Joining Gödel and Zadeh Fuzzy Logics in Fuzzy Description Logics

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems.

Ontologies have succeeded as a knowledge representation formalism in many domains of application. Nevertheless, they are not suitable to represent vague or imprecise information. To overcome this limitation, several extensions to classical ontologies based on fuzzy logic have been proposed. Even though different fuzzy logics lead to fuzzy ontologies with very different logical properties, the combined use of different fuzzy logics has received little attention to date.

This paper proposes a fuzzy extension of the Description Logic $\mathcal{SROIQ}$ --the logic behind the ontology language OWL 2-- that joins G\"{o}del and Zadeh fuzzy logics. We analyze the properties of the new fuzzy Description Logic in order to provide guidelines to ontology developers to exploit the best features of each fuzzy logic. The proposal also considers degrees of truth belonging to a finite set of linguistic terms rather than numerical values, thus being closer to real experts' reasonings. We prove the decidability of the combined logic by presenting a reasoning preserving procedure to obtain a crisp representation for it. This result is generalized to offer a similar reduction that can be applied when any other finite t-norms, t-conorms, negations or implications are considered in the logic.