## Decidability of SHI with Transitive Closure of Roles

author: Chan Le Duc, INRIA Grenoble Rhône-Alpes
published: July 28, 2009,   recorded: June 2009,   views: 3588

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# Description

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.

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