On integrating description logics and rules under minimal hypotheses

A central and much debated topic in the Knowledge Representation and Reasoning community is how to combine open-world with closed-world formalisms, such as Description Logics (DLs) with Logic Programming. We propose an approach to defining the semantics of hybrid theories, composed of a DL and a Normal Logic Program (NLP) parts, which employs standard open-world semantics for the former and Pinto and Pereira's Minimal Hypotheses semantics (MHs) for the latter. As opposed to the currently employed semantics for hybrid DL-NLP KBs based on Stable Model (SM) semantics, our hybrid semantics guarantees the existence of models for any hybrid DL-NLP theory with consistent DL fragment and consistent DL-NLP ensemble. Because MHs features beneficial theoretical properties, like relevance and cumulativity, existential query answering tasks may not need to consider the whole hybrid KB, as it is necessarily the case with current state-of-the-art approaches based on the SM semantics.