In the extensive usage of ontologies envisaged by the Semantic Web there is a compelling need for expressing mappings between the components of heterogeneous ontologies. These mappings are of many different forms and involve the different components of 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. Many real cases, however, highlight the necessity to establish semantic relations between heterogeneous components. For example to map a concept into a relation or vice versa. To support the interoperability of ontologies we need therefore to enrich mapping languages with constructs for the representation of heterogeneous mappings. In this paper, we propose an extension of Distributed Description Logics (DDL) to allow for the representation of mapping between concepts and relations. We provide a semantics of the proposed language and show its main logical properties.
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