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Unification in a Description Logic with Transitive Closure of Roles

F. Baader and R. Küsters

Unification of concept descriptions was introduced by Baader and Narendran as a tool for detecting redundancies in knowledge bases. It was shown that unification in the small description logic FL_0, which allows for conjunction, value restriction, and the top concept only, is already ExpTime-complete. The present paper shows that the complexity does not increase if one additionally allows for composition, union, and transitive closure of roles. It also shows that matching (which is polynomial in FL_0) is PSpace-complete in the extended description logic. These results are proved via a reduction to linear equations over regular languages, which are then solved using automata. The obtained results are also of interest in formal language theory.