Section: Research Program

Ontology matching and alignments

When different representations are used, it is necessary to identify their correspondences. This task is called ontology matching and its result is an alignment [4]. It can be described as follows: given two ontologies, each describing a set of discrete entities, find the relationships, if any, holding between these entities.

An alignment between two ontologies $o$ and $o^{\text{'}}$ is a set of correspondences $\langle e,e^{\text{'}},r\rangle$ such that:

• $e$ and $e^{\text{'}}$ are the entities between which a relation is asserted by the correspondence, e.g., formulas, terms, classes, properties, individuals;

• $r$ is the relation asserted to hold between $e$ and $e^{\text{'}}$. This relation can be any relation applying to these entities, e.g., equivalence, subsumption, exclusion.

In addition, a correspondence may support various types of metadata, in particular measures of the confidence in a correspondence.

Given the semantics of the two ontologies provided by their consequence relation, we define an interpretation of two aligned ontologies as a pair of interpretations $\langle m,m^{\text{'}}\rangle$, one for each ontology. Such a pair of interpretations is a model of the aligned ontologies $o$ and $o^{\text{'}}$ if and only if each respective interpretation is a model of the ontology and they satisfy all correspondences of the alignment.

This definition is extended to networks of ontologies: a collection of ontologies and associated alignments. A model of such a network of ontologies is a tuple of local models such that each alignment is valid for the models involved in the tuple. In such a system, alignments play the role of model filters which select the local models that are compatible with all alignments. So, given a network of ontology, it is possible to interpret it.