We are concerned with the subvariety of commutative, bounded, and integral residuated lattices, satisfying divisibility and prelinearity, namely, BL-algebras. We give an explicit combinatorial description of the category that is dual to finite BL-algebras. Building on this, we obtain detailed structural information on the locally finite subvarieties of BL-algebras that are analogous to Grigolia's subvarieties of finite-valued MV-algebras. As an illustration of the power of the finite duality presented here, we give an exact recursive formula for the cardinality of free finitely generated algebras in such varieties. © Springer-Verlag Berlin Heidelberg 2009.
CITATION STYLE
Aguzzoli, S., Bova, S., & Marra, V. (2009). Applications of finite duality to locally finite varieties of BL-algebras. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5407 LNCS, pp. 1–15). https://doi.org/10.1007/978-3-540-92687-0_1
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