Reasoning with the finitely many-valued Łukasiewicz fuzzy Description Logic SROIQ

  • Authors:

  • Fernando Bobillo;Umberto Straccia

  • Affiliations:

  • Department of Computer Science and Systems Engineering, University of Zaragoza, Spain;Istituto di Scienza e Tecnologie dell'Informazione (ISTI), Consiglio Nazionale delle Ricerche (CNR), Pisa, Italy

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2011

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Abstract

Fuzzy Description Logics are a formalism for the representation of structured knowledge affected by imprecision or vagueness. They have become popular as a language for fuzzy ontology representation. To date, most of the work in this direction has focused on the so-called Zadeh family of fuzzy operators (or fuzzy logic), which has several limitations. In this paper, we generalize existing proposals and show how to reason with a fuzzy extension of the logic SROIQ, the logic behind the language OWL 2, under finitely many-valued Lukasiewicz fuzzy logic. We show for the first time that it is decidable over a finite set of truth values by presenting a reasoning preserving procedure to obtain a non-fuzzy representation for the logic. This reduction makes it possible to reuse current representation languages as well as currently available reasoners for ontologies.