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Reasoning and Quantification in Fuzzy Description Logics

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Fuzzy Logic and Applications (WILF 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3849))

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Abstract

In this paper we introduce reasoning procedures for \(\mathcal{ALCQ}^{+}_{F}\), a fuzzy description logic with extended qualified quantification. The language allows for the definition of fuzzy quantifiers of the absolute and relative kind by means of piecewise linear functions on ℕ and ℚ ∩ [0,1] respectively. In order to reason about instances, the semantics of quantified expressions is defined based on recently developed measures of the cardinality of fuzzy sets. A procedure is described to calculate the fuzzy satisfiability of a fuzzy assertion, which is a very important reasoning task. The procedure considers several different cases and provides direct solutions for the most frequent types of fuzzy assertions.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Artificial Intelligence, University of Granada, Periodista Daniel Saucedo Aranda s/n, 18071, Granada, Spain

    Daniel Sánchez

  2. Department of Information Technologies, University of Milan, Via Bramante 65, I-26013, Crema (CR), Italy

    Andrea G. B. Tettamanzi

Authors
  1. Daniel Sánchez
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  2. Andrea G. B. Tettamanzi
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Editor information

Editors and Affiliations

  1. Dept. TSI, CNRS UMR 5141 LTCI, ENST (Télécom ParisTech), Paris, France

    Isabelle Bloch

  2. Centro Direzionale, DSA, University of Naples, Parthenope, Isola C/4, 80143, Naples, Italy

    Alfredo Petrosino

  3. Dipartimento di Tecnologie dell’Informazione, Università di Milano Crema,  

    Andrea G. B. Tettamanzi

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© 2006 Springer-Verlag Berlin Heidelberg

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Sánchez, D., Tettamanzi, A.G.B. (2006). Reasoning and Quantification in Fuzzy Description Logics. In: Bloch, I., Petrosino, A., Tettamanzi, A.G.B. (eds) Fuzzy Logic and Applications. WILF 2005. Lecture Notes in Computer Science(), vol 3849. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11676935_10

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  • DOI: https://doi.org/10.1007/11676935_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32529-1

  • Online ISBN: 978-3-540-32530-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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