Fuzzy Description Logics under Gödel Semantics

In International Journal of Approximate Reasoning, 2009

Abstract:
Classical ontologies are not suitable to represent vague pieces of information, which has lead to the birth of Fuzzy Description Logics as an appropriate formalism to represent this type of knowledge. Different families of fuzzy operators lead to Fuzzy Description Logics with different properties. This paper studies Fuzzy Description Logics under a semantics given by the G\"{o}del family of fuzzy operators. We investigate some logical properties and show the decidability of a fuzzy extension of the logic $\mathcal{SROIQ}$, theoretical basis of the language OWL 1.1, by providing a reasoning preserving procedure to obtain a crisp
representation for it. Additionally, we show how to represent some types of concept and role modifiers.