Why-provenance information for RDF, rules, and negation

The provenance (i.e., origins) of derived information on the Web is crucial in many applications to allow information quality assessment, trust judgments, accountability, as well as understanding the temporal and spatial status of the information. On the other hand, the inclusion of negative information in knowledge representation both in the form of negation-as-failure and explicit negation is also important to allow various forms of reasoning, provided that weakly negated information is associated with the sources (contexts) in which it holds. In this work, we consider collections of g-RDF ontologies, distributed over the web, along with a set of conflict statements expressing that information within a pair of g-RDF ontologies cannot be combined together for deriving new information. A g-RDF ontology is the combination of (i) a g-RDF graph G (i.e., a set of positive and strongly negated RDF triples, called g-RDF triples) and (ii) a g-RDF program P containing derivation rules with possibly both explicit and scoped weak negation. Information can be inferred through the g-RDF graphs or the derivation rules of the g-RDF ontologies, or through the RDFS derivation rules. We associate each derived grounded g-RDF triple [¬] p(s, o) with the set of names S of the g-RDF ontologies that contributed to its derivation. To achieve this, we define the provenance stable models of a g-RDF ontology collection. We show that our provenance g-RDF semantics faithfully extends RDFS semantics. Finally, we provide an algorithm based on Answer Set Programming that computes all provenance stable models of a g-RDF ontology collection and provides the answer to various kinds of queries. Various complexity results are provided.