Pseudo-t-norms and pseudo-BL algebras |
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Authors: | P Flondor G Georgescu A Iorgulescu |
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Affiliation: | (1) Department of Mathematics, “Politehnica” University, Splaiul Independentei Nr. 313, Bucharest, Romania E-mail: pflondor@euler.math.pub.ro, RO;(2) Institute of Mathematics, Calea Griviţei Nr. 21, P.O. Box 1-764, Bucharest, Romania E-mail: georgescu@funinf.math.unibuc.ro, RO;(3) Department of Computer Science, Academy of Economic Studies, Piaţa Romană Nr. 6-R 70167, Oficiul Poştal 22, Bucharest, Romania E-mail: afrodita@inforec.ase.ro, RO |
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Abstract: | 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, the pseudo-MV algebras extend the MV-algebras in the same way in which the arbitrary l-groups extend the abelian l-groups. We have generalized the BL algebras and pseudo-MV algebras, introducing the pseudo-BL algebras. In this paper we introduce weak-BL algebras and weak-pseudo-BL algebras. We also introduce non-commutative t-norms (we call them pseudo-t-norms) and use them in constructing pseudo-BL algebras and weak-pseudo-BL algebras. |
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Keywords: | MV algebra BL algebra Pseudo-MV algebra Pseudo-BL algebra Weak-BL algebra Weak-pseudo-BL algebra t-norm t-conorm Pseudo-t-norm Pseudo-t-conorm Left continuity Right continuity |
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