A Logic for Hybrid Rules. Bruijn, J. D., Pearce, D., Polleres, A., & Valverde, A. In RuleML 2006 Workshop: Ontology and Rule Integration, November, 2006.
A Logic for Hybrid Rules [pdf]Paper  abstract   bibtex   
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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