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On Uniform Word Problems Involving Bridging Operators on Distributive Lattices

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Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2381))

Abstract

In this paper we analyze some fragments of the universal theory of distributive lattices with many sorted bridging operators. Our interest in such algebras is motivated by the fact that, in description logics, numerical features are often expressed by using maps that associate numerical values to sets (more generally, to lattice elements). We first establish a link between satisfiability of universal sentences with respect to algebraic models and satisfiability with respect to certain classes of relational structures. We use these results for giving a method for translation to clause form of universal sentences, and provide some decidability results based on the use of resolution or hyperresolution. Links between hyperresolution and tableau methods are also discussed, and a tableau procedure for checking satisfiability of formulae of type t 1 ≤ t 2 is obtained by using a hyperresolution calculus.

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Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, Saarbrücken, Germany

    Viorica Sofronie-Stokkermans

Authors
  1. Viorica Sofronie-Stokkermans
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Editor information

Editors and Affiliations

  1. Abteilung Wisssenbasierte Systeme 184/3, Technische Univesität Wien, Favoritenstr. 9-11, 1040, Vienna, Austria

    Uwe Egly

  2. Institut für Computersprachen AG Theoretische Informatik und Logik 185.2, Technische Universität Wien, Favoritenstr. 9-11, 1040, Vienna, Austria

    Chritian G. Fermüller

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Sofronie-Stokkermans, V. (2002). On Uniform Word Problems Involving Bridging Operators on Distributive Lattices. In: Egly, U., Fermüller, C.G. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2002. Lecture Notes in Computer Science(), vol 2381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45616-3_17

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  • DOI: https://doi.org/10.1007/3-540-45616-3_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43929-5

  • Online ISBN: 978-3-540-45616-2

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