A Decision Procedure for $\mathcal{SHOIQ}$ with Transitive Closure of Roles

International audienceThe Semantic Web makes an extensive use of the OWL DL ontology language, underlied by the SHOIQ description logic, to formalize its resources. In this paper, we propose a decision procedure for this logic extended with the transitive closure of roles in concept axioms, a feature needed in several application domains. The most challenging issue we have to deal with when designing such a decision procedure is to represent infinitely non-tree-shaped models, which are different from those of SHOIQ ontologies. To address this issue, we introduce a new blocking condition for characterizing models which may have an infinite non-tree-shaped part