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Pseudo-t-norms and pseudo-BL algebras. (English) Zbl 0995.03048
Summary: BL algebras were introduced by Hájek as algebraic structures for his Basic Logic, starting from continuous t-norms on \([0,1]\). MV algebras, product algebras and Gödel algebras are particular cases of BL algebras. On the other hand, pseudo-MV algebras extend the MV algebras in the same way in which arbitrary \(l\)-groups extend the Abelian \(l\)-groups. Previously, we have generalized BL algebras and pseudo-MV algebras by introducing pseudo-BL algebras. In this paper we introduce weak-BL algebras and weak-pseudo-BL algebras. We also introduce noncommutative t-norms (we call them pseudo-t-norms) and use them for the construction of pseudo-BL algebras and weak-pseudo-BL algebras.

MSC:
03G25 Other algebras related to logic
06D35 MV-algebras
03E72 Theory of fuzzy sets, etc.
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