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Equational characterization of the subvarieties of BL generated by t-norm algebras. (English) Zbl 1045.03048
Summary: We show that the subvarieties of BL, the variety of BL-algebras, generated by single BL-chains on [0, 1], determined by continuous t-norms, are finitely axiomatizable. An algorithm to check the subsethood relation between these subvarieties is provided, as well as another procedure to effectively find the equations of each subvariety. From a logical point of view, the latter corresponds to find the axiomatization of every residuated many-valued calculus defined by a continuous t-norm and its residuum. Actually, the paper proves the results for a more general class than t-norm BL-chains, the so-called regular BL-chains.

MSC:
03G25 Other algebras related to logic
03B52 Fuzzy logic; logic of vagueness
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