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.
Applications of finite duality to locally finite varieties of BL-algebras / S. Aguzzoli, S. Bova, V. Marra - In: Logical foundations of computer science : international symposium, LFCS 2009, Deerfield Beach, FL, USA, january 3-6, 2009 : proceedings / [a cura di] S. Artemov, A. Nerode. - Berlin : Springer, 2009. - ISBN 9783540926863. - pp. 1-15 (( convegno International Symposium on Logical Foundations of Computer Science tenutosi a Deerfield Beach, USA nel 2009.
Applications of finite duality to locally finite varieties of BL-algebras
S. AguzzoliPrimo
;V. MarraUltimo
2009
Abstract
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.Pubblicazioni consigliate
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