Skip to main content
SpringerLink
Log in

Automatic theorem proving. I

  • Published:
Cybernetics Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literature Cited

  1. V. M. Glushkov, “Automated proving system: a short informal description,” in: Automated Processing of Mathematical Texts [in Russian], IK AN UkrSSR, Kiev (1980), pp. 3–30.

    Google Scholar 

  2. A. I. Degtyarev and A. V. Lyaletskii, “Logical deductions in automated proving system,” in: Mathematical Foundations of Artificial Intelligence Systems [in Russian], IK AN UkrSSR, Kiev (1981), pp. 3–11.

    Google Scholar 

  3. V. I. Mart'yanov, “On methods of specification and partial construction of theory by computer,” Kibernetika, No. 6, 102–110 (1982).

    Google Scholar 

  4. V. P. Orevkov, “The British Museum algorithm may be more effective than the resolution method,” in: Mathematical Logic and Automatic Theorem Proving [in Russian], Nauka, Moscow (1983), pp. 314–326.

    Google Scholar 

  5. S. V. Popov, “Inference diagrams in sequential calculi,” Problemy Kibernetiki, No. 41, 49–100 (1984).

    Google Scholar 

  6. A. A. Voronkov, “A proving method,” Vychislit. Systemy, No. 107, 109–124 (1985).

    Google Scholar 

  7. M. Davis, “The prehistory of automated deduction,” Proc. 4th Workshop on Automated Deduction, Austin (1979), pp. 21–35.

  8. H. Wang, “Computer theorem proving and artificial intelligence,” Contemp. Math.,29, 48–70 (1984).

    Google Scholar 

  9. W. W. Bledsoe, “Some automatic proofs in analysis,” Contemp. Math.,29, 89–118 (1984).

    Google Scholar 

  10. R. Nossum, “Automated theorem proving methods,” BIT,25, No. 2, 51–64 (1985).

    Google Scholar 

  11. S. Yu. Maslov, “Deduction theory and some applications,” Kibernetika, No. 4, 139–144 (1975).

    Google Scholar 

  12. S. Yu. Maslov and G. E. Mints, “Deduction theory and the inverse method,” in: Mathematical Logic and Automatic Theorem Proving [in Russian], Nauka, Moscow (1983), pp. 291–314.

    Google Scholar 

  13. A. Newell, J. C. Shaw, and H. A. Simon, “Empirical exploration of the logic theory machine: a case study in heuristics,” Western Joint Computer Conf., vol. 15 (1956), pp. 218–239.

    Google Scholar 

  14. H. Gelernter, J. R. Hanson, and D. L. Loveland, “Empirical exploration of the geometry theorem-proving machine,” Western Joint Computer Conf., vol. 17 (1960), pp. 143–147.

    Google Scholar 

  15. G. Gentzen, “Untersuchungen über das logische Schlissen, I, II,” Math. Z.,39, 176–210; 405–443 (1935).

    Google Scholar 

  16. T. Skolem, “Logisch-combinatorische Untersuchungen über die Efüllbarkeit oder Beweisbarkeit Mathematischer Sätze nebst einem Theoreme über dichte Mengen,” Kristiania Videnskapsselskaps Schrifter, No. 4, 1–36 (1920).

    Google Scholar 

  17. J. Herbrand, Recherches sur la theorie de la demonstration, PhD thesis, Paris (1930).

  18. K. Schütte, Beweistheorie, Springer, Berlin (1960).

    Google Scholar 

  19. P. C. Gilmore, “A proof method for quantification theory: its justification and realization,” IBM J. Res. and Develop.,4, 28–35 (1960).

    Google Scholar 

  20. M. Davis and H. Putnam, “A computing procedure for quantification theory,” J. ACM,7, 201–204 (1960).

    Google Scholar 

  21. E. W. Beth, The Foundations of Mathematics, North-Holland, Amsterdam (1959).

    Google Scholar 

  22. S. Kanger, “A simplified proof method for elementary logic,” in: Computer Programming and Formal Systems, Amsterdam (1963), pp. 87–93.

