Alon Y. Levy, Marie-Christine Rousset
Horn rule languages have formed the basis for many Artificial Intelligence application languages, but are not expressive enough to model domains with a rich hierarchical structure. Description logics have been designed especially to model rich hierarchies. Several applications would significantly benefit from combining the expressive power of both formalisms. This paper focuses on combining recursive function-free Horn rules with the expressive description logic ALCNR, and shows exactly when a hybrid language with decidable inference can be obtained. First, we show that several of the core constructors of description logics lead by themselves to undecidability of inference when combined with recursive function-free Horn rules. We then show that without these constructors we obtain a maximal subset of ALCNR that yields a decidable hybrid language. Finally, we describe a restriction on the Horn rules that guarantees decidable inference when combined with all of ALCNR, and covers many of the common usages of recursive rules.