The Concept of Demodulation in Theorem Proving

  • L. T. Wos
  • G. A. Robinson
  • D. F. Carson
  • L. Shalla
Part of the Symbolic Computation book series (SYMBOLIC)


In many fields of mathematics the richness of the underlying axiom set leads to the establishment of a number of very general equalities. For example, it is easy to prove that in groups (x -1)-1= x and that in rings -x•-y = x •y. In the presence of such an equality, each new inference made during a proof search by a theorem-proving program may immediately yield a set of very closely related inferences. If, for example, b •a = c is inferred in the presence of (x-1)-1= x, substitution immediately yields obviously related inferences such as (b-1)-1 • a = c. Retention of many members of each such set of inferences has seriously impeded the effectiveness of automatic theorem proving. Similar to the gain made by discarding instances of inferences already present is that made by discarding instances of repeated application of a given equality. The latter is achieved by use of demodulation. Its definition, evidence of its value, and a related rule of inference are given. In addition a number of concepts are defined the implementation of which reduces both the number and sensitivity to choice of parameters governing the theorem-proving procedures.


Support Strategy Degree Saturation Related Inference Automatic Theorem Prove Unit Clause 
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.
    Davis, Martin. Computability and Unsolvability. McGraw-Hill, New York, 1958, pp. 95–98.MATHGoogle Scholar
  2. 2.
    Meltzer, B. Theorem-proving for computers: some results on resolution and renaming. Computer J. 8 (1966), 341–343.MATHMathSciNetGoogle Scholar
  3. 3.
    Meltzer, B. and Poogi, P. An improved complete strategy for theorem-proving by resolution. (Unpublished.)Google Scholar
  4. 4.
    Robinson, J. A. A machine-oriented logic based on the resolution principle. J. ACM 12, 1 (Jan. 1965), 23–41.CrossRefMATHGoogle Scholar
  5. 5.
    Robinson, J. A. Automatic deduction with hyper-resolution. Int. J. of Computer Math. 1 (1965), 227–234.MATHGoogle Scholar
  6. 6.
    Robinson, J. A. A review of automatic theorem-proving. Proc. Symp. Appl. Math., Vol. 19. Amer. Math. Soc., Providence, R. I., 1967.Google Scholar
  7. 7.
    Slagle, James. Automatic theorem proving with renamable and semantic resolution. J. ACM 14, 4 (Oct. 1967), 687–697 (this issue).CrossRefGoogle Scholar
  8. 8.
    Wang, H. Formalization and automatic theorem-proving. Proc. IFIP Congr. 65, Vol.1, pp. 51–58 (Spartan Books, Washington, D. C.).Google Scholar
  9. 9.
    Wos, L., Carson, D., and Robinson, G. The unit preference strategy in theorem proving. Proc. AFIPS 1964 Fall Joint Comput. Conf., Vol. 26, Pt. II, pp. 615–621 ( Spartan Books, Washington, D. C. ).Google Scholar
  10. 10.
    Wos, L., Robinson, G. A., and Carson, D. F. Efficiency and completeness of the set of support strategy in theorem proving. J. ACM. 12, 4 (Oct. 1965), 536–541.CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Wos, L., Robinson, G. A., and Carson, D. F. Automatic generation of proofs in the language of mathematics. Proc. IFIP Congr. 65, Vol. 2, pp. 325–326 (Spartan Books, Washington, D. C.).Google Scholar

Copyright information

© Association for Computing Machinery, Inc. 1967

Authors and Affiliations

  • L. T. Wos
  • G. A. Robinson
  • D. F. Carson
  • L. Shalla

There are no affiliations available

Personalised recommendations