SROIQsigma is decidable

Description Logics [1] are logical formalisms for representing information about classes and objects. They are very often used as the basis of knowledge representation systems and have been used recently to develop OWL semantic web language, which can be viewed as an expressive Description Logic. There is an impressive variety of Description Logics with diverse expressiveness and complexity, or even with or without decidability. Yet, all are tailored to describe an established and fixed ontology and reason about its properties. Our goal here is to consider properties over dynamic ontologies. We introduce the notion of substitutions to express changes of ontologies (e.g. addition or deletion of an element, respectively a pair of elements, of a concept, respectively of a role). We investigate the addition of such substitutions in the particular case of the logic SROIQ, an extension of the logic SROIQ [2]. We mainly show that the problem of satisfiability in SROIQ is still decidable. Sect. 2 introduces SROIQ, our version of SROIQ with substitutions. Sect. 3 defines the interpretations for that logic. Sect. 4 proves that SROIQ is decidable by transforming formulae in SROIQ to formulae in SROIQ. Sect. 5 illustrates such transformations. Finally, Sect. 6 concludes the paper.