## Decidability of $\mathcal{SHI}$ with transitive closure of roles

This paper investigates a Description Logic, namely $\mathcal{SHI}_+$, which extends $\mathcal{SHI}$ by adding transitive closure of roles. The resulting logic $\mathcal{SHI}_+$ allows transitive closure of roles to occur not only in concept inclusion axioms but also in role inclusion axioms. We show that $\mathcal{SHI}_+$ is decidable by devising a sound and complete algorithm for deciding satisfiability of concepts in $\mathcal{SHI}_+$ with respect to a set of concept and role inclusion axioms.

Keywords: OWL, decidability, description logics, tableaux, Formal Languages, Inference, Logic, Optimization (Computer Science), Query, Rule of Inference, SPARQL, Semantic Web

Resource URI on the dog food server: http://data.semanticweb.org/conference/eswc/2009/paper/44

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