Combining Tableau and Algebraic Methods for Reasoning with Qualified Number Restrictions in Description Logics

The paper investigates an optimization technique for reasoning with qualified number restrictions in the description logic ALCQHR+ (a.k.a. SHQ), which can be seen as one of the cornerstones for reasoning technology in the context of, for instance, the semantic web activity. We present a hybrid architecture where a standard tableaux calculus is combined with a procedure deciding the satisfiability of linear inequations derived from qualified number restrictions. The advances are demonstrated by an empirical evaluation using the description logic system RACER. The evaluation demonstrates a dramatic speed up compared to other known approaches.