Jos de Bruijn, David Pearce, Axel Polleres, and Agustín Valverde. A logic for hybrid rules. In Proceedings of the Ontology and Rule Integration Workshop at the 2nd International Conference on Rules and Rule Markup Languages for the Semantic Web, Athens, Georgia, USA, November 11 2006.

In the ongoing discussion about rule extensions for Ontology languages on the Semantic Web a recurring issue is how to combine first-order classical logic with nonmonotonic rule languages. Whereas several modular approaches to define a combined semantics for such hybrid knowledge bases focus mainly on decidability issues, we tackle the matter from a more general point of view. In this paper we show how Quantified Equilibrium Logic (QEL) can function as a unified framework that embraces classical logic as well as disjunctive logic programs under the (open) answer set semantics. In the proposed variant of QEL we relax the unique names assumption from earlier versions. Moreover, we show that this framework elegantly captures several modular approaches to nonmonotonic semantics for hybrid knowledge bases.

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