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A prolog technology theorem prover: Implementation by an extended prolog compiler

  • Mark E. Stickel
Logic Programming Oriented Deduction Systems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 230)

Abstract

A Prolog technology theorem prover (PTTP) is an extension of Prolog that is complete for the full first-order predicate calculus. It differs from Prolog in its use of unification with the occurs check for soundness, the model-elimination reduction rule that is added to Prolog inferences to make the inference system complete, and consecutively bounded depth-first search instead of unbounded depth-first search to make the search strategy complete. A Prolog technology theorem prover has been implemented by an extended Prolog-to-Lisp compiler that supports these additional features. It is capable of proving theorems in the full first-order predicate calculus at a rate of thousands of inferences per second.

Keywords

Inference System Unit Clause Automate Deduction Inference Operation Prolog Implementation 
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.

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References

  1. [1]
    Boyer, R.S. and J.S. Moore. The sharing of structure in theorem-proving programs. In B. Meltzer and D. Michie (eds.). Machine Intelligence 7. Edinburgh University Press, Edinburgh, Scotland, 1972.Google Scholar
  2. [2]
    Chang, C.L. and R.C.T. Lee. Symbolic Logic and Mechanical Theorem Proving. Academic Press, New York, New York, 1973.Google Scholar
  3. [3]
    Cohen, J. Describing Prolog by its interpretation and compilation. Communications of the ACM 28, 12 (December 1985), 1311–1324.CrossRefGoogle Scholar
  4. [4]
    Colmerauer, A. Prolog and infinite trees. In Clark, K.L. and S.A. Tarnlund (eds.). Logic Programming. Academic Press, New York, New York, 1982.Google Scholar
  5. [5]
    Fleisig, S., D. Loveland, A.K. Smiley III, and D.L. Yarmush. An implementation of the model elimination proof procedure. Journal of the ACM 21, 1 (January 1974), 124–139.CrossRefGoogle Scholar
  6. [6]
    Korf, R.E. Depth-first iterative-deepening: an optimal admissible tree search. Artificial Intelligence 27, 1 (September 1985), 97–109.MathSciNetGoogle Scholar
  7. [7]
    Lawrence, J.D. and J.D. Starkey. Experimental tests of resolution based theorem-proving strategies. Technical Report, Computer Science Department, Washington State University, Pullman, Washington, April 1974.Google Scholar
  8. [8]
    Loveland, D.W. A simplified format for the model elimination procedure. J. ACM 16, 3 (July 1969), 349–363.CrossRefGoogle Scholar
  9. [9]
    Loveland, D.W. Automated Theorem Proving: A Logical Basis. North-Holland, Amsterdam, the Netherlands, 1978.Google Scholar
  10. [10]
    Loveland, D.W. and M.E. Stickel. The hole in goal trees: some guidance from resolution theory. IEEE Transactions on Computers C-25, 4 (April 1976), 335–341.Google Scholar
  11. [11]
    Lusk, E.L., W.W. McCune, and R.A. Overbeek. Logic Machine Architecture: kernel functions. Proceedings of the 6th Conference on Automated Deduction, New York, New York, June 1982, 70–84.Google Scholar
  12. [12]
    Lusk, E.L., W.W. McCune, and R.A. Overbeek. Logic Machine Architecture: inference mechanisms. Proceedings of the 6th Conference on Automated Deduction, New York, New York, June 1982, 85–108.Google Scholar
  13. [13]
    Lusk, E.L. and R.A. Overbeek. A portable environment for research in automated reasoning. Proceedings of the 7th Conference on Automated Deduction, Napa, California, May 1984, 43–52.Google Scholar
  14. [14]
    Michie, D., R. Ross, and G.J. Shannan. G-deduction. In B. Meltzer and D. Michie (eds.). Machine Intelligence 7. John Wiley and Sons, New York, New York, 1972, pp. 141–165.Google Scholar
  15. [15]
    Nilsson, N.J. Principles of Artificial Intelligence. Tioga Publishing Co., Palo Alto, California, 1980.Google Scholar
  16. [16]
    Plaisted, D.A. The occur-check problem in Prolog. New Generation Computing 2, 4 (1984), 309–322.Google Scholar
  17. [17]
    Reboh, R., B. Raphael, R.A. Yates, R.E. Kling, and C. Velarde. Study of automatic theorem-proving programs. Technical Note 72, Artificial Intelligence Center, SRI International, Menlo Park, California, November 1972.Google Scholar
  18. [18]
    Shostak, R.E. Refutation graphs. Artificial Intelligence 7, 1 (Spring 1976), 51–64.CrossRefGoogle Scholar
  19. [19]
    Stickel, M.E. A Prolog technology theorem prover. New Generation Computing 2, 4 (1984), 371–383.Google Scholar
  20. [20]
    Stickel, M.E. and W.M. Tyson. An analysis of consecutively bounded depth-first search with applications in automated deduction. Proceedings of the Ninth International Joint Conference on Artificial Intelligence, Los Angeles, California, August 1985, 1073–1075.Google Scholar
  21. [21]
    Warren, D.H.D. An abstract Prolog instruction set. Technical Note 309, Artificial Intelligence Center, SRI International, Menlo Park, California, October 1983.Google Scholar
  22. [22]
    Wilson, G.A. and J. Minker. Resolution, refinements, and search strategies: a comparative study. IEEE Transactions on Computers C-25, 8 (August 1976), 782–801.Google Scholar
  23. [23]
    Wos, L.T. Unpublished notes, Argonne National Laboratory, about 1965.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Mark E. Stickel
    • 1
  1. 1.Artificial Intelligence Center SRI InternationalMenlo Park

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