Rules with Contextually Scoped Negation. Polleres, A., Feier, C., & Harth, A. In Proceedings of the 3rd European Semantic Web Conference (ESWC2006), volume 4011, of Lecture Notes in Computer Science (LNCS), pages 332–347, Budva, Montenegro, June, 2006. Springer.
Rules with Contextually Scoped Negation [pdf]Paper  abstract   bibtex   
Knowledge representation formalisms used on the Semantic Web adhere to a strict open world assumption. Therefore, nonmonotonic reasoning techniques are often viewed with scepticism. Especially negation as failure, which intuitively adopts a closed world view, is often claimed to be unsuitable for the Web where knowledge is notoriously incomplete. Nonetheless, it was suggested in the ongoing discussions around rules extensions for languages like RDF(S) or OWL to allow at least restricted forms of negation as failure, as long as negation has an explicitly defined, finite scope. Yet clear definitions of such ``scoped negation'' as well as formal semantics thereof are missing. We propose logic programs with contexts and scoped negation and discuss two possible semantics with desirable properties. We also argue that this class of logic programs can be viewed as a rule extension to a subset of RDF(S).

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