Implication-Space Semantics for RDF

The Semantic Web is a deployed inferential practice: hundreds of communities publish, in the formal language of RDF, both the claims they endorse and the schema triples that license inference among them. Its official semantics has been model-theoretic throughout its history; this note gives it an inferentialist one, for the entailment regimes presented by closure under rules. We provide RDF with an implication-space semantics in the sense of Hlobil and Brandom, encoding triples as bearers of a single ternary property over generalized RDF, and prove two recovery results. First, for any base over RDF triples, implication in the models fit for the base is exactly the base lifted through a substitutional clause for blank nodes; the semantics adds nothing to the practice that supplies the base. Second, for every entailment regime presented by closure under Horn rules, including rules concluding false, the base the regime specifies is recovered exactly: simple RDF entailment, RDFS entailment, and OWL 2 RL are instances, and a graph is incoherent in the semantics exactly when the regime’s rules derive false. The frames the regimes induce come out monotone, closed under Cut, and explosive, so that the substructural machinery of implication-space semantics is idle on them. That idleness is not a limitation of the semantics. It locates what the regimes leave out: the domain knowledge, as well as the constraints and query-side practices through which communities actually handle defeat, about which classical RDF semantics is silent. We conclude by sketching how every inferential commitment in RDF knowledge graph construction — assertions, ontologies, published incompatibilities, constraints, and human curation — can be brought into one nonmonotone, nonexplosive consequence relation of which the regimes are the monotone corner.