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Fuzzy Description Logics – A Survey

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Scalable Uncertainty Management (SUM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10564))

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Abstract

Mathematical Fuzzy Logics [51, 60] have a long tradition with roots going back to the many-valued logics of Łukasiewicz, Gödel, and Kleene [57, 68, 73] and the Fuzzy Set Theory of Zadeh [111]. Their purpose is to model vagueness or imprecision in the real world, by introducing new degrees of truth as additional shades of gray between the Boolean true and false. For example, one can express the distinction between a person x having a high fever or a low fever as the degree of truth of the logical statement \(\mathsf {Fever} (x)\). One of the central properties of fuzzy logics is truth functionality—the truth degree of a complex logical formula is uniquely determined by the truth degrees of its subformulas. This is a fundamental difference to other quantitative logics like probabilistic or possibilistic logics [56, 83].

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Notes

  1. 1.

    https://www.w3.org/TR/owl2-primer/.

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Authors and Affiliations

  1. Chair for Automata Theory, Technische Universität Dresden, Dresden, Germany

    Stefan Borgwardt

  2. KRDB Research Centre, Free University of Bozen-Bolzano, Bolzano, Italy

    Rafael Peñaloza

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  1. Stefan Borgwardt
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  2. Rafael Peñaloza
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Correspondence to Rafael Peñaloza .

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Editors and Affiliations

  1. University of Granada, Granada, Spain

    Serafín Moral

  2. University of Rennes I, Lannion, France

    Olivier Pivert

  3. University of Granada, Granada, Spain

    Daniel Sánchez

  4. University of Granada, Granada, Spain

    Nicolás Marín

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Borgwardt, S., Peñaloza, R. (2017). Fuzzy Description Logics – A Survey. In: Moral, S., Pivert, O., Sánchez, D., Marín, N. (eds) Scalable Uncertainty Management. SUM 2017. Lecture Notes in Computer Science(), vol 10564. Springer, Cham. https://doi.org/10.1007/978-3-319-67582-4_3

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  • DOI: https://doi.org/10.1007/978-3-319-67582-4_3

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