Combining Tableaux and Algebraic Methods for Reasoning with Qualified Number Restrictions

This paper investigates an optimization technique for reasoning with qualified number restrictions in the description logic ALCQHR+ . We present a hybrid architecture where a standard tableaux calculus is combined with a procedure deciding the satisfiability of linear (in)equations derived from qualified number restrictions. The advances are demonstrated by an empirical evaluation using the description logic system RACER which implements TBox and ABox reasoning for ALCQHIR+ . The evaluation demonstrates a dramatic speed up compared to other known approaches.