BL-algebras are the Lindenbaum algebras of the propositional calculus coming from the continuous triangular norms and their residua in the real unit interval. Any BL-algebra is a subdirect product of local (linear) BL-algebras. A local BL-algebra is either locally finite (and hence an MV-algebra) or perfect or peculiar. Here we study extensively perfect BL-algebras characterizing, with a finite scheme of equations, the generated variety. We first establish some results for general BL-algebras, afterwards the variety is studied in detail. All the results are parallel to those ones already existing in the theory of perfect MV-algebras, but these results must be reformulated and reproved in a different way, because the axioms of BL-algebras are obviously weaker than those for MV-algebras.
THE VARIETY GENERATED FROM PERFECT BL-ALGEBRAIC APPROACH IN FUZZY LOGIC SETTING / Sessa, Salvatore; DI NOLA, A.; Godo, L.; Garcia, P.; Esteva, F.. - In: ANNALS OF MATHEMATICS AND OF ARTIFICIAL INTELLIGENCE. - ISSN 1012-2443. - STAMPA. - 35:1-4(2002), pp. 197-214. [10.1023/A:1014539401842]
THE VARIETY GENERATED FROM PERFECT BL-ALGEBRAIC APPROACH IN FUZZY LOGIC SETTING
SESSA, SALVATORE;
2002
Abstract
BL-algebras are the Lindenbaum algebras of the propositional calculus coming from the continuous triangular norms and their residua in the real unit interval. Any BL-algebra is a subdirect product of local (linear) BL-algebras. A local BL-algebra is either locally finite (and hence an MV-algebra) or perfect or peculiar. Here we study extensively perfect BL-algebras characterizing, with a finite scheme of equations, the generated variety. We first establish some results for general BL-algebras, afterwards the variety is studied in detail. All the results are parallel to those ones already existing in the theory of perfect MV-algebras, but these results must be reformulated and reproved in a different way, because the axioms of BL-algebras are obviously weaker than those for MV-algebras.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.