ISSN 1000-9825, CODEN RUXUEW E-mail: jos@ Journal of Software , Vol.20, No.3, March 2009, pp.515−523 doi: 10.3724/SP.J.1001.2009.03381 Tel/Fax: +86-10 © by Institute of Software , the Chinese Academy of Sciences . All rights reserved. ∗ 逻辑系统 NMG 的满足性和紧致性 1+ 1,2 周红军 , 王国俊 1( 陕西师范大学 数学与信息科学学院,陕西 西安 710062) 2(西安交通大学 基础科学研究中心,陕西 西安 710049) Satisfiability and Compactness of NMG-Logic System ZHOU Hong-Jun1+, WANG Guo-Jun1,2 1(College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China) 2(Research Center for Science, Xi’an Jiaotong University, Xi’an 710062, China) + Corresponding author: E-mail: hjzhou@ Zhou HJ, Wang GJ. Satisfiability and compactness of NMG-logic system. Journal of Software, 2009,20(3): 515−523. /1000-9825/3381.htm Abstract : Compactness is an important property of fuzzy logic systems. It was proved that Łukasiewicz propositional logic, Gödel propositional logic, Product propositional logic and the formal deductive system L* are all compact. The aim of the present paper is to prove the compactness of the fuzzy logic system NMG by characterizing maximally consistent theories and by proving the satisfiability of consistent theories over NMG. Key words: fuzzy logic; logic system NMG; maximally consistent theory; satisifiability; compactness; Cantor space 摘 要: 紧致性是模糊逻辑的一个重要性质.现已经证明 Łukasiewicz 命题逻辑、Gödel 命题逻辑、乘积命题逻 辑和形式系统 L*都是紧的.通过刻画逻辑系统NMG 中的极大相容理论和证明NMG 的满足性,进而证明了NMG 也是紧的. 关键词: 模糊逻辑;逻辑系统NMG;极大相容理论;满足性;紧致性;Cantor 空间 中图法分类号: TP18 文