Reasoning with a Network of Aligned Ontologies

In the context of the Semantic Web or semantic peer to peer systems, many ontologies may exist and be developed independently. Ontology alignments help integrating, mediating or reasoning with a system of networked ontologies. Though different formalisms have already been defined to reason with such systems, they do not consider ontology alignments as first class objects designed by third party ontology matching systems. Correspondences between ontologies are often asserted from an external point of view encompassing both ontologies. We study consistency checking in a network of aligned ontologies represented in Integrated Distributed Description Logics (

IDDL

). This formalism treats local knowledge (ontologies) and global knowledge (inter-ontology semantic relations,

i.e.

alignments) separately by distinguishing local interpretations and global interpretation so that local systems do not need to directly connect to each other. We consequently devise a correct and complete algorithm which, although being far from tractacle, has interesting properties: it is independent from the local logics expressing ontologies by encapsulating local reasoners. This shows that consistency of a

IDDL

system is decidable whenever consistency of the local logics is decidable. Moreover, the expressiveness of local logics does not need to be known as long as local reasoners can handle at least

$\mathcal{ALC}$

.