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First Steps Towards Taming Description Logics with Strings

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Logics in Artificial Intelligence (JELIA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14281))

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Abstract

We consider the description logic \(\mathcal {A}\mathcal {L}\mathcal {C}\mathcal {F}^{\mathcal {P}}(\mathcal {D}_{\varSigma })\) over the concrete domain \(\mathcal {D}_{\varSigma } = (\varSigma ^*,\prec ,=,(=_{\mathfrak {w}})_{\mathfrak {w}\in \varSigma ^*})\), where \(\prec \) is the strict prefix order over finite strings in \(\varSigma ^*\). Using an automata-based approach, we show that the concept satisfiability problem w.r.t. general TBoxes for \(\mathcal {A}\mathcal {L}\mathcal {C}\mathcal {F}^{\mathcal {P}}(\mathcal {D}_{\varSigma })\) is ExpTime-complete for all finite alphabets \(\varSigma \). As far as we know, this is the first complexity result for an expressive description logic with a nontrivial concrete domain on strings.

The second author is supported by the Deutsche Forschungsgemeinschaft (DFG), project 504343613.

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Author information

Authors and Affiliations

  1. Université Paris-Saclay, CNRS, ENS Paris-Saclay, Laboratoire Méthodes Formelles, 91190, Gif-Sur-Yvette, France

    Stéphane Demri

  2. Fakultät für Mathematik und Informatik, Universität Leipzig, Leipzig, Germany

    Karin Quaas

Authors
  1. Stéphane Demri
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  2. Karin Quaas
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Correspondence to Stéphane Demri or Karin Quaas .

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Editors and Affiliations

  1. TU Dresden, Dresden, Germany

    Sarah Gaggl

  2. Artificial Intelligence Research Institute - IIIA CSIC, Barcelona, Spain

    Maria Vanina Martinez

  3. Umeå University, Umeå, Sweden

    Magdalena Ortiz

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Demri, S., Quaas, K. (2023). First Steps Towards Taming Description Logics with Strings. In: Gaggl, S., Martinez, M.V., Ortiz, M. (eds) Logics in Artificial Intelligence. JELIA 2023. Lecture Notes in Computer Science(), vol 14281. Springer, Cham. https://doi.org/10.1007/978-3-031-43619-2_23

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  • DOI: https://doi.org/10.1007/978-3-031-43619-2_23

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