In the context of the Semantic Web, several approaches for combining 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 overcoming 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 article, we present three embeddings of normal and three embeddings of disjunctive nonground logic programs under the stable model semantics into first-order AEL. While all embeddings correspond with respect to objective ground atoms, differences arise when considering nonatomic 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.

The Resource Description Framework (RDF) is a Semantic Web standard that provides a data language, simply called RDF, as well as a lightweight ontology language, called RDF Schema. We investigate embeddings of RDF in logic and show how standard logic programming and description logic technology can be used for reasoning with RDF. We subsequently consider extensions of RDF with datatype support, considering D entailment, defined in the RDF semantics specification, and D* entailment, a semantic weakening of D entailment, introduced by ter Horst. We use the embeddings and properties of the logics to establish novel upper bounds for the complexity of deciding entailment. We subsequently establish two novel lower bounds, establishing that RDFS entailment is PTime-complete and that simple-D entailment is coNP-hard, when considering arbitrary datatypes, both in the size of the entailing graph. The results indicate that RDFS may not be as lightweight as one may expect.

Abstract Recently, there has been a lot of interest in the integration of Description Logics (DL) and rules on the Semantic Web. We defineguarded hybrid knowledge bases(org-hybrid knowledge bases) as knowledge bases that consist of a Description Logic knowledge base and aguardedlogic program, similar to the $\mathcal{DL}$ +logknowledge bases from Rosati (In Proceedings of the 10th International Conference on Principles of Knowledge Representation and Reasoning, AAAI Press, Menlo Park, CA, 2006, pp. 68–78.). 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 asguardsas well. Decidability of satisfiability checking of g-hybrid knowledge bases is shown for the particular DL $\mathcal{DLRO}^{\-{le}}$ , 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 $\mathcal{DL}$ +logknowledge bases.

The Semantic Web languages RDFS and OWL have been around for some time now. However, the presence of these languages has not brought the breakthrough of the Semantic Web the creators of the languages had hoped for. OWL has a number of problems in the area of interoperability and usability in the context of many practical application scenarios which impede the connection to the Software Engineering and Database communities. In this paper we present OWL Flight, which is loosely based on OWL, but the semantics is grounded in Logic Programming rather than Description Logics, and it borrows the constraint-based modeling style common in databases. This results in different types of modeling primitives and enforces a different style of ontology modeling. We analyze the modeling paradigms of OWL DL and OWL Flight, as well as reasoning tasks supported by both languages. We argue that different applications on the Semantic Web require different styles of modeling and thus both types of languages are required for the Semantic Web.