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Finite Fuzzy Description Logics and Crisp Representations

  • Conference paper
Uncertainty Reasoning for the Semantic Web II (URSW 2010, URSW 2009, URSW 2008, UniDL 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7123))

Abstract

Fuzzy Description Logics (DLs) are a formalism for the representation of structured knowledge that is imprecise or vague by nature. In fuzzy DLs, restricting to a finite set of degrees of truth has proved to be useful, both for theoretical and practical reasons. In this paper, we propose finite fuzzy DLs as a generalization of existing approaches. We assume a finite totally ordered set of linguistic terms or labels, which is very useful in practice since expert knowledge is usually expressed using linguistic terms. Then, we consider fuzzy DLs based on any smooth t-norm defined over this set. Initially we focus on the finite fuzzy DL \(\mathcal{ALCH}\), studying some logical properties, and showing the decidability of the logic by presenting a reasoning preserving reduction to the classical case. Finally, we extend our logic in two directions: by considering non-smooth t-norms and by considering additional DL constructors.

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Author information

Authors and Affiliations

  1. Dpt. of Computer Science and Systems Engineering, University of Zaragoza, Spain

    Fernando Bobillo

  2. Istituto di Scienza e Tecnologie dell’Informazione (ISTI - CNR), Pisa, Italy

    Umberto Straccia

Authors
  1. Fernando Bobillo
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  2. Umberto Straccia
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Systems Engineering, University of Zaragoza, Ada Byron Building, Maria de Luna 1, 50018, Zaragoza, Spain

    Fernando Bobillo

  2. Department of Systems Engineering and Operations Research, George Mason University, Engineering Building, 4400 University Drive, 22030-4444, Fairfax, VA, USA

    Paulo C. G. Costa

  3. Dipatimento di Informatica, Università degli Studi di Bari, Via Orabona 4, 70125, Bari, Italy

    Claudia d’Amato

  4. Dipatimento di Informatica and CILA, Università degli Studi di Bari, Via Orabona 4, 70125, Bari, Italy

    Nicola Fanizzi

  5. Department of Systems Engineering and Operations Research, George Mason University, Engineering Building, 4400 University Drive, 22030-4444, Fairfax, VA, USA

    Kathryn B. Laskey

  6. MIRTE Corporation, M/S H305, 7515 Colshire Drive, 22102-7508, McLean, VA, USA

    Kenneth J. Laskey

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

    Thomas Lukasiewicz

  8. Technische Universität München, Abteilung für Informatk, Boltzmannstraße 3, 85748, Garching, Germany

    Matthias Nickles

  9. Goldman Sachs, 30 Hudson Street, 07302-4699, Jersey City, NJ, USA

    Michael Pool

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Bobillo, F., Straccia, U. (2013). Finite Fuzzy Description Logics and Crisp Representations. In: Bobillo, F., et al. Uncertainty Reasoning for the Semantic Web II. URSW URSW URSW UniDL 2010 2009 2008 2010. Lecture Notes in Computer Science(), vol 7123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35975-0_6

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  • DOI: https://doi.org/10.1007/978-3-642-35975-0_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35974-3

  • Online ISBN: 978-3-642-35975-0

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