期刊
ARCHIVE FOR MATHEMATICAL LOGIC
卷 40, 期 6, 页码 467-473出版社
SPRINGER-VERLAG
DOI: 10.1007/s001530100088
关键词
many-valued logic; fuzzy logic; MV-algebra; BL-algebra; residuated lattice
类别
BL-algebras rise as Lindenbaum algebras from many valued logic introduced by Hajek [2]. In this paper Boolean ds and implicative ds of BL-algebras are defined and studied. The following is proved to be equivalent: (i) a ds D is implicative, (ii) D is Boolean, (iii) LID is a Boolean algebra. Moreover, a BL-algebra L contains a proper Boolean ds iff L is bipartite. Local BL-algebras, too, are characterized. These results generalize some theorems presented in [4], [5], [6] for MV-algebras which are BL-algebras fulfiling an additional double negation law x = x**.
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