Formalizing Ontology Alignment and its Operations with Category Theory

Antoine ZimmermannAntoine Zimmermann, Markus KrötzschMarkus Krötzsch, Jérôme EuzenatJérôme Euzenat, Pascal HitzlerPascal Hitzler

ISBN: 978-1-58603-685-0

Antoine Zimmermann, Markus Krötzsch, Jérôme Euzenat, Pascal Hitzler
Formalizing Ontology Alignment and its Operations with Category Theory
In Brandon Bennett and Christiane Fellbaum, eds., Proceedings of the Fourth International Conference on Formal Ontology in Information Systems (FOIS 2006), volume 150 of Frontiers in Artificial Intelligence and Applications, 277--288, November 2006. IOS Press

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KurzfassungAbstract
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 composition, 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
Forschungsgruppe:Research Group: Wissensbasierte SystemeKnowledge-Based Systems

@inproceedings{ZKEH2006,
  author    = {Antoine Zimmermann and Markus Kr{\"{o}}tzsch and
               J{\'{e}}r{\^{o}}me  Euzenat and Pascal Hitzler},
  title     = {Formalizing Ontology Alignment and its Operations with Category
               Theory},
  editor    = {Brandon Bennett and Christiane Fellbaum},
  booktitle = {Proceedings of the Fourth International Conference on Formal
               Ontology in Information Systems (FOIS 2006)},
  series    = {Frontiers in Artificial Intelligence and Applications},
  volume    = {150},
  publisher = {IOS Press},
  year      = {2006},
  month     = {November},
  pages     = {277--288}
}