Combining Answer Set Programming with Description Logics for the Semantic Web

Abstract

We propose a combination of logic programming under the answer set semantics with the description logics SHIF(D) and SHOIN(D), which underly the Web ontology languages OWL Lite and OWL DL, respectively. To this end, we introduce description logic programs (or dl-programs), which consist of a description logic knowledge base L and a finite set P of description logic rules (or dl-rules). Such rules are similar to usual rules in nonmonotonic logic programs, but they may also contain queries to L, possibly under default negation, in their bodies. They allow for building rules on top of ontologies but also, to a limited extent, building ontologies on top of rules. We define a suite of semantics for various classes of dl-programs, which conservatively extend the standard semantics of the respective classes and coincide with it in absence of a description logic knowledge base. More concretely, we generalize positive, stratified, and arbitrary normal logic programs to dl-programs, and define a Herbrand model semantics for them. We show that they have similar properties as ordinary logic programs, and also provide fixpoint characterizations in terms of (iterated) consequence operators. For arbitrary dl-programs, we define answer sets by generalizing Gelfond and Lifschitz's notion of a transform, leading to a strong and a weak answer set semantics, which are based on reductions to the semantics of positive dl-programs and ordinary positive logic programs, respectively. We also show how the weak answer sets can be computed utilizing answer sets of ordinary normal logic programs. Furthermore, we show how some advanced reasoning tasks for the Semantic Web, including different forms of closed-world reasoning and default reasoning, as well as DL-safe rules, can be realized on top of dl-programs. Finally, we give a precise picture of the computational complexity of dl-programs, and we describe efficient algorithms and a prototype implementation of dl-programs which is available on the Web.