When Does It Pay Off to Use Sophisticated Entailment Engines in ILP?

  • José Santos
  • Stephen Muggleton
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6489)


Entailment is an important problem in computational logic particularly relevant to the Inductive Logic Programming (ILP) community as it is at the core of the hypothesis coverage test which is often the bottleneck of an ILP system. Despite developments in resolution heuristics and, more recently, in subsumption engines, most ILP systems simply use Prolog’s left-to-right, depth-first search selection function for SLD-resolution to perform the hypothesis coverage test.

We implemented two alternative selection functions for SLD-resolution: smallest predicate domain (SPD) and smallest variable domain (SVD); and developed a subsumption engine, Subsumer. These entailment engines were fully integrated into the ILP system ProGolem.

The performance of these four entailment engines is compared on a representative set of ILP datasets. As expected, on determinate datasets Prolog’s built-in resolution, is unrivalled. However, in the presence of even little non-determinism, its performance quickly degrades and a sophisticated entailment engine is required.


Entailment engines Coverage testing SLD-resolution 


  1. 1.
    Blockeel, H., Dehaspe, L., Demoen, B., Janssens, G., Ramon, J., Vandecasteele, H.: Improving the efficiency of Inductive Logic Programming through the use of query packs. J. Artif. Intell. Res. (JAIR) 16, 135–166 (2002)MATHGoogle Scholar
  2. 2.
    Botta, M., Giordana, A., Saitta, L., Sebag, M.: Relational learning as search in a critical region. Journal of Machine Learning Research 4, 431–463 (2003)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Santos Costa, V., Sagonas, K.F., Lopes, R.: Demand-Driven Indexing of Prolog Clauses. In: Dahl, V., Niemelä, I. (eds.) ICLP 2007. LNCS, vol. 4670, pp. 395–409. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Santos Costa, V., Srinivasan, A., Camacho, R., Blockeel, H., Demoen, B., Janssens, G., Struyf, J., Vandecasteele, H., Van Laer, W.: Query transformations for improving the efficiency of ILP systems. Journal of Machine Learning Research 4, 465–491 (2003)CrossRefGoogle Scholar
  5. 5.
    Kapur, D., Narendran, P.: Np-completeness of the set unification and matching problems. In: Siekmann, J.H. (ed.) CADE 1986. LNCS, vol. 230, pp. 489–495. Springer, Heidelberg (1986)Google Scholar
  6. 6.
    Kowalski, R.A., Kuehner, D.: Linear resolution with selection function. Artif. Intell. 2(3/4), 227–260 (1971)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Kuzelka, O., Zelezný, F.: Fast estimation of first-order clause coverage through randomization and maximum likelihood. In: Cohen, W.W., McCallum, A., Roweis, S.T. (eds.) ICML. ACM International Conference Proceeding Series, vol. 307, pp. 504–511. ACM, New York (2008)CrossRefGoogle Scholar
  8. 8.
    Kuzelka, O., Zelezný, F.: A restarted strategy for efficient subsumption testing. Fundam. Inform. 89(1), 95–109 (2008)MATHGoogle Scholar
  9. 9.
    Maloberti, J., Sebag, M.: Fast theta-subsumption with constraint satisfaction algorithms. Machine Learning 55(2), 137–174 (2004)MATHCrossRefGoogle Scholar
  10. 10.
    Markovitch, S., Scott, P.D.: Automatic ordering of subgoals - a machine learning approach. In: NACLP, pp. 224–240 (1989)Google Scholar
  11. 11.
    Muggleton, S., Santos, J., Tamaddoni-Nezhad, A.: ProGolem: A system based on relative minimal generalisation. In: De Raedt, L. (ed.) ILP 2009. LNCS, vol. 5989, pp. 131–148. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Alan Robinson, J.: A machine-oriented logic based on the resolution principle. J. ACM 12(1), 23–41 (1965)CrossRefGoogle Scholar
  13. 13.
    Santos, J., Muggleton, S.: Subsumer: A Prolog theta-subsumption engine. In: Technical communications of the 26th Int. Conference on Logic Programming, Leibniz International Proc. in Informatics, Edinburgh, Scotland (2010)Google Scholar
  14. 14.
    Sebag, M., Rouveirol, C.: Tractable induction and classification in first order logic via stochastic matching. In: IJCAI, vol. (2), pp. 888–893 (1997)Google Scholar
  15. 15.
    Smith, D.E., Genesereth, M.R.: Ordering conjunctive queries. Artif. Intell. 26(2), 171–215 (1985)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • José Santos
    • 1
  • Stephen Muggleton
    • 1
  1. 1.Department of ComputingImperial College LondonUK

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