, Volume 18, Issue 2, pp 144–165 | Cite as

Formulating the template ILP consistency problem as a constraint satisfaction problem

  • Roman Barták
  • Radomír Černoch
  • Ondřej Kuželka
  • Filip Železný


Inductive Logic Programming (ILP) deals with the problem of finding a hypothesis covering positive examples and excluding negative examples, where both hypotheses and examples are expressed in first-order logic. In this paper we employ constraint satisfaction techniques to model and solve a problem known as template ILP consistency, which assumes that the structure of a hypothesis is known and the task is to find unification of the contained variables. In particular, we present a constraint model with index variables accompanied by a Boolean model to strengthen inference and hence improve efficiency. The efficiency of models is demonstrated experimentally.


Constraint modeling Inductive logic programming Meta-reasoning 


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  1. 1.
    Alphonse, E., & Osmani, A. (2009). Empirical study of relational learning algorithms in the phase transition framework. In Machine learning and knowledge discovery in databases (pp. 51–66).Google Scholar
  2. 2.
    Baptiste, P., Le Pape, C., Nuijten, W. (2001). Constraint-based scheduling: Applying constraint programming to scheduling problems. Kluwer Academic Publishers.Google Scholar
  3. 3.
    Barabási, A.-L., & Réka, A. (1999). Emergence of scaling in random networks. Science, 286(5439), 509–512.MathSciNetCrossRefGoogle Scholar
  4. 4.
    Barták, R. (2010). Constraint models for reasoning on unification in inductive logic programming. In Artificial Intelligence: Methodology, Systems, and Applications (AIMSA 2010) (pp. 101–110). Springer Verlag.Google Scholar
  5. 5.
    Barták, R., Kuželka,O., Železný, F. (2010). Using constraint satisfaction for learning hypotheses in inductive logic programming. In Proceedings of the 23rd international Florida AI Research Society conference (FLAIRS 2010) (pp. 440–441). AAAI Press.Google Scholar
  6. 6.
    Bordeaux, L., & Monfroy, E. (2002). Beyond NP: Arc-Consistency for quantified constraints. In Principles and practice of Constraint Programming—CP 2002 (pp. 17–32). Springer Verlag.Google Scholar
  7. 7.
    Botta, M. Challenging relational learning—dipartimento di informatica—università di torino. Accessed 6 February 2013.
  8. 8.
    Carlsson, M., & Beldiceanu, N. (2002). Arc-Consistency for a chain of lexicographic ordering constraints. Accessed 6 February 2013.
  9. 9.
    Chovanec, A., & Barták, R. (2011). On generating templates for hypothesis in inductive logic programming. In Advances in artificial intelligence (proceedings of 10th Mexican International Conference on Artificial Intelligence (MICAI 2011), Part 1 (pp. 162–173). Springer VerlagGoogle Scholar
  10. 10.
    Dechter, R. (2003). Constraint processing. Morgan Kaufmann Publishers Inc.Google Scholar
  11. 11.
    Džeroski, S., & Lavrač, N. (2001). Relational data mining. Springer Verlag.Google Scholar
  12. 12.
    Erdős, P., & Rényi, A. (1959). On the evolution of random graphs. Publicationes Mathematicae, 6, 290—297.Google Scholar
  13. 13.
    Garey, M.R., & Johnson, D.S. (1979). Computers and intractability: A guide to the theory of NP-Completeness. W. H. Freeman & Co.Google Scholar
  14. 14.
    Giunchiglia, F., & Sebastiani, R. (1996). Building decision procedures for modal logics from propositional decision procedures—the case study of modal K(m). In CADE13: Proceedings of 13th international conference on automated deduction (pp. 583–597). Springer Verlag.Google Scholar
  15. 15.
    Gottlob, G., Leone, N., Scarcello, F. (1999). On the complexity of some inductive logic programming problems. New Generation Computing, 17(1), 53–75.CrossRefGoogle Scholar
  16. 16.
    Horváth, T., Sloan, R.H., Turán, G. (1997). Learning logic programs by using the product homomorphism method. In COLT ’97: Proceedings of the 10th annual conference on computational learning theory (pp. 10–20). New York, NY: ACM.CrossRefGoogle Scholar
  17. 17.
    Landwehr, N., Kersting, K., De Raedt, L. (2005). nFOIL: Integrating naive bayes and FOIL. In Proceedings of the 20th national conference on Artificial intelligence—Volume 2 (pp. 795–800). AAAI Press.Google Scholar
  18. 18.
    Maloberti, J., & Sebag, M. (2004). Fast Theta-Subsumption with constraint satisfaction algorithms. Machine Learning, 55(2), 137–174.MATHCrossRefGoogle Scholar
  19. 19.
    Muggleton, S., & De Raedt, L. (1994). Inductive logic programming: theory and methods. Journal of Logic Programming, 19(20), 629–679.MathSciNetCrossRefGoogle Scholar
  20. 20.
    Plotkin, G., Meltzer, B., Michie, D. (1970). A note on inductive generalization. Machine Intelligence, 5, 153–163.Google Scholar
  21. 21.
    Sabin, D., & Freuder, E.C. (1994). Contradicting conventional wisdom in constraint satisfaction. Principles and practice of constraint programming (pp. 162–173). Springer Verlag.Google Scholar
  22. 22.
    Srinivasan, A. Aleph manual. Accessed 6 February 2013.

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Roman Barták
    • 1
  • Radomír Černoch
    • 2
  • Ondřej Kuželka
    • 2
  • Filip Železný
    • 2
  1. 1.Faculty of Mathematics and PhysicsCharles University in PraguePraha 1Czech Republic
  2. 2.Faculty of Electrical EngineeringCzech Technical University in PraguePraha 1Czech Republic

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