A PSPACE-algorithm for deciding ALCNIR+-satisfiability

ALCNIR+—ALCN augmented with transitive and inverse roles—is an expressive Description Logic which is especially well-suited for the representation of complex, aggregated objects. Despite its expressiveness, it has been conjectured that concept satisfiability for this logic could be decided in a comparatively efficient way. In this paper we prove the correctness of this conjecture by presenting a PSPACE algorithm for deciding satisfiability and subsumption of ALCNIR+-concepts. The space-efficiency of this tableau-based algorithm is due to a sophisticated guidance of the search for a solution. Moreover, this space-efficiency is not paid for with time-consumption; on the contrary, the guidance technique leads to very early refutation. This algorithm will be the basis for an efficient implementation