How well are non-horn clauses handled?

  • Xumin Nie
Communications Logic For Artificial Intelligence
Part of the Lecture Notes in Computer Science book series (LNCS, volume 542)


We analyze the search space of two clause-based proof procedures, the Model Elimination procedure and Near-Horn Prolog, both of Loveland. We study how the search space changes with respect to the degree of how “non-Horn” a clause set is. The “non-Hornness” of a clause set is measured by the average number of negative subgoals in a clause. We show that Near-Horn Prolog performs better at the very beginning of the “non-Hornness” scale. But when the clause set becomes more and more non-Horn, model elimination has a clear advantage over Near-Horn Prolog. We also observe an interesting symmetrical property of the search space of model elimination. The reason for this symmetry is that model elimination treats positive literals and negative literals in the same way.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Aaspvall, B., M.F. Plass and R.E. Tarjan, “A Linear-time Algorithm for Testing the Truth of Certain Quantified Boolean Formulas”, Information Processing Letters 8(3): 121–123, 1979.Google Scholar
  2. [2]
    Cook, S.A. “The Complexity of Theorem-proving Procedures”, Third Annual ACM Symp. on Theory of Computing, pp. 151–158, 1971.Google Scholar
  3. [3]
    Graham, R.L., D.E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, 1989.Google Scholar
  4. [4]
    Korf, R.E., “Depth-first Iterative Deepening: an Optimal Admissible Tree Search”, Artificial Intelligence 27: 97–109, 1985.Google Scholar
  5. [5]
    Lloyd, J.W., Foundations of Logic Programming, Springer-Verlag, 1987.Google Scholar
  6. [6]
    Loveland, D.W., “A Simplified Format for the Model Elimination Theorem-Proving Procedure”, Journal of ACM 16(3): 349–363, 1969.Google Scholar
  7. [7]
    Loveland, D.W., “Near-Horn Prolog and Beyond”, Journal of Automated Reasoning 7: 1–26, 1991.Google Scholar
  8. [8]
    Nie, X., “Complexities of Non-Horn Clause Logic Programming”, 5th International Symposium on Methodologies for Intelligent Systems, October, 1990, Knoxville, Tennessee.Google Scholar
  9. [9]
    Plaisted, D.A., “A Sequent Style Model Elimination Strategy and a Positive Refinement”, Journal of Automated Reasoning 6: 389–402, 1990.Google Scholar
  10. [10]
    Stickel, M.E. and M.W. Tyson, “An Analysis of Consecutively Bounded Depth-first Search with Application in Automated Deduction”, Proc. of IJCAI, pp. 1073–1075, 1985.Google Scholar
  11. [11]
    Stickel, M.E., “A PROLOG Technology Theorem Prover”, Journal of Automated Reasoning 4: 353–380, 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Xumin Nie
    • 1
  1. 1.Institute for Programming and Logics Department of Computer ScienceState University of New York at AlbanyAlbanyUSA

Personalised recommendations