A recent development of a Semantic Web language is OWL 2, an extension of OWL. So far OWL 2 has been designed by W3C as the language for representing a web ontology. Earlier we have developed a meta-logical approach for reasoning with Semantic Web ontologies expressed in OWL, with the new extension-OWL 2, in this paper we shall extend our previous work to support this richer language. A meta-interpreter, defined by a demo(.) predicate together with auxiliary axioms, is proposed and used for reasoning with OWL 2 ontologies expressed in terms of meta-programs. Finally we demonstrate some expressiveness of the meta-interpreter.