International audienceWe develop the theory of a possibilistic framework for OWL 2 axiom testing against RDF datasets, as an alternative to statistics-based heuristics. The intuition behind it is to evaluate the credibility of OWL 2 axioms based on the evidence available in the form of a set of facts contained in a chosen RDF dataset. To achieve it, we first define the notions of development, content, support , confirmation and counterexample of an axiom. Then we use these notions to define the possibility and necessity of an axiom and its acceptance/rejection index combining both of them. Finally, we report a practical application of the proposed framework to test SubClassOf axioms against the DBpedia RDF dataset