Journal of Intelligent Information Systems

, Volume 47, Issue 3, pp 447–467 | Cite as

Measuring similarity of individuals in description logics over the refinement space of conjunctive queries

  • Antonio A. Sánchez-RuizEmail author
  • Santiago Ontañón
  • Pedro A. González-Calero
  • Enric Plaza


Similarity assessment is a key operation in several areas of artificial intelligence. This paper focuses on measuring similarity in the context of Description Logics (DL), and specifically on similarity between individuals. The main contribution of this paper is a novel approach based on measuring similarity in the space of Conjunctive Queries, rather than in the space of concepts. The advantage of this approach is two fold. On the one hand, it is independent of the underlying DL and therefore there is no need to design similarity measures for different DL, and, on the other hand, the approach is computationally more efficient than searching in the space of concepts.


Similarity assessment Description logics Conjunctive queries 



This research has been partially supported by the Spanish Government projects Cognitio (TIN2012-38450-C03-03) and PerSO (TIN2014-55006-R).


  1. Aamodt, A., & Plaza, E. (1994). Case-based reasoning: foundational issues, methodological variations, and system approaches. AI Communications, 7(1), 39–59.Google Scholar
  2. Alqadah, F., & Bhatnagar, R. (2011). Similarity measures in formal concept analysis. Annals of Mathematics and Artificial Intelligence, 61(3), 245–256.MathSciNetCrossRefzbMATHGoogle Scholar
  3. Armengol, E., & Plaza, E. (2003). Relational case-based reasoning for carcinogenic activity prediction. Artificial Intelligence Review, 20(1-2), 121–141.CrossRefGoogle Scholar
  4. Ashburner, M. (2000). Gene ontology: tool for the unification of biology. Nature Genetics, 25, 25–29.CrossRefGoogle Scholar
  5. Baader, F., Calvanese, D., McGuinness, D.L., Nardi, D., & Patel-Schneider, P.F. (Eds.) (2003). The Description Logic Handbook: Theory, Implementation and Applications. New York: Cambridge University Press.Google Scholar
  6. Bergmann, R., & Stahl, A. (1998). Similarity measures for object-oriented case representations. In: Proc. European workshop on case-based reasoning, ewcbr-98, lecture notes in artificial intelligence (pp. 8–13). Springer Verlag.Google Scholar
  7. Bisson, G. (1992). Learing in FOL with a similarity measure. In: Proceedings of AAAI 1992 (pp. 82–87).Google Scholar
  8. Bodenreider, O., Smith, B., Kumar, A., & Burgun, A. (2007). Investigating subsumption in SNOMED CT: an exploration into large description logic-based biomedical terminologies. Artificial Intelligence in Medicine, 39, 183–195. doi: 10.1016/j.artmed.2006.12.003. Scholar
  9. Carpenter, B. (1992). The logic of typed feature structures. New York.Google Scholar
  10. Cojan, J., & Lieber, J. (2010). An algorithm for adapting cases represented in an expressive description logic. In: Case-based reasoning. Research and development, 18th international conference on case-based reasoning, ICCBR 2010, Alessandria, Italy, July 19-22, 2010. Proceedings (pp. 51–65).Google Scholar
  11. d’Amato, C., Staab, S., & Fanizzi, N. (2008). On the influence of description logics ontologies on conceptual similarity. In: Proceedings of the 16th international conference on knowledge engineering, lecture notes in computer science (Vol. 5268, pp. 48–63). Springer-Verlag.Google Scholar
  12. Emde, W., & Wettschereck, D. (1996). Relational instance based learning. In: L. Saitta (ed.) Machine learning - proceedings 13th international conference on machine learning (pp. 122–130). Morgan Kaufmann Publishers.Google Scholar
  13. Fanizzi, N., dAmato, C., & Esposito, F. (2008). Learning with kernels in description logics. In: Inductive logic programming (pp. 210–225). Springer.Google Scholar
  14. Formica, A. (2006). Ontology-based concept similarity in formal concept analysis. Information Sciences, 176(18), 2624–2641.MathSciNetCrossRefzbMATHGoogle Scholar
  15. González-Calero, P.A., Díaz-Agudo, B., & Gómez-Albarrán, M. (1999). Applying DLs for retrieval in case-based reasoning. In: Proceedings of the 1999 description logics workshop (DL’99).Google Scholar
  16. Grau, B.C., Halaschek-Wiener, C., Kazakov, Y., & Suntisrivaraporn, B. (2010). Incremental classification of description logics ontologies. JAR, 44(4), 337–369.MathSciNetCrossRefzbMATHGoogle Scholar
  17. Horridge, M. (2009). A practical guide to building OWL ontologies using protege 4 and CO-ODE tools. Edition 1.2. Tech. rep., The University Of Manchester.
  18. Horváth, T., Wrobel, S., & Bohnebeck, U. (2001). Relational instance-based learning with lists and terms. Machine Learning, 43(1-2), 53–80.CrossRefzbMATHGoogle Scholar
