On the Properties of Metamodeling in OWL

A common practice in conceptual modeling is to separate the conceptual from the data model. Although very intuitive, this approach is inadequate for many complex domains, in which the borderline between the two models is not clear-cut. Therefore, OWL Full, the most expressive of the Semantic Web ontology languages, allows us to combine the conceptual and the data model by a feature we refer to as metamodeling. In this article, we show that the semantics of metamodeling adopted in OWL Full leads to the undecidability of basic inference problems due to the free usage of the built-in vocabulary. Based on this result, we propose two alternative semantics for metamodeling: the contextual and the HiLog semantics. We present several examples showing how to use the latter semantics to axiomatize the interaction between concepts and metaconcepts. Finally, we show that $\mathcal{SHOIQ}$(D)—the description logic underlying OWL DL—is still decidable when extended with metamodeling under either semantics.