Jos de Bruijn. Semantic Web Language Layering with Ontologies, Rules, and Meta-Modeling. PhD thesis, Faculty of Mathematics, Computer Science and Physics of the University of Innsbruck, Innsbruck, Austria, 2008.

The recent advent of the Semantic Web has increased the interest in the use of formal Knowledge Representation (KR) languages in order to allow automated processing of, and reasoning with, information on the Web. A prominent KR paradigm on the Web is the family of Description Logics (DLs), which are subsets of classical First-Order Logic (FOL); the W3C Web Ontology Language OWL, and especially its sub-language OWL DL, is strongly related to DL. Another KR paradigm receiving widespread attention in this context is that of rules, in the form of Logic Programming (LP); it is used in, for example, Semantic Web policies and Semantic Web services. Meta-modeling is a feature many deem useful, or even necessary, for the Semantic Web, and is present in the Semantic Web languages RDFS and OWL Full. F-Logic is a formalism that allows meta-modeling, in the spirit of RDFS, but is in many respects more in line with standard KR and database languages.
It is the goal of this thesis to combine DL ontologies, LP rules, and meta-modeling capabilities in a single unifying language framework for the Semantic Web.
We propose WSML as such a unifying framework. The WSML-DL sub-language corresponds to the DL SHIQ, and the WSML-Rule sub-language corresponds to LP with negation, extended with F-Logic-based meta-modeling. Interoperation between these sub-languages can be achieved through a common subset (WSML-Core) or a common superset (WSML-Full). In the technical design of the subset and the superset we face two major challenges: the combination of DL-style and F-Logic-style ontology modeling, and the interoperation between ontologies based on classical FOL (e.g., DL) and rules based on nonmonotonic LP.
- We address the combination of DL-style and F-Logic-style ontology modeling by defining a straightforward translation from FOL to F-Logic, and show that this translation preserves validity for the class of cardinal formulas. We exhibit a novel class of cardinal formulas that includes the DL SHIQ. We use this result to show that the translation from SHIQ to F-Logic preserves entailment.
- We address the interoperation between FOL and LP by analyzing a number of representational issues that occur when combining FOL theories with logic programs, and present a novel approach to combining FOL and LP using first-order autoepistemic logic, an expressive nonmonotonic logic, as a unifying formalism that features a tight integration between the rules and the ontology. We show how different embeddings of logic programs lead to difference semantics for the combination.
Using these technical results, we specify a semantic framework for WSML, define WSML-Core and WSML-Full, and discuss language layering in WSML.
To address the relationship with the basic Semantic Web language RDF(S) we define embeddings of the language in F-Logic, and demonstrating how standard KR techniques can be used for reasoning with and extending RDFS. Finally, we consider intensional OWL, a variant of OWL Full more suitable for rule-based processing and extension.

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