On relating heterogeneous elements from different ontologies

In the extensive usage of ontologies envisaged by the Semantic Web there is a compelling need for expressing mappings between different elements of heterogeneous ontologies. State of the art languages for ontology mapping enable to express semantic relations between homogeneous components of different ontologies; namely, they allow to map concepts into concepts, individuals into individuals, and properties into properties. In many real world cases this is not enough; for example when relations in an ontology correspond to a class in another ontology (i.e. reification of relations). To support this kind of interoperability we need therefore richer mapping languages, offering constructs for the representation of heterogeneous mappings. In this paper, we propose an extension of Distributed Description Logics (DDL) with mappings between concepts and relations. We provide a semantics of the proposed extension and sound and complete characterisation of the effects of these mappings in terms of the new ontological knowledge they entail.