Skip to main content
SpringerLink
Log in

An Efficient Algorithm for Reducing Clauses Based on Constraint Satisfaction Techniques

  • Conference paper
Inductive Logic Programming (ILP 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3194))

Included in the following conference series:

Abstract

This paper presents a new reduction algorithm which employs Constraint Satisfaction Techniques for removing redundant literals of a clause efficiently. Inductive Logic Programming (ILP) learning algorithms using a generate and test approach produce hypotheses with redundant literals. Since the reduction is known to be a co-NP-complete problem, most algorithms are incomplete approximations. A complete algorithm proposed by Gottlob and Fermüller is optimal in the number of θ-subsumption calls. However, this method is inefficient since it exploits neither the result of the θ-subsumption nor the intermediary results of similar θ-subsumption calls. Recently, Hirata has shown that this problem is equivalent to finding a minimal solution to a θ-subsumption of a clause with itself, and proposed an incomplete algorithm based on a θ-subsumption algorithm of Scheffer. This algorithm has a large memory consumption and performs many unnecessary tests in most cases. In this work, we overcome this problem by transforming the θ-subsumption problem in a Constraint Satisfaction Problem, then we use an exhaustive search algorithm in order to find a minimal solution. The experiments with artificial and real data sets show that our algorithm outperforms the algorithm of Gottlob and Fermüller by several orders of magnitude, particularly in hard cases.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bessière, C., Régin, J.-C.: MAC and combined heuristics: Two reasons to forsake FC (and CBJ?) on hard problems. In: Freuder, E.C. (ed.) CP 1996. LNCS, vol. 1118, pp. 61–75. Springer, Heidelberg (1996)

    Google Scholar 

  2. De Raedt, L., Bruynooghe, M.: A theory of clausal discovery. In: Proc. Thirteenth International Joint Conference on Artificial Intelligence, pp. 1058–1063. Morgan-Kaufmann, San Francisco (1993)

    Google Scholar 

  3. Dehaspe, L., De Raedt, L.: Mining association rules in multiple relations. In: Džeroski, S., Lavrač, N. (eds.) ILP 1997. LNCS, vol. 1297, pp. 125–132. Springer, Heidelberg (1997)

    Google Scholar 

  4. Ferilli, S., Di Mauro, N., Basile, T.M.A., Esposito, F.: A complete subsumption algorithm. In: Cappelli, A., Turini, F. (eds.) AI*IA 2003. LNCS, vol. 2829, pp. 1–13. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  5. Gent, I.P., MacIntyre, E., Prosser, P., Walsh, T.: The constrainedness of search. In: AAAI/IAAI, vol. 1, pp. 246–252 (1996)

    Google Scholar 

  6. Gottlob, G., Fermüller, C.G.: Removing redundancy from a clause. Artificial Intelligence 61(2), 263–289 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  7. Haralick, R.M., Eliott, G.L.: Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence 14(1), 263–313 (1980)

    Article  Google Scholar 

  8. Hirata, K.: On condensation of a clause. In: Horváth, T., Yamamoto, A. (eds.) ILP 2003. LNCS (LNAI), vol. 2835, pp. 164–179. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  9. Kietz, J.-U., Lübbe, M.: An efficient subsumption algorithm for inductive logic programming. In: Cohen, W.W., Hirsh, H. (eds.) Proc. Eleventh International Conference on Machine Learning, pp. 130–138. Morgan-Kaufmann, San Francisco (1994)

    Google Scholar 

  10. King, R.D., Karwath, A., Clare, A., Dephaspe, L.: Genome scale prediction of protein functional class from sequence using data mining. In: Proc. Sixth ACM SIGKDD international conference on Knowledge Discovery and Data mining, pp. 384–389. ACM Press, New York (2000)

    Chapter  Google Scholar 

  11. Mackworth, K.: Consistency in networks of relations. Artificial Intelligence 8(1), 99–118 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  12. Maloberti, J., Sebag, M.: Theta-subsumption in a constraint satisfaction perspective. In: Rouveirol, C., Sebag, M. (eds.) ILP 2001. LNCS (LNAI), vol. 2157, pp. 164–178. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  13. Maloberti, J., Sebag, M.: Fast theta-subsumption with constraint satisfaction algorithms. Machine Learning Journal 55(2), 137–174 (2004)

    Article  MATH  Google Scholar 

  14. Maloberti, J., Suzuki, E.: Improving efficiency of frequent query discovery by eliminating non-relevant candidates. In: Grieser, G., Tanaka, Y., Yamamoto, A. (eds.) DS 2003. LNCS (LNAI), vol. 2843, pp. 220–232. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  15. Muggleton, S., Feng, C.: Efficient induction of logic programs. In: Proc. First Conference on Algorithmic Learning Theory, Ohmsma, Tokyo, Japan, pp. 368–381 (1990)

    Google Scholar 

  16. Plotkin, G.D.: A note on inductive generalization. In: Machine Intelligence, vol. 5, pp. 153–163. Edinburgh University Press, Edinburgh (1970)

    Google Scholar 

  17. Reddy, C., Tadepalli, P.: Learning first-order acyclic horn programs from entailment. In: Page, D.L. (ed.) ILP 1998. LNCS, vol. 1446, pp. 23–37. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  18. 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)

    Article  Google Scholar 

  19. Scheffer, T., Herbrich, R., Wysotzki, F.: Efficient θ-subsumption based on graph algorithms. In: Proc. Seventh International Workshop on Inductive Logic Programming, pp. 212–228. Springer, Berlin (1997)

    Google Scholar 

  20. Srinivasan, A., King, R.D., Muggleton, S.H., Sternberg, M.: The predictive toxicology evaluation challenge. In: Proc. Fifteenth International Joint Conference on Artificial Intelligence (IJCAI 1997), pp. 1–6. Morgan-Kaufmann, San Francisco (1997)

    Google Scholar 

  21. Srinivasan, S.H., Muggleton, M.J.E.: Sternberg, and R. D. King. Theories for mutagenicity: a study in first order and feature-based induction. Artificial Intelligence 85(1-2), 277–299 (1996)

    Article  Google Scholar 

  22. Tsang, E.: Foundations of Constraint Satisfaction. Academic Press, London (1993)

    Google Scholar 

  23. Ullman, J.D.: Principles of Database and Knowledge-Base Systems, vol. I. Computer Science Press, Rockville (1988)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université Paris-Sud, Laboratoire de Recherche en Informatique (LRI), Bât. 490, F-91405, Orsay Cedex, France

    Jérôme Maloberti

  2. Electrical and Computer Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya, Yokohama, 240-8501, Japan

    Jérôme Maloberti & Einoshin Suzuki

Authors
  1. Jérôme Maloberti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Einoshin Suzuki
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculdade de Engenharia & LIAAD, Universidade do Porto, Portugal

    Rui Camacho

  2. Department of Computer Science, Penglais, Aberystwyth, Ceredigion, University of Wales, SY23 3DB, Wales, UK

    Ross King

  3. Dept. of Computer Science and Engineering & Centre for Health Informatics, University of New South Wales, Sydney

    Ashwin Srinivasan

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Maloberti, J., Suzuki, E. (2004). An Efficient Algorithm for Reducing Clauses Based on Constraint Satisfaction Techniques. In: Camacho, R., King, R., Srinivasan, A. (eds) Inductive Logic Programming. ILP 2004. Lecture Notes in Computer Science(), vol 3194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30109-7_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-30109-7_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22941-4

  • Online ISBN: 978-3-540-30109-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation