Abstraction using generalization functions

  • David A. Plaisted
Special Deduction Systems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 230)


We show how a generalization operator may be incorporated into resolution as a method of guiding the search for a proof. After each resolution, a “generalization operation” may be performed on the resulting caluse. This leads to a more general proof than the usual resolution proof. These general proofs may then be used as guides in the search for an ordinary resolution proof. This method overcomes some of the limitations of the abstraction strategies with which the author has experimented for several years. Some of the results of these previous experiments and comparisons of the two approaches are given.


Selection Function Function Symbol Generalization Operator Automate Theorem Prove Generalization Function 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

9. References

  1. Andrews, P.B., Theorem proving via general matings, J. ACM 28 (1981) 193–214.CrossRefGoogle Scholar
  2. Bibel, W., Automated Theorem Proving, Vieweg, 1982.Google Scholar
  3. Boyer, R., Locking, a restriction of resolution, Ph.D. thesis, University of Texas at Austin, TX (1971).Google Scholar
  4. Bundy, A., The Computer Modelling of Mathematical Reasoning (Academic Press, New York, 1983).Google Scholar
  5. Chang, C. and Lee, R., Symbolic Logic and Mechanical Theorem Proving (Academic Press, New York, 1973).Google Scholar
  6. Kling, R., A paradigm for reasoning by analogy, Aritifical Intelligence 2 (1971) 147–178.CrossRefGoogle Scholar
  7. Loveland, D., Automated theorem proving: a quarter century review, in Automated Theorem Proving: After 25 Years, W. Bledsoe and D. Loveland, eds., (American Mathematical Society, Providence, RI, 1984), pp. 1–45.Google Scholar
  8. Manna, Z., Mathematical Theory of Computation (McGraw-Hill, New York, 1974).Google Scholar
  9. Plaisted, D., and Greenbaum, S., Problem representations for back chaining and equality in resolution theorem proving, First Annual AI Applications Conference, Denver, Colorado, December, 1984.Google Scholar
  10. Plaisted, D., Theorem proving with abstraction, Artificial Intelligence 16 (1981) 47–108.CrossRefGoogle Scholar
  11. Plaisted, D., A simplified problem reduction format, Artificial Intelligence 18 (1982) 227–261.CrossRefGoogle Scholar
  12. Robinson, J., A machine oriented logic based on the resolution principle, J. ACM 12 (1965) 23–41.CrossRefGoogle Scholar
  13. Stickel, M.E., A Prolog technology theorem prover, Proceedings of the 1984 International Symposium on Logic Programming, IEEE, Atlantic City, New Jersey, February, 1984, pp. 212–217.Google Scholar
  14. Winston, P.H., Artificial Intelligence (Addison-Wesley, Reading, Mass., 1977).Google Scholar
  15. Wos, L., Overbeek, R., Lusk, E., and Boyle, J., Automated Reasoning: Introduction and Applications (Prentice-Hall, Englewood Cliffs, NJ, 1984).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • David A. Plaisted
    • 1
  1. 1.Department of Computer ScienceUniversity of North Carolina at Chapel HillChapel Hill

Personalised recommendations