Integrating rules and ontologies in the first-order stable model semantics (preliminary report

Abstract. We present an approach to integrating rules and ontologies on the basis of the first-order stable model semantics defined by Ferraris, Lee and Lifschitz. We show that a few existing integration proposals can be uniformly related to the first-order stable model semantics.

Embedding Non-Ground Logic Programs into Autoepistemic Logic for Knowledge Base Combination

In the context of the Semantic Web, several approaches to the combination of ontologies, given in terms of theories of classical first-order logic and rule bases, have been proposed. They either cast rules into classical logic or limit the interaction between rules and ontologies. Autoepistemic logic (AEL) is an attractive formalism which allows to overcome these limitations, by serving as a uniform host language to embed ontologies and nonmonotonic logic programs into it. For the latter, so far only the propositional setting has been considered. In this paper, we present three embeddings of normal and three embeddings of disjunctive non-ground logic programs under the stable model semantics into first-order AEL. While the embeddings all correspond with respect to objective ground atoms, differences arise when considering non-atomic formulas and combinations with first-order theories. We compare the embeddings with respect to stable expansions and autoepistemic consequences, considering the embeddings by themselves, as well as combinations with classical theories. Our results reveal differences and correspondences of the embeddings and provide useful guidance in the choice of a particular embedding for knowledge combination.Comment: 52 pages, submitte

Reasoning with Forest Logic Programs and f-hybrid Knowledge Bases

Open Answer Set Programming (OASP) is an undecidable framework for integrating ontologies and rules. Although several decidable fragments of OASP have been identified, few reasoning procedures exist. In this article, we provide a sound, complete, and terminating algorithm for satisfiability checking w.r.t. Forest Logic Programs (FoLPs), a fragment of OASP where rules have a tree shape and allow for inequality atoms and constants. The algorithm establishes a decidability result for FoLPs. Although believed to be decidable, so far only the decidability for two small subsets of FoLPs, local FoLPs and acyclic FoLPs, has been shown. We further introduce f-hybrid knowledge bases, a hybrid framework where \SHOQ{} knowledge bases and forest logic programs co-exist, and we show that reasoning with such knowledge bases can be reduced to reasoning with forest logic programs only. We note that f-hybrid knowledge bases do not require the usual (weakly) DL-safety of the rule component, providing thus a genuine alternative approach to current integration approaches of ontologies and rules

Combining open and closed world reasoning for the semantic web

Dissertação para obtenção do Grau de Doutor em InformáticaOne important problem in the ongoing standardization of knowledge representation languages for the Semantic Web is combining open world ontology languages, such as the OWL-based ones, and closed world rule-based languages. The main difficulty of such a combination is that both formalisms are quite orthogonal w.r.t. expressiveness and how decidability is achieved. Combining non-monotonic rules and ontologies is thus a challenging task that requires careful balancing between expressiveness of the knowledge representation language and the computational complexity of reasoning. In this thesis, we will argue in favor of a combination of ontologies and nonmonotonic rules that tightly integrates the two formalisms involved, that has a computational complexity that is as low as possible, and that allows us to query for information instead of calculating the whole model. As our starting point we choose the mature approach of hybrid MKNF knowledge bases, which is based on an adaptation of the Stable Model Semantics to knowledge bases consisting of ontology axioms and rules. We extend the two-valued framework of MKNF logics to a three-valued logics, and we propose a well-founded semantics for non-disjunctive hybrid MKNF knowledge bases. This new semantics promises to provide better efficiency of reasoning,and it is faithful w.r.t. the original two-valued MKNF semantics and compatible with both the OWL-based semantics and the traditional Well- Founded Semantics for logic programs. We provide an algorithm based on operators to compute the unique model, and we extend SLG resolution with tabling to a general framework that allows us to query a combination of non-monotonic rules and any given ontology language. Finally, we investigate concrete instances of that procedure w.r.t. three tractable ontology languages, namely the three description logics underlying the OWL 2 pro les.Fundação para a Ciência e Tecnologia - grant contract SFRH/BD/28745/200

Forschungsbericht Universität Mannheim 2008 / 2009

Die Universität Mannheim hat seit ihrer Entstehung ein spezifisches Forschungsprofil, welches sich in ihrer Entwicklung und derz eitigen Struktur deutlich widerspiegelt. Es ist geprägt von national und international sehr anerkannten Wirtschafts- und Sozialwissenschaften und deren Vernetzung mit leistungsstarken Geisteswissenschaften, Rechtswissenschaft sowie Mathematik und Informatik. Die Universität Mannheim wird auch in Zukunft einerseits die Forschungsschwerpunkte in den Wirtschafts- und Sozialwissenschaften fördern und andererseits eine interdisziplinäre Kultur im Zusammenspiel aller Fächer der Universität anstreben

Guarded hybrid knowledge bases

Recently, there has been a lot of interest in the integration of Description Logics and rules on the Semantic Web.We define guarded hybrid knowledge bases (or g-hybrid knowledge bases) as knowledge bases that consist of a Description Logic knowledge base and a guarded logic program, similar to the DL+log knowledge bases from (Rosati 2006). G-hybrid knowledge bases enable an integration of Description Logics and Logic Programming where, unlike in other approaches, variables in the rules of a guarded program do not need to appear in positive non-DL atoms of the body, i.e. DL atoms can act as guards as well. Decidability of satisfiability checking of g-hybrid knowledge bases is shown for the particular DL DLRO, which is close to OWL DL, by a reduction to guarded programs under the open answer set semantics. Moreover, we show 2-EXPTIME-completeness for satisfiability checking of such g-hybrid knowledge bases. Finally, we discuss advantages and disadvantages of our approach compared with DL+log knowledge bases.Comment: 18 page