Journal of Automated Reasoning

, Volume 4, Issue 4, pp 353–380

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

  • Mark E. Stickel
Article

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 depth-first iterative-deepening search instead of unbounded depthfirst 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.

Key words

Automated theorem proving model elimination procedure Prolog 

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References

  1. 1.
    Andrews, P. B., ‘Theorem proving via general matings’, Journal of the ACM 28, 2 (April 1981) 193–214.Google Scholar
  2. 2.
    Antoniou, G. and Ohlbach, H. J., ‘TERMINATOR’. Proceedings of the Eighth International Joint Conference on Artificial Intelligence, Karlsruhe, West Germany (August 1983) 916–919.Google Scholar
  3. 3.
    Bayerl, S., Kurfess, F., Letz, R., and Schumann, J., ‘PROTHEO/2: sequential PROLOG-like theorem prover based on the connection method’ (1986).Google Scholar
  4. 4.
    Bibel, W., Automated Theorem Proving. Friedr. Vieweg & Sohn, Braunschweig, West Germany (1982).Google Scholar
  5. 5.
    Butler, R., Lusk, E., McCune, W., and Overbeek, R., ‘Paths to high-performance automated theorem proving’. Proceedings of the 8th Conference on Automated Deduction, Oxford, England (July 1986) 588–597.Google Scholar
  6. 6.
    Boyer, R. S. and Moore, J. S., ‘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
  7. 7.
    Bürckert, H. J., Wang, H., and Zheng, R., ‘MKRP: a performance test by working mathematicians’. Memo SEKI-83-1, Institut für Informatik I, Universität Karlsruhe Karlsruhe, West Germany (1983).Google Scholar
  8. 8.
    Chang, C. L. and Lee, R. C. T., Symbolic Logic and Mechanical Theorem Proving. Academic Press, New York, New York (1973).Google Scholar
  9. 9.
    Cohen, J., ‘Describing Prolog by its interpretation and compilation’. Communications of the ACM 28, 12 (December 1985) 1311–1324.Google Scholar
  10. 10.
    Colmerauer, A., ‘Prolog and infinite trees’. In Clark, K. L. and Tarnlund, S. A. (eds.). Logic Programming. Academic Press, New York, New York (1982).Google Scholar
  11. 11.
    Eder, G. ‘A PROLOG-like interpreter for non-Horn clauses’. D.A.I. Research Report No. 26, Department of Artificial Intelligence, University of Edinburgh, Edinburgh, Scotland, September (1976).Google Scholar
  12. 12.
    Fleisig, S., Loveland, D., SmileyIII, A. K., and Yarmush, D. L., ‘An implementation of the model climination proof procedure’: Journal of the ACM 21, 1 (January 1974) 124–139.Google Scholar
  13. 13.
    Korf, R. E., Depth-first iterative-deepening: an optimal admissible tree search. Artificial Intelligence 27, 1 (September 1985) 97–109.Google Scholar
  14. 14.
    Kowalski, R. and Kuehner, D., ‘Linear resolution with selection function’. Artificial Intelligence 2 (1971) 227–260.Google Scholar
  15. 15.
    Lawrence, J. D. and Starkey, J. D., ‘Experimental tests of resolution based theorem-proving strategies’. Technical Report. Computer Science Department, Washington State University, Pullman, Washington (April 1974).Google Scholar
  16. 16.
    Loveland, D. W., ‘A simplified format for the model elimination procedure’. Journal of the ACM 16, 3 (July 1969) 349–363.Google Scholar
  17. 17.
    Loveland, D. W., Automated Theorem Proving: A Logical Basis. North-Holland, Amsterdam, the Netherlands (1978)Google Scholar
  18. 18.
    Loveland, D. W., ‘Automated theorem proving: mapping logic into AI’ Proceedings of the International Symposium on Methodologies for Intelligent Systems, Knoxville, Tennessee (October 1986) 214–229.Google Scholar
  19. 19.
    Loveland, D. W., ‘Near-Horn Prolog’. Proceedings of the Fourth International Conference on Logic Programming, Melbourne, Australia (May 1987) 456–469.Google Scholar
  20. 20.
    Loveland, D. W. and Stickel, M. E., ‘The hole in goal trees: some guidance from resolution theory’. IEEE Transactions on Computers C-25, 4 (April 1976) 335–341.Google Scholar