  23. D. Prawitz, “An improved proof procedure,” Theoria,26, 102–139 (1960).

    Google Scholar 

  24. H. Wang, “Toward mechanical mathematics,” IBM J. Res. and Develop.,4, No. 1, 2–22 (1960).

    Google Scholar 

  25. J. A. Robinson, “A machine-oriented logic based on the resolution principle,” J. ACM,12, 23–41 (1965).

    Google Scholar 

  26. S. Yu. Maslov, “The inverse method of establishing derivability in classical predicate calculus,” Dokl. AN SSSR,159, No. 1, 17–20 (1964).

    Google Scholar 

  27. C. Chang and R. Lee, Symbolic Logic and Mechanical Theorem Proving, Academic Press, NY (1973).

    Google Scholar 

  28. L. Wos, G. Robinson, P. Carson, et al., “The concept of demodulation in theorem proving,” J. ACM,14, 698–709 (1967).

    Google Scholar 

  29. G. Robinson and L. Wos, “Paramodulation and theorem proving in first-order theories with equality,” Machine Intelligence, No. 4, Edinburgh Univ. (1969), pp. 135–150.

    Google Scholar 

  30. G. D. Plotkin, “Building-in equatorial theories,” Machine Intelligence, No. 7, Edinburgh Univ. (1972), pp. 73–89.

    Google Scholar 

  31. J. Siekmann and P. Szabo, “Universal unification and the classification of equatorial theories,” Lecture Notes Computer Sci.,138, 369–389 (1982).

    Google Scholar 

  32. G. Huet and D. C. Oppen, “Equations and rewrite rules: a survey,” Formal Languages Theory: Perspectives and Open Problems, Academic Press, NY (1980), pp. 349–350.

    Google Scholar 

  33. D. Knuth and P. Bendix “Simple word problems in universal algebra,” Combinatorial Problems in Abstract Algebra, Pergamon Press, NY (1970), pp. 263–270.

    Google Scholar 

  34. A. I. Degytarev and A. A. Voronkov, “Equality control methods in machine theorem proving,” Kibernetika, No. 3, 34–41 (1986).

    Google Scholar 

  35. F. V. Anufriev, V. V. Fedyurko, A. A. Letichevskii, et al., “A theorem proving algorithm in group theory,” Kibernetika (1966), pp. 23–29.

  36. W. W. Bledsoe, “Non-resolution theorm proving,” Artificial Intelligence,9, No. 1, 1–35 (1977).

    Google Scholar 

  37. J. R. Slagle, “Automatic theorem proving with built-in theories including equality, partial ordering and sets,” J. ACM,19, No. 1, 120–135, (1972).

    Google Scholar 

  38. W. W. Bledsoe, R. S. Boyer, and N. H. Honneman, “Computer proofs of limit theorems,” Artificial Intelligence,3, 27–60 (1972).

    Google Scholar 

  39. W. W. Bledsoe, “Using examples to generate instantiations of set variables,” Proc. 8th Int. Joint Conf. Artificial Intelligence (Karlsruhe, Aug. 1983), vol. 2, Karlsruhe (1983), pp. 892–901.

    Google Scholar 

  40. L. Wos, “Solving open questions with an automated theorem proving program,” Lecture Notes Compute Sci.,138, 1–31 (1982).

    Google Scholar 

  41. A. K. Zherlov and V. I. Mart'yanov, “Automatic theorem proving in group theory,” in: Algorithmic Topics in Algebraic Systems and Computers [in Russian], Irkutsk. Univ., Irkutsk (1979), pp. 36–64.

    Google Scholar 

  42. V. F. Kleimenov, “Automated theorem proving in category theory,” in: Algorithmic Topics in Algebraic Systems and Computers [in Russian], Irkutsk. Univ., Irkutsk (1979), pp. 65–83.

    Google Scholar 

  43. A. B. Nikolenko, “Automated theorem proving in axiomatic set theory,” in: Algorithmic Topics in Algebraic Systems and Computers [in Russian], Irkutsk. Univ., Irkutsk (1979), pp. 177–190.

    Google Scholar 

  44. A. B. Nikolenko, “The method of invariant transformations and logical deduction,” Mat. Zametki,36, No. 1, 3–17 (1984).

    Google Scholar 

  45. A. V. Mantsivoda, “On p-transformations of formulas,” 7th All-Union Conf. on Math. Logic [in Russian], IM SO AN SSSR, Novosibirsk (1984), p. 97.

    Google Scholar 

  46. V. I. Mart'yanov, “On invariant transformations of formulas,” Mat. Zametki,36, No. 6, 571–581 (1984).

    Google Scholar 

  47. J. A. Robinson, “Computational logic: the unification computation,” Machine Intelligence, No. 4, Edinburgh Univ. (1969), pp. 77–94.

