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NExpTime-Complete Description Logics with Concrete Domains

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Automated Reasoning (IJCAR 2001)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2083))

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Abstract

Concrete domains are an extension of Description Logics (DLs) allowing to integrate reasoning about conceptual knowledge with reasoning about “concrete properties” of objects such as sizes, weights, and durations. It is known that reasoning with ALC(D), the basic DL admitting concrete domains, is PSpace-complete. In this paper, it is shown that the upper bound is not robust: we give three examples for seemingly harmless extensions of ALC(D)—namely acyclic TBoxes, inverse roles, and a role-forming concrete domain constructor—that make reasoning NExpTime-hard. As a corresponding upper bound, we show that reasoning with all three extensions together is in NExpTime.

Acknowledgements

My thanks go to Franz Baader, Ulrike Sattler, and Stephan Tobies for inspiring discussions. The work in this paper was supported by the DFG Project BA1122/3-1 “Combinations of Modal and Description Log- ics”.

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Author information

Authors and Affiliations

  1. LuFG Theoretical Computer Science, RWTH Aachen, Germany

    Carsten Lutz

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  1. Carsten Lutz
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Editor information

Editors and Affiliations

  1. Automated Reasoning Project and Department of Computer Science, Australian National University, Canberra, ACT, 0200, Australia

    Rajeev Goré

  2. AG Theoretische Informatik und Logik, Institut für Computersprachen, Technische Universität Wien, Favoritenstr. 9, E185-2, 1040, Wien, Austria

    Alexander Leitsch

  3. Institut für Informatik, Technische Universität München, 80290, München, Germany

    Tobias Nipkow

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Lutz, C. (2001). NExpTime-Complete Description Logics with Concrete Domains. In: Goré, R., Leitsch, A., Nipkow, T. (eds) Automated Reasoning. IJCAR 2001. Lecture Notes in Computer Science, vol 2083. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45744-5_5

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  • DOI: https://doi.org/10.1007/3-540-45744-5_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42254-9

  • Online ISBN: 978-3-540-45744-2

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