  19. Hutchinson, A. (1997). Metrics on terms and clauses. In: ECML ’97: Proceedings of the 9th European conference on machine learning, lecture notes in computer science (Vol. 1224, pp. 138–145). Springer.Google Scholar
  20. Jaccard, P. (1901). Etude comparative de la distribution florale dans une portion des Alpes et du Jura. Impr. Corbaz.Google Scholar
  21. Kashima, H., Tsuda, K., & Inokuchi, A. (2003). Marginalized kernels between labeled graphs. In: Proceedings of the twentieth international conference (ICML 2003) (pp. 321–328). AAAI Press.Google Scholar
  22. Kazakov, Y., & Klinov, P. (2013). Incremental reasoning in el+ without bookkeeping. In: T. Eiter, B. Glimm, Y. Kazakov, M. Krötzsch (eds.), Description logics, CEUR workshop proceedings (vol. 1014, pp. 294–315.) Scholar
  23. Kramer, S., Lavraċ, N., & Flach, P. (2001). Propositionalization approaches to relational data mining. Springer.Google Scholar
  24. van der Laag, P.R.J., & Nienhuys-Cheng, S.H. (1998). Completeness and properness of refinement operators in inductive logic programming. Journal of Logic Programming, 34(3), 201–225.MathSciNetCrossRefzbMATHGoogle Scholar
  25. Larson, J., & Michalski, R.S. (1977). Inductive inference of VL decision rules. SIGART Bulletin, 63(63), 38–44. doi: 10.1145/1045343.1045369.CrossRefGoogle Scholar
  26. Lehmann, J., & Hitzler, P. (2007). A refinement operator based learning algorithm for the LC description logic. In: H. Blockeel, J. Ramon, J.W. Shavlik, P. Tadepalli (eds.), ILP, Lecture notes in computer science (Vol. 4894, pp. 147–160). Springer.Google Scholar
  27. Motik, B. (2006). Reasoning in description logics using resolution and deductive databases. Ph.D. thesis, Univesitat Karlsruhe (TH), Karlsruhe, Germany.Google Scholar
  28. Nienhuys-Cheng, S.H. (1997). Distance between Herbrand interpretations. A measure for approximations to a target concept. Springer.Google Scholar
  29. Ontañón, S., & Plaza, E. (2009). On similarity measures based on a refinement lattice. in: D. Wilson, L. McGinty (eds.) Proceedings of ICCBR-2009, no. 5650 in lecture notes in artificial intelligence (pp. 240–255). Springer-Verlag.Google Scholar
  30. Ontanón, S., & Plaza, E. (2012). Similarity measures over refinement graphs. Machine Learning, 87, 57–92.MathSciNetCrossRefzbMATHGoogle Scholar
  31. Parsia, B., Halaschek-Wiener, C., & Sirin, E. (2006). Towards incremental reasoning through updates in OWL-DL. In: Reasoning on the web workshop-WWW2006. Edinburgh.Google Scholar
  32. Ramon, J. (2002). Clustering and instance based learning in first order logic. Ph.D. thesis, Ph. D. Thesis, KU Leuven.Google Scholar
  33. Raymond, J.W., Blankley, C.J., & Willett, P. (2003). Comparison of chemical clustering methods using graph- and fingerprint-based similarity measures. Journal of Molecular Graphics and Modelling, 21(5), 421–433.CrossRefGoogle Scholar
  34. Raymond, J.W., Gardiner, E.J., & Willett, P. (2002). Rascal: calculation of graph similarity using maximum common edge subgraphs. Computer Journal, 45(6), 631–644.CrossRefzbMATHGoogle Scholar
  35. Resnik, P. (1995). Using information content to evaluate semantic similarity in a taxonomy. arXiv:cmp-lg/9511007.
  36. Rouveirol, C. (1994). Flattening and saturation: two representation changes for generalization. Machine Learning, 14(2), 219–232.CrossRefzbMATHGoogle Scholar
  37. Sánchez-Ruiz-Granados, A.A., González-Calero, P.A., & Díaz-Agudo, B. (2009). Abstraction in knowledge-rich models for case-based planning. In: Case-based reasoning research and development, proc. 8th ICCBR, lecture notes in computer science (Vol. 5650, pp. 313–327). Springer.Google Scholar
  38. Sánchez-Ruiz-Granados, A.A., Ontañón, S., González-Calero, P.A., & Plaza, E. (2011). Measuring similarity in description logics using refinement operators. In: ICCBR (pp. 289–303).Google Scholar
  39. Ullman, J.D. (2000). Information integration using logical views. Theoretical Computer Science, 239(2), 189–210.MathSciNetCrossRefzbMATHGoogle Scholar
  40. Willett, P., Barnard, J.M., & Downs, G.M. (1998). Chemical similarity searching. Journal of Chemical Information and Computer Sciences, 38(6), 983–996.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Antonio A. Sánchez-Ruiz
    • 1
    Email author
  • Santiago Ontañón
    • 2
  • Pedro A. González-Calero
    • 1
  • Enric Plaza
    • 3
  1. 1.Departamento Ingeniería del Software e Inteligencia ArtificialUniversidad Complutense de MadridMadridSpain
  2. 2.Computer Science DepartmentDrexel UniversityPhiladelphiaUSA
  3. 3.IIIA-CSIC, Artificial Intelligence Research InstituteCampus Campus de la Universitat Autònoma de BarcelonaBarcelonaSpain

Personalised recommendations