On the Properties of Metamodeling in OWL

A common practice in conceptual modeling is to divide the model into intensional and extensional parts. Although very intuitive, this approach falls short in many complex domains, where the borderline between the two parts is not clear-cut. Therefore, OWL-Full, the most expressive of the Semantic Web ontology languages, allows mixing the intensional and the extensional model by a feature we refer to as metamodeling. In this paper, we show that the semantics of metamodeling adopted in OWL-Full leads to undecidability of basic inference problems, due to free mixing of logical and metalogical symbols. Based on this result, we propose two alternative semantics for metamodeling: the contextual and the HiLog semantics. We show that SHOIQ— a description logic underlying OWL-DL— under either semantics is decidable. Finally, we show how the latter semantics can be used in practice to axiomatize the logical interaction between concepts and metaconcepts.