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.
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.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2002年第4期745-752,共8页
Acta Mathematica Sinica：Chinese Series
关键词
模糊逻辑
强正则剩余格
形式系统￡^N
扩张
完备性
Fuzzy logic
Strong regular residuated lattice
Formal system LN
Extension
Completeness
