Horn-SHIQ has been identified as a fragment of the description logic SHIQ for which inferencing is in PTIME with respect to the size of the ABox. This enables reasoning with larger ABoxes in situations where the TBox is static, and represents one approach towards tractable description logic reasoning. In this paper, we show that reasoning in Horn-SHIQ, in spite of its low datacomplexity, is ExpTIME-hard with respect to the overall size of the knowledge base. While this result is not unexpected, the proof is not a mere modification of existing reductions since it has to account for the restrictions of Hornness. We establish the result for Horn-FLE, showing that Hornness does not simplify TBox reasoning even for very restricted description logics. Moreover, we derive a context-free grammar that defines Horn-SHIQ in a simpler and more intuitive way than existing characterisations.
& Hitzler, P.
(2006). On the Complexity of Horn Description Logics. CEUR Workshop Proceedings, 216.