Answer Set Programming for the Semantic Web

Abstract

This thesis makes a contribution to the research e orts of integrating rule-based inference methods with current knowledge representation formalisms in the Semantic Web. Ontology languages such as OWL and RDF Schema seem to be widely accepted and successfully used for semantically enriching knowledge on the Web and thus prepare it for machinereadability. However, these languages are of restricted expressivity if it comes to inferring new from existing knowledge. On the other side, rule formalisms have a long tradition in logic programming, being a common and intuitive tool for problem speci cations. It is evident that the Semantic Web needs a powerful rule language complementing its ontology formalisms in order to facilitate sophisticated reasoning tasks. Ontology languages commonly derive from Description Logics. As a fragment of rst-order logic, their semantics diverge signi cantly from logic programming languages like Datalog and its various descendants especially if we consider the powerful category of non-monotonic logic programming. In order to overcome this gap, di erent approaches have been presented how to combine Description Logics with rules, varying in the degree of integration. Answer-set programming (ASP) is one of the most prominent and successful semantics for non-monotonic logic programs. The speci c treatment of default negation under ASP allows for the generation of multiple models for a single program, which in this respect can be seen as the encoding of a problem speci cation. Highly e cient reasoners for ASP are available, each extending the core language by various sophisticated features such as aggregates or weak constraints. In the rst part of this thesis, 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. This combination allows for building rules on top of ontologies but also, to a limited extent, building ontologies on top of rules. We introduce description logic programs (dl-programs), which consist of a description logic knowledge base L and a nite set of description logic rules (dl-rules) P . Such rules are similar to usual rules in logic programs with negation as failure, but may also contain queries to L, possibly default-negated, in their bodies. We show that consistent strati ed dl-programs can be associated with a unique minimal Herbrand model that is characterized through iterative least Herbrand models. We then de ne strong and weak answer-set semantics which both properly generalize answer sets of ordinary normal logic programs, based on a reduction to the least model semantics of positive dl-programs and to the answer-set semantics of ordinary logic programs respectively. We also present a de nition of the well-founded semantics for dl-programs, based on a generalization of the notion of unfounded sets. We then give xpoint characterizations for the (unique) minimal Herbrand model semantics of positive and strati ed dl-programs as well as for the wellfounded semantics, and show how to compute these models by nite xpoint iterations. Furthermore, we give a precise picture of the complexity of deciding answer set existence for a dl-program, and of brave, cautious, and well-founded reasoning. We lay out possible

DOI: 10.1007/978-3-540-74610-2_3

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@inproceedings{Eiter2007AnswerSP, title={Answer Set Programming for the Semantic Web}, author={Thomas Eiter}, booktitle={ICLP}, year={2007} }