Learnability of Simply-Moded Logic Programs from Entailment

  • M. R. K. Krishna Rao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3321)


In this paper, we study exact learning of logic programs from entailment queries and present a polynomial time algorithm to learn a rich class of logic programs that allow local variables and include many standard programs like addition, multiplication, exponentiation, member, prefix, suffix, length, append, merge, split, delete, insert, insertion-sort, quick-sort, merge-sort, preorder and inorder traversal of binary trees, polynomial recognition, derivatives, sum of a list of naturals. Our algorithm asks at most polynomial number of queries and our class is the largest of all the known classes of programs learnable from entailment.


Polynomial Time Logic Program Inductive Logic Programming Unit Clause Output Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Angluin, D.: Learning with hints. In: Proc. COLT 1988, pp. 223–237 (1988)Google Scholar
  2. 2.
    Angluin, D.: Queries and concept learning. Machine Learning 2, 319–342 (1988)Google Scholar
  3. 3.
    Apt, K.R., Luitjes, I.: Verification of logic programs with delay declarations. In: Alagar, V.S., Nivat, M. (eds.) AMAST 1995. LNCS, vol. 936, pp. 66–90. Springer, Heidelberg (1995)Google Scholar
  4. 4.
    Arimura, H.: Learning acyclic first-order Horn sentences from entailment. In: Li, M. (ed.) ALT 1997. LNCS (LNAI), vol. 1316, pp. 432–445. Springer, Heidelberg (1997)Google Scholar
  5. 5.
    Cohen, W., Hirsh, H.: Learnability of description logics. In: Proc. COLT 1992, pp. 116–127 (1992)Google Scholar
  6. 6.
    Dzeroski, S., Muggleton, S., Russel, S.: PAC-learnability of determinate logic programs. In: Proc. of COLT 1992, pp. 128–135 (1992)Google Scholar
  7. 7.
    Frazier, M., Pitt, L.: Learning from entailment: an application to propositional Horn sentences. In: Proc. ICML 1993, pp. 120–127 (1993)Google Scholar
  8. 8.
    Frazier, M., Pitt, L.: CLASSIC learning. In: Proc. COLT 1994, pp. 23–34 (1994)Google Scholar
  9. 9.
    Idestam-Almquist, P.: Efficient induction of recursive definitions by structural analysis of saturations. In: De Raedt, L. (ed.) Advances in inductive logic programming, pp. 192–205. IOS Press, Amsterdam (1996)Google Scholar
  10. 10.
    Krishna Rao, M.R.K.: Incremental learning of logic programs. Theoretical Computer Science 185, 193–213 (1998)Google Scholar
  11. 11.
    Krishna Rao, M.R.K.: Some classes of Prolog programs inferable from positive data. Theoretical Computer Science 241, 211–234 (2000)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Krishna Rao, M.R.K., Sattar, A.: Learning linearly-moded programs from entailment. In: Lee, H.-Y. (ed.) PRICAI 1998. LNCS (LNAI), vol. 1531, pp. 482–493. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  13. 13.
    Krishna Rao, M.R.K., Sattar, A.: Polynomial-time earnability of logic programs with local variables from entailment. Theoretical Computer Science 268, 179–198 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Lloyd, J.W.: Foundations of Logic Programming. Springer, Heidelberg (1987)zbMATHGoogle Scholar
  15. 15.
    Muggleton, S., De Raedt, L.: Inductive logic programming: theory and methods. J. Logic Prog., 19–20, 629–679 (1994)Google Scholar
  16. 16.
    Nienhuys-Cheng, S.H., de Wolf, R.: The subsumption theorem for several forms of resolution, Tech. Rep. EUR-FEW-CS-96-14, Erasmus Uni., Rotterdam (1995)Google Scholar
  17. 17.
    Page, C.D.: Anti-Unification in Constrained Logics: Foundations and Applications to Learnability in First-Order Logic, to Speed-up Learning and to Deduction, Ph.D. Thesis, Uni. of Illinois, Urbana (1993)Google Scholar
  18. 18.
    Page, C.D., Frish, A.M.: Generalization and learnability: a study of constrained atoms. In: Muggleton (ed.) Inductive Logic programming, pp. 29–61 (1992)Google Scholar
  19. 19.
    Reddy, C., Tadepalli, P.: Learning first order acyclic Horn programs from entailment. In: Proc. of Inductive Logic Programming, ILP 1998 (1998)Google Scholar
  20. 20.
    Rouveirol, C.: Extensions of inversion of resolution applied to theory completion. In: Muggleton (ed.) Inductive Logic programming, pp. 63–92 (1992)Google Scholar
  21. 21.
    Shapiro, E.: Inductive inference of theories from facts, Tech. Rep., Yale Univ (1981)Google Scholar
  22. 22.
    Shapiro, E.: Algorithmic Program Debugging. MIT Press, Cambridge (1983)Google Scholar
  23. 23.
    Sterling, L., Shapiro, E.: The Art of Prolog. MIT Press, Cambridge (1994)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • M. R. K. Krishna Rao
    • 1
  1. 1.Information and Computer Science DepartmentKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia

Personalised recommendations