Model Theory and Entailment Rules for RDF Containers, Collections and Reification

An RDF graph is, at its core, just a set of statements consisting of subjects, predicates and objects. Nevertheless, since its inception practitioners have asked for richer data structures such as containers (for open lists, sets and bags), collections (for closed lists) and reification (for quoting and provenance). Though this desire has been addressed in the RDF primer and RDF Schema specification, they are explicitely ignored in its model theory. In this paper we formalize the intuitive semantics (as suggested by the RDF primer, the RDF Schema and RDF semantics specifications) of these compound data structures by two orthogonal extensions of the RDFS model theory (RDFCC for RDF containers and collections, and RDFR for RDF reification). Second, we give a set of entailment rules that is sound and complete for the RDFCC and RDFR model theories. We show that complexity of RDFCC and RDFR entailment remains the same as that of simple RDF entailment.