  21. 21.
    Lusk, E. L., McCune, W. W., and Overbeek, R. A., Logic Machine Architecture: kernel functions’. Proceedings of the 6th Conference on Automated Deduction, New York, New York (June 1982) 70–84.Google Scholar
  22. 22.
    Lusk, E. L., McCune, W. W., and Overbeek, R. A., ‘Logic Machine Architecture: inference mechanisms’. Proceedings of the 6th Conference on Automated Deduction, New York, New York (June 1982) 85–108.Google Scholar
  23. 23.
    Lusk, E. L. and Overbeek, R. A., ‘A portable environment for research in automated reasoning’. Proceedings of the 7th Conference on Automated Deduction, Napa, California (May 1984) 43–52.Google Scholar
  24. 24.
    Malachi, Y., Nonclausal Logic Programming. Ph.D. Dissertation, Department of Computer Science, Stanford University, March 1986.Google Scholar
  25. 25.
    Michie, D., Ross, R., and Shannan, G. J., ‘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
  26. 26.
    Nilsson, N. J., Principles of Artificial Intelligence. Tioga Publishing Co., Palo Alto, California (1980).Google Scholar
  27. 27.
    Plaised, D. A., ‘A simplified problem reduction format’. Artificial Intelligence 18, 2 (March 1982) 227–261.Google Scholar
  28. 28.
    Plaisted, D. A., ‘Non-Horn clause logic programming without contrapositives’ (1987).Google Scholar
  29. 29.
    Rao, V. N., Kumar, V., and Ramesh, K., ‘A parallel implementation of iterative-deepening A*’. Proceedings of the AAAI-87 National Conference on Artificial Intelligence, Seattle, Washington (July 1987) 178–181.Google Scholar
  30. 30.
    Raph, Karl Mark G., ‘The Markgraf Karl Refutation Procedure’. Memo SEKI-MK-84-01, Fachbereich Informatik, Universität Kaiserslautern, Kaiserslautern, West Germany (January 1984).Google Scholar
  31. 31.
    Reboh, R., Raphael, B., Yates, R. A., Kling, R. E., and Verlarde, C., ‘Study of automatic theoremproving programs’. Technical Note, 75, Artificial Intelligence Center, Stanford Research Institute, Menlo Park, California (November 1972).Google Scholar
  32. 32.
    Shostak, R. E., ‘Refutation graphs’. Artificial Intelligence 7, 1 (Spring 1976) 51–64.Google Scholar
  33. 33.
    Slate, D. J., and Atkin, L. R., ‘CHESS 4.5 — The Northwestern University chess program’. In Frey, P. W. (ed.), Chess Skill in Man and Machine, Springer-Verlag, New York, New York (1977) 82–118.Google Scholar
  34. 34.
    Stickel, M. E., ‘A Prolog technology theorem prover’. New Generation Computing 2, 4 (1984) 371–383.Google Scholar
  35. 35.
    Stickel, M. E. and Tyson, W. M., ‘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
  36. 36.
    Umrigar, Z. D. and Pitchumani, V., ‘An experiment in programming with full first-order logic’. Proceedings of the 1985 Symposium on Logic Programming, Boston, Massachusetts (July 1985) 40–47.Google Scholar
  37. 37.
    Warren, D. H. D., ‘An abstract Prolog instruction set’. Technical Note 309, Artificial Intelligence Center, SRI International Menlo Park, California (October 1983).Google Scholar
  38. 38.
    Wilkins, D. E., ‘QUEST: a non-clausal theorem proving system’. M.Sc. Thesis, University of Essex, Essex, England, 1973.Google Scholar
  39. 39.
    Wilson, G. A. and Minker, J., ‘Resolution, refinements, and search strategies: a comparative study’. IEEE Transactions on Computers C-25, 8 (August 1976) 782–801.Google Scholar
  40. 40.
    Wos, L., Veroff, R., Smith, B., and McCune, W., ‘The linked inference principle, II: the user's viewpoint’. Proceedings of the 7th International Conference on Automated Deduction, Napa, California (May 1984) 316–332.Google Scholar
  41. 41.
    Wos, L. T., Unpublished notes, Argonne National Laboratory (about 1965).Google Scholar

Copyright information

© Kluwer Academic Publishers 1988

Authors and Affiliations

  • Mark E. Stickel
    • 1
  1. 1.Artificial Intelligence CenterSRI InternationalMenlo ParkU.S.A.

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