Abstract We present a novel reasoning procedure for Horn SHIQ ontologies—SHIQ ontologies that can be translated to the Horn fragment of fifirst-order logic. In contrast to traditional reasoning procedures for ontologies, our procedure does not build models or model representations, but works by deriving new consequent axioms. The procedure is closely related to the so-called completion-based procedure for EL++ ontologies, and can be regarded as an extension thereof. In fact, our procedure is theoretically optimal for Horn SHIQ ontologies as well as for the common fragment of EL++ and SHIQ. A preliminary empirical evaluation of our procedure on large medical ontologies demonstrates a dramatic improvement over existing ontology reasoners. Specififically, our implementation allows the classifification of the largest available OWL version of Galen. To the best of our knowledge no other reasoner is able to classify this ontology