Two results in term rewriting theorem proving

  • Jieh Hsiang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 202)


Two results are presented in this paper. (1) We extend the term rewriting approach to first order theorem proving, as described in [HsD83], to the theory of first order predicate calculus with equality. Consequently, we have showed that the term rewriting method can be as powerful as paramodulation and resolution combined. Possible improvements of efficiency are also discussed.

(2) In [KaN84], Kapur & Narendran proposed a method similar to [HsD83]. Motivated by the Kapur-Narendran method, we introduce a notion of splitting for theorem proving in first order predicate calculus. The splitting strategy provides a better utilization of the reduction mechanism of term rewriting systems than the N-strategy in [HsD83], although it generates more critical pairs. Comparisons and the relation between the splitting strategy, Kapur-Narendran method, and the N-strategy are also given.

We conjecture that our way of dealing with first order theories with full equality can be extended to the splitting and the Kapur-Narendran methods as well.

Due to the lack of space, we only give a sketch of the proofs of the completeness of the two theorem proving methods. They will be provided in detail in a longer version of the paper.


Theorem Prove Atomic Formula Failure Node Predicate Symbol Critical Pair 
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. [BeK82]
    J. A. Bergstra and J. W. Klop, Conditional Rewrite Rules: Confluency and Termination, IW 198/82, SMC, Amsterdam, 1982.Google Scholar
  2. [BDJ79]
    D. Brand, J. A. Darringer and W. H. Joyner, Completeness of Conditional Reductions, Proc. 4th Conference on Automated Deduction, 1979, 36–42.Google Scholar
  3. [Buc76]
    B. Buchberger, A Theoretical Basis for the Reduction of Polynomials to Canonical Forms, ACM-SIGSAM Bulletin, August, 1976, 19–29.Google Scholar
  4. [ChL73]
    C. L. Chang and C. T. Lee, Symbolic Logic and Mechanical Theorem Proving, Academic Press, 1973.Google Scholar
  5. [Der82]
    N. Dershowitz, Orderings for Term Rewriting Systems, J. TCS 17, 3 (1982), 279–301.Google Scholar
  6. [HsJ83]
    J. Hsiang and N. A. Josephson, TeRSe: A Term Rewriting Theorem Prover, The Rewrite Rule Laboratory Workshop, Schenectady, NY 12345, September 1983.Google Scholar
  7. [HsD83]
    J. Hsiang and N. Dershowitz, Rewrite Methods for Clausal and Nonclausal Theorem Proving, Proc. 10th ICALP, July 1983, 331–346.Google Scholar
  8. [HuD80]
    G. Huet and D. C. Oppen, Equations and Rewrite Rules: A Survey, in Formal Languages: Perspectives and Open Problems, R. Book (ed.), Academic Press, 1980.Google Scholar
  9. [Hue81]
    G. Huet, A Complete Proof of Correctness of Knuth-Bendix Completion Algorithm, J. Computer and System Sciences 23, (1981), 11–21.Google Scholar
  10. [JoK84]
    J. Jouannaud and H. Kirchner, Completion of a Set of Rules Modulo a Set of Equations, 11th Symposium on Principles of Programming Languages, Salt Lake City, Utah, January, 1984.Google Scholar
  11. [Kap83]
    S. Kaplan, Conditional Rewrite Rules, Report No 150, CNRS, France, December, 1983.Google Scholar
  12. [KaN84]
    D. Kapur and P. Narendran, An Equational Approach to Theorem Proving in First-Order Predicate Calculus, Unpiblished manuscript, GE Research Lab, April 1984.Google Scholar
  13. [KnB70]
    D. E. Knuth and P. B. Bendix, Simple Word Problems in Universal Algebras, in Computational Algebra, J. Leach (ed.), Pergamon Press, 1970, 263–297.Google Scholar
  14. [Lan79]
    D. S. Lankford, Some New Approaches to the Theory and Application of Conditional Term Rewriting Systems, Report, Louisiana Tech Univ., 1979.Google Scholar
  15. [Les83]
    P. Lescanne, Computer Experiments with the REVE Term Rewriting System Generator, 10th ACM Symp. on Prin. of Programming Languages, 1983.Google Scholar
  16. [Mur82]
    N. Murray, Completely Non-Clausal Theorem Proving, Artificial Intelligence 18, (1982), 67–85.Google Scholar
  17. [Pau84]
    E. Paul, A New Interpretation of the Resolution Principle, 7th Conf. on Automated Deduction, Nappa Valley, CA, May, 1984, 333–355.Google Scholar
  18. [PeS81]
    G. E. Peterson and M. E. Stickel, Complete Sets of Reductions for Some Equational Theories, J. ACM 28, (1981), 233–264.Google Scholar
  19. [Pet83]
    G. E. Peterson, A Technique for Establishing Completness Results in Theorem Proving with Equality, SIAM J. of Computing 12, 1 (1983), 82–100.Google Scholar
  20. [Rem83]
    J. L. Remy, Conditional Term rewriting System for Abstract Data Types, Submitted for Publication, University of Nancy, France, June 1983.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Jieh Hsiang
    • 1
  1. 1.Department of Computer ScienceState University of New York at Stony BrookStony Brook

Personalised recommendations