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A Tableau Algorithm for Fuzzy Description Logics over Residuated De Morgan Lattices

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Web Reasoning and Rule Systems (RR 2012)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 7497))

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Abstract

Fuzzy description logics can be used to model vague knowledge in application domains. This paper analyses the consistency and satisfiability problems in the description logic \({\mathcal{SHI}}\) with semantics based on a complete residuated De Morgan lattice. The problems are undecidable in the general case, but can be decided by a tableau algorithm when restricted to finite lattices. For some sublogics of \({\mathcal{SHI}}\), we provide upper complexity bounds that match the complexity of crisp reasoning.

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Authors and Affiliations

  1. Theoretical Computer Science, TU Dresden, Germany

    Stefan Borgwardt & Rafael Peñaloza

Authors
  1. Stefan Borgwardt
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  2. Rafael Peñaloza
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Editors and Affiliations

  1. Department of Computer Science, University of Oxford, Parks Road, Wolfson Building, OX1 3QD, Oxford, UK

    Markus Krötzsch

  2. ISTI - CNR, Via G. Moruzzi, 1, 56124, Pisa, Italy

    Umberto Straccia

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Borgwardt, S., Peñaloza, R. (2012). A Tableau Algorithm for Fuzzy Description Logics over Residuated De Morgan Lattices. In: Krötzsch, M., Straccia, U. (eds) Web Reasoning and Rule Systems. RR 2012. Lecture Notes in Computer Science, vol 7497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33203-6_3

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  • DOI: https://doi.org/10.1007/978-3-642-33203-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33202-9

  • Online ISBN: 978-3-642-33203-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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