An Integrated Distance for Atoms

  • Vicent Estruch
  • César Ferri
  • José Hernández-Orallo
  • M. José Ramírez-Quintana
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6009)


In this work, we introduce a new distance function for data representations based on first-order logic (atoms, to be more precise) which integrates the main advantages of the distances that have been previously presented in the literature. Basically, our distance simultaneously takes into account some relevant aspects, concerning atom-based presentations, such as the position where the differences between two atoms occur (context sensitivity), their complexity (size of these differences) and how many times each difference occur (the number of repetitions). Although the distance is defined for first-order atoms, it is valid for any programming language with the underlying notion of unification. Consequently, many functional and logic programming languages can also use this distance.


First-order logic distance functions similarity knowledge representation 


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  1. 1.
    Aleksovski, D., Erwig, M., Dzeroski, S.: A functional programming approach to distance-based machine learning. In: Conference on Data Mining and Data Warehouses (SiKDD 2008), Jozef Stefan Institute (2008)Google Scholar
  2. 2.
    Bille, P.: A survey on tree edit distance and related problems. Theoretical computer science 337(1-3), 217–239 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Blockeel, H., De Raedt, L., Ramon, J.: Top-down induction of clustering trees. In: Proc. of the 15th International Conference on Machine Learning (ICML 1998), pp. 55–63. Morgan Kaufmann, San Francisco (1998)Google Scholar
  4. 4.
    Cheney, J.: Flux: functional updates for XML. In: Proceeding of the 13th ACM SIGPLAN international conference on Functional programming, ICFP, pp. 3–14. ACM, New York (2008)CrossRefGoogle Scholar
  5. 5.
    Estruch, V., Ferri, C., Hernández-Orallo, J., Ramírez-Quintana, M.J.: A new context-sensitive and composable distance for first-order terms. Technical report, Departament de Sistemes Informatics i Computacio, Universitat Politecnica de Valencia (2009),
  6. 6.
    Ferri, C., Hernández-Orallo, J., Ramírez-Quintana, M.J.: Incremental learning of functional logic programs. In: Kuchen, H., Ueda, K. (eds.) FLOPS 2001. LNCS, vol. 2024, pp. 233–247. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  7. 7.
    Ferri, C., Hernández-Orallo, J., Ramírez-Quintana, M.J.: Learning MDL-guided decision trees for conctructor based languages. In: Codognet, P. (ed.) ILP 2005. LNCS, vol. 3625, pp. 87–102. Springer, Heidelberg (2001)Google Scholar
  8. 8.
    Flener, P., Schmid, U.: An introduction to inductive programming. Artificial Intelligence Review 29(1), 45–62 (2008)CrossRefGoogle Scholar
  9. 9.
    Hernández, J., Ramírez, M.J.: Inverse narrowing for the induction of functional logic programs. In: Proceedings of the Joint Conference on Declarative Programming, Univ. de la Coruña (1998)Google Scholar
  10. 10.
    Hernández-Orallo, J., Ramírez-Quintana, M.J.: A strong complete schema for inductive functional logic programming. In: Džeroski, S., Flach, P.A. (eds.) ILP 1999. LNCS (LNAI), vol. 1634, pp. 116–127. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  11. 11.
    Hutchinson, A.: Metrics on terms and clauses. In: van Someren, M., Widmer, G. (eds.) ECML 1997. LNCS, vol. 1224, pp. 138–145. Springer, Heidelberg (1997)Google Scholar
  12. 12.
    Nagata, J., Hart, K.P., Vaughan, J.E.: Encyclopedia of General Topology. Elsevier, Amsterdam (2003)Google Scholar
  13. 13.
    Lavrač, N., Džeroski, S.: Inductive Logic Programming: Techniques and Applications. Ellis Horwood (1994)Google Scholar
  14. 14.
    Levina, E., Bickel, P.J.: The earth mover’s distance is the mallows distance: Some insights from statistics. In: 8th International Conference on Computer Vision, pp. 251–256. IEEE, Los Alamitos (2001)Google Scholar
  15. 15.
    Marzal, A., Vidal, E.: Computation of normalized edit distance and applications. IEEE Transactions on Pattern Analysis and Machine Learning Intelligence 15(9), 915–925 (1993)CrossRefGoogle Scholar
  16. 16.
    Mitchell, T.M.: Machine Learning. McGraw-Hill, New York (1997)zbMATHGoogle Scholar
  17. 17.
    Muggleton, S.: Inductive Logic Programming. New Generation Computing 8(4), 295–318 (1991)zbMATHCrossRefGoogle Scholar
  18. 18.
    Nienhuys-Cheng, S.H., de Wolf, R.: Foundations of Inductive Logic Programming. LNCS (LNAI), vol. 1228. Springer, Heidelberg (1997)Google Scholar
  19. 19.
    Plotkin, G.: A note on inductive generalisation. Machine Intelligence 5, 153–163 (1970)MathSciNetGoogle Scholar
  20. 20.
    Ramon, J., Bruynooghe, M.: A framework for defining distances between first-order logic objects. In: Page, D.L. (ed.) ILP 1998. LNCS, vol. 1446, pp. 271–280. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  21. 21.
    Ramon, J., Bruynooghe, M., Van Laer, W.: Distance measures between atoms. In: CompulogNet Area Meeting on Computational Logic and Machine Learing, pp. 35–41. University of Manchester, UK (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Vicent Estruch
    • 1
  • César Ferri
    • 1
  • José Hernández-Orallo
    • 1
  • M. José Ramírez-Quintana
    • 1
  1. 1.DSICUniv. Politècnica de ValènciaValènciaSpain

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