Practical reasoning with qualified number restrictions: A hybrid Abox calculus for the description logic SHQ

This article presents a hybrid Abox tableau calculus for SHQ which extends the basic description logic ALC with role hierarchies, transitive roles, and qualified number restrictions. The prominent feature of our hybrid calculus is that it reduces reasoning about qualified number restrictions to integer linear programming. The calculus decides SHQ Abox consistency w.r.t. a Tbox containing general axioms. The presented approach ensures a more informed calculus which adequately handles the interaction between numerical and logical restrictions in SHQ concept and individual descriptions. A prototype reasoner for deciding ALCHQ concept satisfiability has been implemented. An empirical evaluation of our hybrid reasoner and its integrated optimization techniques for a set of synthesized benchmarks featuring qualified number restrictions clearly demonstrates the effectiveness of our hybrid calculus.