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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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