Syntactic proof of equivalence between [BL?] system and IMTL system

Computer Engineering and Applications ›› 2016, Vol. 52 ›› Issue (5): 41-46.

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Syntactic proof of equivalence between [BL?] system and IMTL system

ZHOU Jianren1，2, WU Hongbo2

1.College of Mathematics and Statistics, Hexi University, Zhangye, Gansu 734000, China
2.College of Mathematics and Information Sciences, Shaanxi Normal University, Xi’an 710062, China

Online:2016-03-01 Published:2016-03-17

[BL?]系统和IMTL系统等价性的语构证明

周建仁1，2，吴洪博2

1.河西学院数学与统计学院，甘肃张掖 734000
2.陕西师范大学数学与信息科学学院，西安 710062

Abstract

Abstract: The formal deductive system [BL?] of propositional calculus and the formal deductive system IMTL of propositional calculus are the basic formal deductive systems of propositional calculus that are proposed from different perspectives. Through careful comparative study to both of them in this paper, the equivalence of them is proved from aspects of syntactic, so the relationships are more clear and definite among basic fuzzy propositional calculus systems including [BL?] system, MTL system, BL system, IMTL system. The work of this paper is a useful reference for the study of fuzzy propositional calculus systems.

Key words: fuzzy logic, syntactic theory, IMTL system, [BL?] system, equivalence

摘要： [BL?]命题演算形式演绎系统和IMTL命题演算形式演绎系统是从不同的角度出发建立的两种基础模糊命题演算的形式演绎系统。对两者进行了较细致的比较研究，从语构方面证明了两种命题演算形式演绎系统的等价性，从而进一步明确了基础命题演算形式演绎系统[BL?]系统，MTL系统，BL系统，IMTL系统之间的联系，为各种模糊命题演算形式演绎系统的研究提供了一个有益的参考。

关键词: 模糊逻辑, 语构理论, IMTL命题系统, [BL?]命题系统, 等价性

ZHOU Jianren1，2, WU Hongbo2. Syntactic proof of equivalence between [BL?] system and IMTL system[J]. Computer Engineering and Applications, 2016, 52(5): 41-46.

周建仁1，2，吴洪博2. [BL?]系统和IMTL系统等价性的语构证明[J]. 计算机工程与应用, 2016, 52(5): 41-46.

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Syntactic proof of equivalence between [BL?] system and IMTL system

[BL?]系统和IMTL系统等价性的语构证明

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