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