An algorithm for the retrieval of unifiers from discrimination trees

  • Hans de Nivelle
Automated Reasoning
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1126)


We present a modification of the unification algorithm which is adapted to the extraction of simultaneously unifiable literals from discrimination trees. The algorithm is useful for efficient implementation of binary resolution, hyperresolution, and paramodulation. The algorithm is able to traverse simultaneously more than one discrimination tree and to construct a unifier at the same time. In this way backtracking can be minimized.


Automated Theorem Proving Implementation Algorithms 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Chnglee73]
    C-L. Chang, R. C-T. Lee, Symbolic Logic and Mechanical Theorem Proving, Academic Press, New York, 1973.Google Scholar
  2. [Christ93]
    J. Christian, Flatterms, Discrimination Nets, and Fast Term Rewriting, Journal of Automated Reasoning 10, pp. 95–113, 1993.MathSciNetGoogle Scholar
  3. [Graf94]
    P. Graf, Extended Path-Indexing, CADE 12, Ed. Alan Bundy, pp. 514–528, 1994.Google Scholar
  4. [Joyn76]
    W.H. Joyner, Resolution Strategies as Decision Procedures, J. ACM 23 (1), pp. 398–417, 1976.CrossRefGoogle Scholar
  5. [KowHay69]
    R. Kowalski, P.J. Hayes, Semantic Trees in Automated Theorem Proving, Machine Intelligence 4, ed. B. Meltzer and D. Michie, 1969.Google Scholar
  6. [Lovlnd78]
    D. W. Loveland, Automated Theorem Proving, A Logical Basis, North Holland Publishing Company, Amsterdam, New York, Oxford, 1978.Google Scholar
  7. [McCune92]
    W. McCune, Experiments with Discrimination-Tree Indexing and Path Indexing for Term Retrieval, Journal of Automated Reasoning, Vol. 9, pp. 147–167, 1992.CrossRefGoogle Scholar
  8. [McCune94]
    W. McCune, OTTER 3.0 Reference Manual and Guide + source, obtainable from, 1994.Google Scholar
  9. [Nivelle94]
    H. de Nivelle, Resolution Games and Non-Liftable Resolution Orderings, In CSL'94, pp. 279–293, Springer Verlag, 1994.Google Scholar
  10. [Robins65]
    J. A. Robinson, A Machine Oriented Logic Based on the Resolution Principle, Journal of the ACM, Vol. 12, pp. 23–41, 1965.CrossRefGoogle Scholar
  11. [Robins65a]
    J. A. Robinson, Automated Deduction with Hyperresolution, International Journal of Computer Mathematics 1, pp. 227–234, 1965.Google Scholar
  12. [Stickel89]
    M. Stickel, The Path-Indexing Method for Indexing Terms, Technical Note 473, Artificial Intelligence Center SRI International, Menlo Park CA, 1989.Google Scholar
  13. [Wos92]
    L. Wos, A Note on McCune's Article on Discrimination Trees, Journal of Automated Reasoning 9, pp. 145–146, 1992.CrossRefGoogle Scholar
  14. [Zam72]
    N.K. Zamov: On a Bound for the Complexity of Terms in the Resolution Method, Trudy Mat. Inst. Steklov 128, pp. 5–13, 1972.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Hans de Nivelle
    • 1
    • 2
  1. 1.Department of PhilosophyTilburg UniversityThe Netherlands
  2. 2.Faculty of Mathematics and Computer ScienceDelft University of TechnologyBL DelftThe Netherlands

Personalised recommendations