An Algebra of Qualitative Taxonomical Relations for Ontology Alignments

Algebras of relations were shown useful in managing ontology alignments. They make it possible to aggregate alignments disjunctively or conjunctively and to propagate alignments within a network of ontologies. The previously considered algebra of relations contains taxonomical relations between classes. However, compositional inference using this algebra is sound only if we assume that classes which occur in alignments have nonempty extensions. Moreover, this algebra covers relations only between classes. Here we introduce a new algebra of relations, which, first, solves the limitation of the previous one, and second, incorporates all qualitative taxonomical relations that occur between individuals and concepts, including the relations “is a” and “is not”. We prove that this algebra is coherent with respect to the simple semantics of alignments.