逻辑系统NMG 的满足性和紧致性

周红军; 王国俊

引用本文:	周红军,王国俊.逻辑系统NMG 的满足性和紧致性.软件学报,2009,20(3):515-523

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逻辑系统NMG 的满足性和紧致性
周红军¹, 王国俊^1,2
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

摘要:

紧致性是模糊逻辑的一个重要性质.现已经证明?ukasiewicz 命题逻辑、G?del 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

DOI：

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基金项目:Supported by the National Natural Science Foundation of China under Grant No.10771129 (国家自然科学基金); the SuperiorDissertation Foundation of Shaanxi Normal University of China under Grant No.S2006YB06 (陕西师范大学优秀博士学位论文基金)

Satisfiability and Compactness of NMG-Logic System

ZHOU Hong-Jun,WANG Guo-Jun

Abstract:

Compactness is an important property of fuzzy logic systems. It was proved that ?ukasiewicz propositional logic, G?del 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