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Well−Founded Semantics for Description Logic Programs in the Semantic Web

Thomas Eiter‚ Thomas Lukasiewicz‚ Roman Schindlauer and Hans Tompits

Abstract

In previous work, towards the integration of rules and ontologies in the SemanticWeb, we have proposed 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. More precisely, we have introduced description logic programs (or dl-programs), which consist of a description logic knowledge base L and a finite set of description logic rules P, and we have defined their answer set semantics. In this paper, we continue this line of research. Here, as a central contribution, we present the well-founded semantics for dl-programs, and we analyze its semantic properties. In particular, we show that it generalizes the well-founded semantics for ordinary normal programs. Furthermore, we show that in the general case, the well-founded semantics of dl-programs is a partial model that approximates the answer set semantics, whereas in the positive and the stratified case, it is a total model that coincides with the answer set semantics. Finally, we also provide complexity results for dl-programs under the well-founded semantics.

Book Title
Proceedings of the 3rd International Workshop on Rules and Rule Markup Languages for the Semantic Web‚ RuleML 2004‚ Hiroshima‚ Japan‚ November 8‚ 2004
Editor
Grigoris Antoniou and Harold Boley
ISBN
3−540−23842−5
Pages
81−97
Publisher
Springer
Series
Lecture Notes in Computer Science
Volume
3323
Year
2004