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Formalizing ontology alignment and its operations with category theory

Abstract : An ontology alignment is the expression of relations between different ontologies. In order to view alignments independently from the language expressing ontologies and from the techniques used for finding the alignments, we use a category-theoretical model in which ontologies are the objects. We introduce a categorical structure, called V-alignment, made of a pair of morphisms with a common domain having the ontologies as codomain. This structure serves to design an algebra that describes formally what are ontology merging, alignment compo- sition, union and intersection using categorical constructions. This enables combining alignments of various provenance. Although the desirable properties of this algebra make such abstract manipulation of V-alignments very simple, it is practically not well fitted for expressing complex alignments: expressing subsumption between entities of two different ontologies demands the definition of non-standard categories of ontologies. We consider two approaches to solve this problem. The first one extends the notion of V-alignments to a more complex structure called W-alignments: a formalization of alignments relying on "bridge axioms". The second one relies on an elaborate concrete category of ontologies that offers high expressive power. We show that these two extensions have different advantages that may be exploited in different contexts (vi
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https://hal.inria.fr/hal-00825949
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Antoine Zimmermann, Markus Krötzsch, Jérôme Euzenat, Pascal Hitzler. Formalizing ontology alignment and its operations with category theory. Proc. 4th International conference on Formal ontology in information systems (FOIS), Nov 2006, Baltimore, United States. pp.277-288. ⟨hal-00825949⟩

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