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METEOR: Exploring model elimination theorem proving

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Abstract

In this paper we describe the theorem proverMETEOR which is a high-performance model elimination prover running in sequential, parallel, and distributed computing environments.METEOR has a very high inference rate. But, as is the case with better chess-playing programs, speed alone is not sufficient when exploring large search spaces; intelligent search is necessary. We describe modifications to traditional iterative deepening search mechanisms whose implementation inMETEOR result in performance improvements of several orders of magnitude and that have permitted the discovery of proofs unobtainable by top-down model elimination provers.

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References

  1. Ali, K. A. M. and Karlsson, R.: The muse or-parallel Prolog model and its performance, in S. Debray and M. Hermenegildo (eds),Proc. North American Conference on Logic Programming, 1990, pp. 757–776.

  2. Astrachan, O. L.: Investigations in model elimination based theorem proving, PhD thesis, Duke University, 1992.

  3. Astrachan, O. L. and Loveland, D. W.: METEORs: High performance theorem provers using model elimination, in R. S. Boyer (ed.),Automated Reasoning: Essays in Honor of Woody Bledsoe, Kluwer Academic Publishers, 1991.

  4. Astrachan, O. L. and Sickel, M. E.: Caching and lemmaizing in model elimination theorem provers. Technical Report 513, SRI International, Menlo Park, Ca., 1991.

  5. Astrachan, O. L. and Stickel, M. E.: Caching and lemmaizing in model elimination theorem provers, in Deepak Kapur (ed.),Proc. 11th International Conference on Automated Deduction, Springer-Verlag, Berlin, 1992.

    Google Scholar 

  6. Bachmair, L., Dershowitz, N., and Plaisted, D. A.: Completion without failure, in H. AïtKaci and M. Nivat (eds),Resolution of Equations in Algebraic Structures, vol. II: Rewriting Techniques, Academic Press, New York, 1989, pp. 1–30.

    Google Scholar 

  7. Bayer, R. and Schkolnick, M.: Concurrency of operations in b-trees,Acta Informatica 9 (1977), 1–21.

    Google Scholar 

  8. Bledsoe, W. W.: Challenge problems in elementary calculus,J. Automated Reasoning 6(3) (1990), 341–359.

    Google Scholar 

  9. Bonacina, M. P. and Hsiang, J.: Distributed deduction by clause-diffusion: The Aquarius prover, in Alfonso Miola (ed.),Proc. International Symposium on Design and Implementation of Symbolic Computation Systems, Lecture Notes in Comput. Sci. 722, Springer-Verlag, 1993, pp. 272–287.

  10. Bose, S., Clarke, E., Long, D. E., and Michaylov, S.: Parthenon: A parallel theorem prover for non-Horn clauses, inProc. Symposium on Logic in Computer Science, 1989.

  11. Bose, S, Clarke, E., Long, D. E., and Michaylov, S.: Parthenon: A parallel theorem prover for non-Horn clauses,J. Automated Reasoning 8 (1992), 153–181.

    Google Scholar 

  12. Dershowitz, N.: Orderings for term-rewriting systems,Theoretical Computer Science 17 (1982), 279–301.

    Google Scholar 

  13. Ellis, C. S.: Concurrent search and insertion in 2–3 trees,Acta Informatica 14 (1980), 63–86.

    Google Scholar 

  14. Fleisig, S., Loveland, D., Smiley, A., and Yarmash, D.: An implementation of the model elimination proof procedure,JACM 21 (1974), 124–139.

    Google Scholar 

  15. Jindal, A., Overbeek, R., and Kabat, W. C.: Exploitation of parallel processing for implementing high-performance deduction systems,J. Automated Reasoning 8 (1992), 23–38.

    Google Scholar 

  16. Korf, R. E.: Depth-first iterative deepening: An optimal admissible tree search,Artificial Intelligence 27 (1985), 97–109.

    Google Scholar 

  17. Kotz, D. and Ellis, C. S.: Evaluation of concurrent pools, inProc. 9th International Conference on Distributed Computing Systems, 1989, pp. 378–385.

