Title: Bounded Predicates in Description Logics with Counting
Abstract: A distinguishing feature of Description Logics (DLs), aimed at dealing with information incompleteness, is the ability to describe and reason about anonymous objects, that is, elements in the domain of interest that are not represented by known individuals but whose existence is logically implied by the background knowledge. And while this feature significantly contributes to the expressiveness of DLs, it also causes substantial computational challenges if the number of anonymous is not bounded. However, in many practical scenarios, numeric constraints present in the ontology allows us to infer an upper bound on the number of anonymous objects in extensions of relevant predicates. In this talk, I will present the results from our recent paper that investigates reasoning about upper bounds on predicate sizes for ontologies written in the expressive DL ALCHOIQ with closed predicates using integer programming.