    Google Scholar 

  48. L. Siklossy and V. Marinov, “Heuristic search vs exhaustive search,” Proc. 2nd Int. Conf. Artificial Intelligence, London (1971), pp. 524–530.

  49. D. Prawitz, “A proof procedure with matrix reduction,” Symp. Automatic Demonstration, Springer, Berlin (1970), pp. 207–214.

    Google Scholar 

  50. P. B. Andrews, “Transforming matings into natural deduction proofs,” Lecture Notes Computer Sci.,87, 281–292 (1980).

    Google Scholar 

  51. P. B. Andrews, “Theorem proving via general matings,” J. ACM,28, No. 2, 193–214 (1981).

    Google Scholar 

  52. W. Bibel, Automated Theorem Proving, Vieweg Verlag, Wiesbaden (1982).

    Google Scholar 

  53. W. Bibel, “Computationally improved versions of Herbrand theorem,” Herbrand Sym. Logic Colloq. 81, North-Holland, Amsterdam (1982), pp. 11–28.

    Google Scholar 

  54. J. Pfennig, “Analytic and non-analytic proofs,” Lecture Notes Computer Sci.,170, 394–413 (1984).

    Google Scholar 

  55. D. A. Miller, “Expansion tree proofs and their conversions into natural deduction proofs,” Lecture Notes Computer Sci.,170, 375–393 (1984).

    Google Scholar 

  56. E. L. Lusk, W. W. McCune, and R. A. Overbeek, “Logic machine architecture: kernel functions,” Lecture Notes Computer Sci.,138, 78–84 (1982).

    Google Scholar 

  57. E. L. Lusk, W. W. McCune, and R. A. Overbeek, “Logic machine architecture: inference mechanisms,” Lecture Notes Computer Sci.,138, 85–108 (1982).

    Google Scholar 

  58. E. L. Lusk and R. A. Overbeek, “A portable environment for research in automated reasoning,” Lectures Notes Coputer Sci.,170, 43–52 (1984).

    Google Scholar 

  59. I. V. Gorskaya, M. A. Korotkova, and S. V. Popov, A Translator for a Deduction-Seeking System [in Russian], Preprint AN SSSR, IPM, No. 42, Moscow (1985).

  60. I. V. Gorskaya, M. A. Korotkova and S. V. Popov, Input Languages for a Deduction Seeking System [in Russian], Preprint AN SSSR, IPM, No. 43, Moscow (1985).

  61. V. M. Glushkov, A. A. Letichevskii, Yu. V. Kapitonova, et al., “On the construction of a practical formal language for mathematical theories,” Kibernetika, No. 5, 18–28 (1972).

    Google Scholar 

  62. V. M. Glushkov, K. P. Vershinin, Yu. V. Kapitonova, et al., “On a formal language for mathematical texts,” in: Automated Theorem Proving in Mathematics [in Russian], IK AN UkrSSR, Kiev (1974).

    Google Scholar 

  63. N. Nakanishi, M. Nagata, and K. Veda, “An automatic prover generating a proof in natural language,” Proc. 6th Int. Joint Conf. on Artificial Intelligence (Tokyo, Aug. 1979), vol. 2, Tokyo (1979), pp. 626–638.

    Google Scholar 

  64. M. P. Morokhovets, “On proof editing,” in: Automated Processing of Mathematical Texts [in Russian], IK AN UkrSSR, Kiev (1980), pp. 53–61.

    Google Scholar 

  65. I. A. Shanin, G. V. Davydov, S. Yu. Maslov, et al., An Algorithm for Machine Search of a Natural Logical Deduction in Propositional Calculus [in Russian], Nauka, Leningrad (1966).

    Google Scholar 

Download references

Authors
  1. A. A. Voronkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. I. Degtyarev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The article is based on a lecture read at the All-Union Conference on Applied Logic (Novosibirsk, Oct. 1985).

Translated from Kibernetika, No. 3, pp. 27–33, May–June, 1986.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Voronkov, A.A., Degtyarev, A.I. Automatic theorem proving. I. Cybern Syst Anal 22, 290–297 (1986). https://doi.org/10.1007/BF01069967

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01069967

Keywords

Search

Navigation