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Applications of Finite Duality to Locally Finite Varieties of BL-Algebras

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Logical Foundations of Computer Science (LFCS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5407))

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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.

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Author information

Authors and Affiliations

  1. Dipartimento di Scienze dell’Informazione, Università degli Studi di Milano, via Comelico 39/41, I-20135, Milano, Italy

    Stefano Aguzzoli

  2. Dipartimento di Matematica e Informatica, Università degli Studi di Siena, Pian dei Mantellini 44, I-53100, Siena, Italy

    Simone Bova

  3. Dipartimento di Informatica e Comunicazione, Università degli Studi di Milano, via Comelico 39/41, I-20135, Milano, Italy

    Vincenzo Marra

Authors
  1. Stefano Aguzzoli
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  2. Simone Bova
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  3. Vincenzo Marra
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Editor information

Editors and Affiliations

  1. Computer Science, CUNY Graduate Center, 365 Fifth Avenue, NY 10016, New York, USA

    Sergei Artemov

  2. Department of Mathematics, Cornell University, 545 Malott Hall, NY 14853, Ithaca, USA

    Anil Nerode

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Aguzzoli, S., Bova, S., Marra, V. (2008). Applications of Finite Duality to Locally Finite Varieties of BL-Algebras. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2009. Lecture Notes in Computer Science, vol 5407. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92687-0_1

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  • DOI: https://doi.org/10.1007/978-3-540-92687-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-92686-3

  • Online ISBN: 978-3-540-92687-0

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