Algebras of Ontology Alignment Relations

  • Jérôme Euzenat
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5318)


Correspondences in ontology alignments relate two ontology entities with a relation. Typical relations are equivalence or subsumption. However, different systems may need different kinds of relations. We propose to use the concepts of algebra of relations in order to express the relations between ontology entities in a general way. We show the benefits in doing so in expressing disjunctive relations, merging alignments in different ways, amalgamating alignments with relations of different granularity, and composing alignments.


Base Relation Relation Algebra Ontology Language Ontology Match Algebraic Reasoning 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Allen, J.: Maintaining knowledge about temporal intervals. Communication of the ACM 26(11), 832–843 (1983)CrossRefzbMATHGoogle Scholar
  2. 2.
    Bennacer, N.: Formalizing mappings for OWL spatiotemporal ontologies. In: Bressan, S., Küng, J., Wagner, R. (eds.) DEXA 2006. LNCS, vol. 4080, pp. 368–378. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Bouquet, P., Ehrig, M., Euzenat, J., Franconi, E., Hitzler, P., Krötzsch, M., Serafini, L., Stamou, G., Sure, Y., Tessaris, S.: Specification of a common framework for characterizing alignment. Deliverable D2.2.1, Knowledge web NoE (2004)Google Scholar
  4. 4.
    Ehrig, M., Euzenat, J.: Relaxed precision and recall for ontology matching. In: Proc. K-CAP Workshop on Integrating Ontologies, Banff (CA), pp. 25–32 (2005)Google Scholar
  5. 5.
    Euzenat, J.: Granularity in relational formalisms with application to time and space representation. Computational intelligence 17(4), 703–737 (2001)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Euzenat, J.: An API for ontology alignment. In: McIlraith, S.A., Plexousakis, D., van Harmelen, F. (eds.) ISWC 2004. LNCS, vol. 3298, pp. 698–712. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Euzenat, J.: Semantic precision and recall for ontology alignment evaluation. In: Proc. 20th International Joint Conference on Artificial Intelligence (IJCAI), Hyderabad (IN), pp. 348–353 (2007)Google Scholar
  8. 8.
    Euzenat, J., Shvaiko, P.: Ontology matching. Springer, Heidelberg (2007)zbMATHGoogle Scholar
  9. 9.
    Fagin, R., Kolaitis, P., Popa, L., Tan, W.-C.: Composing schema mappings: Second-order dependencies to the rescue. ACM Transactions on Database Systems 30(4), 994–1005 (2005)CrossRefGoogle Scholar
  10. 10.
    Freksa, C.: Temporal reasoning based on semi-intervals. Artificial intelligence 54(1), 199–227 (1992)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Gal, A., Anaby-Tavor, A., Trombetta, A., Montesi, D.: A framework for modeling and evaluating automatic semantic reconciliation. The VLDB Journal 14(1), 50–67 (2005)CrossRefGoogle Scholar
  12. 12.
    Ligozat, G., Renz, J.: What is a qualitative calculus? a general framework. In: Zhang, C., W. Guesgen, H., Yeap, W.-K. (eds.) PRICAI 2004. LNCS (LNAI), vol. 3157, pp. 53–64. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  13. 13.
    Madhavan, J., Halevy, A.: Composing mappings among data sources. In: Proc. 29th International Conference on Very Large Data Bases, Berlin (DE), pp. 572–583 (2003)Google Scholar
  14. 14.
    Prud’hommeaux, E., Seaborne, A. (eds.): SPARQL query language for RDF. Working draft, W3C (2007)Google Scholar
  15. 15.
    Rahm, E., Bernstein, P.: A survey of approaches to automatic schema matching. The VLDB Journal 10(4), 334–350 (2001)CrossRefzbMATHGoogle Scholar
  16. 16.
    Sheth, A., Larson, J.: Federated database systems for managing distributed, heterogeneous, and autonomous databases. ACM Computing Surveys 22(3), 183–236 (1990)CrossRefGoogle Scholar
  17. 17.
    Smiljanić, M., van Keulen, M., Jonker, W.: Formalizing the XML schema matching problem as a constraint optimization problem. In: Andersen, K.V., Debenham, J., Wagner, R. (eds.) DEXA 2005. LNCS, vol. 3588, pp. 333–342. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  18. 18.
    Sotnykova, A., Vangenot, C., Cullot, N., Bennacer, N., Aufaure, M.-A.: Semantic mappings in description logics for spatio-temporal database schema integration. Journal on Data Semantics III, 143–167 (2005)zbMATHGoogle Scholar
  19. 19.
    Tarski, A.: On the calculus of relations. Journal of symbolic logic 6(3), 73–89 (1941)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Zimmermann, A.: Sémantique des connaissances distribuées. PhD thesis, Université Joseph-Fourier, Grenoble (FR) (2008)Google Scholar
  21. 21.
    Zimmermann, A., Krötzsch, M., Euzenat, J., Hitzler, P.: Formalizing ontology alignment and its operations with category theory. In: Proc. 4th International Conference on Formal Ontology in Information Systems (FOIS), Baltimore (MD US), pp. 277–288 (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jérôme Euzenat
    • 1
  1. 1.INRIA & LIGGrenobleFrance

Personalised recommendations