Managing vagueness in ontologies

Abstract

The use of ontologies as appropriate formalisms for the representation of the knowledge of many different domains of application has received a lot of attention recently, Nevertheless, classical ontologies are not suitable to represent imprecise, vague and uncertain knowledge, which is inherent to several real-world domains. As a solution, fuzzy ontologies have been proposed as a combination of ontologies with techniques from fuzzy set theory and fuzzy logic. This dissertation presents several contributions to the field of fuzzy ontologies. Our chosen formalism is a fuzzy extension of the very expressive fuzzy Description Logic SROIQ(D), the basis of the language OWL 2. After a definition of the logic, their main properties are investigated. A reasoning algorithm is provided, based on a reduction to a classical ontology which allows to reuse current languages and reasoners. Two semantics, based on two different families of fuzzy operators (Zadeh and Gödel), are considered, and the properties of the reduction (correctness, modularity, and complexity) are studied in detail. Several optimizations have also been investigated. A possibilistic extension enabling an additional representation of uncertain pieces of knowledge is also outlined. Finally, the reasoning algorithm is implemented in a prototype called DeLorean, the first reasoner that supports fuzzy extensions of the standard language for ontology representation OWL and its recent extension OWL 2.