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On Expressive Description Logics with Composition of Roles in Number Restrictions

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Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2514))

Abstract

Description Logics are knowledge representation formalisms which have been used in a wide range of application domains. Owing to their appealing expressiveness, we consider in this paper extensions of the well-known concept language ALC allowing for number restrictions on complex role expressions. These have been first introduced by Baader and Sattler as ALCN(M) languages, with the adoption of role constructors M ⊆ ◯,-,⊔,⊓.

In particular, as far as languages equipped with role composition are concerned, they showed in 1999 that, although ALCN(◯) is decidable, the addition of other operators may easily lead to undecidability: in fact, ALCN(◯,⊓) and ALCN(◯,-,⊔) were proved undecidable. In this work, we further investigate the computational properties of the ALCN family, aiming at narrowing the decidability gap left open by Baader and Sattler’s results. In particular, we will show that ALCN(◯) extended with inverse roles both in number and in value restrictions becomes undecidable, whereas it can be safely extended with qualified number restrictions without losing decidability of reasoning.

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Author information

Authors and Affiliations

  1. CSITE-CNR and DEIS, Alma Mater Studiorum - Università di Bologna, Viale Risorgimento 2, I-40136, Bologna, Italy

    Fabio Grandi

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  1. Fabio Grandi
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Editor information

Editors and Affiliations

  1. Abteilung für Theoretische Informatik, Institut für Algebra und Diskrete Mathematik, Wiedner Hauptstr. 8-10, 1040, Wien, Austria

    Matthias Baaz

  2. Department of Computer Science, University of Manchester, Kilburn Building, Oxford Road, Manchester, M13, 9PL, UK

    Andrei Voronkov

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© 2002 Springer-Verlag Berlin Heidelberg

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Grandi, F. (2002). On Expressive Description Logics with Composition of Roles in Number Restrictions. In: Baaz, M., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2002. Lecture Notes in Computer Science(), vol 2514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36078-6_14

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  • DOI: https://doi.org/10.1007/3-540-36078-6_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00010-5

  • Online ISBN: 978-3-540-36078-0

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