  18. Lamport, L.: Concurrent reading and writing,Communications of the ACM 20(11) (1977), 806–811.

    Google Scholar 

  19. Letz, R, Bayerl, S., Schumann, J., and Bibel, W.: SETHEO — a high-performance theorem prover,J. Automated Reasoning 8 (1992), 183–212.

    Google Scholar 

  20. Loveland, D. W.:Automated Theorem Proving: A Logical Basis, North-Holland, Amsterdam, 1978.

    Google Scholar 

  21. Loveland, D. W.: Mechanical theorem proving by model elimination,JACM 15(2) (1968), 236–251.

    Google Scholar 

  22. Loveland, D. W.: A simplified format for the model elimination procedure,JACM 16(3) (1969), 349–363.

    Google Scholar 

  23. Lusk, E., McCune, W. W., and Slaney, J.: Roo: A parallel theorem prover, in Deepak Kapur (ed.),Proc. 11th International Conference on Automated Deduction, Springer-Verlag, 1992.

  24. McCune, W.: Otter 2.0. In Mark Stickel (ed.),Proc. 10th International Conference on Automated Deduction, Springer-Verlag, 1990, pp. 663–664.

  25. Manber, U.: On maintaining dynamic information in a concurrent environment,SIAM J. Computing 15(4) (1986), 1130–1142.

    Google Scholar 

  26. Plaisted, D.: Non-Horn clause logic programming without contrapositives,J. Automated Reasoning 4(3) (1988), 287–325.

    Google Scholar 

  27. Schumann, J. and Letz, R.: PARTHEO: A high performance parallel theorem prover, inProc. 10th International Conference on Automated Deduction, 1990, pp. 40–56.

  28. Spencer, B.: Avoiding duplicate proofs, in S. Debray and M. Hermenegildo (eds),Proc. North American Conference on Logic Programming, 1990, pp. 569–584.

  29. Stevens, W. R.:UNIX Network Programming, Prentice-Hall, 1990.

  30. Stickel, M. E.: A Prolog technology theorem prover,New Generation Computing 2(4) (1984), 371–383.

    Google Scholar 

  31. Stickel, M. E.: A Prolog technology theorem prover: Implementation by an extended Prolog compiler, inProc. 8th International Conference on Automated Deduction, Springer-Verlag, 1986, pp. 573–587.

  32. Stickel, M. E.: A Prolog technology theorem prover: Implementation by an extended Prolog compiler,J. Automated Reasoning 4 (1988), 343–380.

    Google Scholar 

  33. Stickel, M. E. and Tyson, W. A.: An analysis of consecutively bounded depth-first search with applications in automated deduction, inProc. 9th International Joint Conference on Artificial Intelligence, 1985, pp. 1073–1075.

  34. Wang, T. C., and Bledsoe, W. W.: Hierarchical deduction,J. Automated Reasoning 3 (1987), 35–77.

    Google Scholar 

  35. Warren, D. H. D.: An abstract Prolog instruction set. Technical Report 309, SRI International, Menlo Park, Ca., 1983.

  36. Wilson, G. A. and Minker, J.: Resolution, refinements, and search strategies: A comparative study,IEEE Trans. Computers C-25(8) (1976), 782–801.

    Google Scholar 

  37. Wos, L.:Automated Reasoning: 33 Basic Research Problems, Prentice-Hall, 1988.

  38. Wos, L and Overbeek, R.: Subsumption, a sometimes undervalued procedure, in J.-L. Lassez and G. Plotkin (eds),Computational Logic, Essays in Honor of Alan Robinson, MIT Press, 1991.

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  1. Department of Computer Science, Duke University, Durham, NC, USA

    Owen Astrachan

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  1. Owen Astrachan
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Astrachan, O. METEOR: Exploring model elimination theorem proving. J Autom Reasoning 13, 283–296 (1994). https://doi.org/10.1007/BF00881946

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