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强正则剩余格值逻辑系统L~N及其完备性
引用本文:裴道武.强正则剩余格值逻辑系统L~N及其完备性[J].数学学报,2002,45(4):745-752.
作者姓名:裴道武
作者单位:西安交通大学理学院 陕西 西安 710049 盐城师范学院数学系 江苏 盐城224002
摘    要:正则剩余格是一类重要的模糊逻辑代数系统,而常见的模糊逻辑形式系统大多数带有非联接词,并且相应的Lindenbaum代数都是正则剩余格.本文以强正则剩余格为语义,建立了一个一般的命题演算形式系统LN,并且证明了这个系统的完备性.几种常见的带有非联接词的模糊逻辑形式系统都是系统LN的扩张.

关 键 词:模糊逻辑  强正则剩余格  形式系统(?)N  扩张  完备性

A Logic System Based on Strong Regular Residuated Lattices and Its Completeness
Institution:Dao Wu PEI(Faculty of Science, Xi'an Jiaotong University Xi'an 710049, P. R. China) (Department of Mathematics, Yancheng Teachers College, Yancheng 224002, P. R. China)(E-mail: pdw0302@sina.com)
Abstract:The regular residuated lattices are a kind of important fuzzy logic algebra systems, and many formal systems in fuzzy logic have negation connective whose Lindenbaum algebras are all regular residuated lattices. In this paper, a general propo-sitional calculus formal system based on strong regular residuated lattices is built up, and its completeness is proved.
Keywords:Fuzzy logic  Strong regular residuated lattice  Formal system LN  Extension  Completeness
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