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On Finitely Valued Fuzzy Description Logics: The Łukasiewicz Case

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Advances in Computational Intelligence (IPMU 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 298))

Abstract

Following the guidelines proposed by Hájek in [1], some proposals of research on Fuzzy Description Logics (FDLs) were given in [2]. One of them consists in the definition and development of a family of description languages, each one having as underlying fuzzy logic the expansion with an involutive negation and truth constants of the logic defined by a divisible finite t-norm. A general framework for finitely valued FDLs was presented in [3]. In the present paper we study the family of languages \(\mathcal{ALC}_{\textbf{\L}_n^c}\) based on the finitely valued Łukasiewicz logics with truth constants. In addition, we provide an interpretation of these FDLs into fuzzy multi-modal systems. We also deal with the corresponding reasoning tasks and their relationships, and we report some results on decidability and computational complexity.

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Author information

Authors and Affiliations

  1. Artificial Intelligence Research Institute, IIIA - CSIC, Campus de la UAB, 08193, Bellaterra, Catalonia, Spain

    Marco Cerami, Francesc Esteva & Àngel García-Cerdaña

  2. Departament de Lògica, Història i Filosofia de la Ciència, Universitat de Barcelona, Montalegre 6, 08001, Barcelona, Catalonia, Spain

    Àngel García-Cerdaña

Authors
  1. Marco Cerami
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  2. Francesc Esteva
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  3. Àngel García-Cerdaña
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Editor information

Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco  & Benedetto Matarazzo  & 

  2. Université Pierre et Marie Curie - Paris6, CNRS UMR 7606, DAPA, LIP6 8, rue du Capitaine Scott, F-75015, Paris, France

    Bernadette Bouchon-Meunier

  3. Dip. Matematica e Informatica, Università di Perugia, 06123, Perugia, Italy

    Giulianella Coletti

  4. Department of Computer and Management Science, University of Trento, Via Inama 5, 38122, Trento, Italy

    Mario Fedrizzi

  5. Machine Intelligence Institute, IONA College, 10801, New Rochelle, NY, USA

    Ronald R. Yager

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© 2012 Springer-Verlag Berlin Heidelberg

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Cerami, M., Esteva, F., García-Cerdaña, À. (2012). On Finitely Valued Fuzzy Description Logics: The Łukasiewicz Case. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31715-6_26

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  • DOI: https://doi.org/10.1007/978-3-642-31715-6_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31714-9

  • Online ISBN: 978-3-642-31715-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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