Skip to main content
Log in

Theory of deduction search and some applications of it

  • Published:
Cybernetics Aims and scope

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

Access this article

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

Instant access to the full article PDF.

Literature Cited

  1. Collection “Mathematical Theory of Logical Deduction” [in Russian], Moscow (1967).

  2. S. C. Kleene, Introduction to Metamathematics [Russian translation], Moscow (1957).

  3. D. Prawitz, Natural Deduction, Stokholm (1965).

  4. G. Kreisel, “A survey of proof theory,” J. Symbolic Logic,33, No. 4, (1968).

  5. V. A. Lifshits, “Specialization of the form of a deduction in a predicate calculus with equality,” Tr. Mat. Inst. Akad. Nauk SSSR,98 (1968).

  6. S. Yu. Maslov and S. A. Norgela, “On rules of section type in calculi of general form,” Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,40, (1974).

  7. G. E. Mints, “Variation of deduction search tactics in sequential calculi,” Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,4 (1967).

  8. S. Yu. Maslov, “Reversible variant of a constructive predicate calculus,” Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,4 (1967).

  9. S. A. Norgela, “Complication of deductions under the introduction of minus normality,” in: Theory of Logical Deduction, Part I [in Russian], Moscow (1974).

  10. S. Yu. Maslov, “On deduction search in calculi of general type,” Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,32 (1972).

  11. S. Yu. Maslov, “Deduction search as a model of a heuristic process,” Kibernetika, No. 5 (1972).

  12. S. Yu. Maslov, “Proof-search strategies for methods of the resolution type,” Machine Intelligence,6 (1971).

  13. J. A. Robinson, “A review of automatic theorem proving,” Proc. Symp. Appl. Math.,19 (1967).

  14. J. Slagle, Artificial Intelligence, McGraw-Hill.

  15. S. Yu. Maslov, “Inverse method of establishing deducibility for logical calculi,” Tr. Mat. Inst. Akad. Nauk SSSR,98 (1968).

  16. S. Yu. Maslov, “Inverse method and tactics of establishing deducibility,” Tr. Mat. Inst. Akad. Nauk SSSR,121 (1972).

  17. S. Yu. Maslov, “Connection between the tactics of the inverse method and of the resolution method,” Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,16 (1969).

  18. G. V. Davydov, “Synthesis of the resolution method with the inverse method,” Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,20 (1971).

  19. D. Kuchner, “A note on the relation between resolution and Maslov's inverse method,” Machine Intelligence,6 (1971).

  20. N. G. Robitashvili, “Combination of the inverse method and the resolution method,” Soobshch. Akad. Nauk GruzSSR,64, No. 2 (1971).

    Google Scholar 

  21. S. Yu. Maslov, G. E. Mints, and V. P. Orevkov, “Unsolvability in a constructive calculus of certain classes of formulas containing only one-place variables,” Dokl. Akad. Nauk SSSR,163, No. 2 (1965).

  22. V. P. Orevkov, “Unsolvable classes of double negations of prenex formulas,” in: Third All-Union Conference on Mathematical Logic, Abstracts of Reports. [in Russian], Novosibirsk (1974).

  23. Yu. Sh. Gurevich, “On an effective recognition of the fulfillment of the formulas of RPC (restricted predicate calculus),” Algebra Logika,5, No. 2 (1966).

  24. S. Yu. Maslov, “Inverse method of establishing deducibility in the classical calculus,” Dokl. Akad. Nauk SSSR,159, No. 1 (1964).

  25. V. P. Orevkov, “Two unsolvable classes of formulas of classical predicate calculus,” Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,8 (1968).

  26. V. P. Orevkov, “On biconjunctive classes of reduction,” Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,20 (1971).

  27. S. O. Aanderaa and H. Lewis, “Prefix classes of Krom formulas,” J. Symbolic Logic,38 (1973).

  28. S. O. Aanderaa and W. D. Goldfarb, “The finite controllability of the Maslov case,” J. Symbolic Logic,39, No. 3 (1974).

    Google Scholar 

  29. S. Yu. Maslov, “Application of the inverse method to the theory of solvable fragments of classical calculus,” Dokl. Akad. Nauk SSSR,171, No. 6 (1966).

  30. A. Church, Introduction to Mathematical Logic, Krauss Reprint (1944).

  31. S. Yu. Maslov and V. P. Orevkov, “Solvable classes reducing to one-quantifier ones,” Tr. Mat. Inst. Akad. Nauk SSSR,121 (1972).

  32. V. A. Lifshits, “Certain reduction classes and unsolvable theories,” Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,4 (1967).

  33. Yu. L. Ershov et al., “Elementary theories,” Usp. Mat. Nauk,20, No. 4 (1965).

  34. V. P. Orevkov, “Certain reduction classes and solvable classes for the constructive calculus,” Dokl. Akad. Nauk SSSR,163, No. 1 (1965).

    Google Scholar 

  35. G. E. Mints, “Proof theory,” in: Arithmetic and Analysis [in Russian], Leningrad (1975).

  36. G. E. Mints, “Tranfinite evolutes,” Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,49 (1975).

  37. G. E. Mints, “Finite investigation of transfinite deductions,” Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,49 (1975).

  38. V. P. Orevkov, “On Glivenko classes of sequences,” Tr. Mat. Inst. Akad. Nauk SSSR,98 (1968).

  39. G. E. Mints and V. P. Orekov, “On immersing operations,” Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,4 (1967).

  40. M. G. Gel'fond, “On the relation of classical and constructive construction of mathematical analysis,” Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,32 (1972).

  41. Computers and Thought, Part 1, Sec. 2 [in Russian], Moscow (1967).

  42. N. A. Shanin, et al., Algorithm for a Machine Search of a Natural Logical Deduction [in Russian], Moscow-Leningrad (1965).

  43. G. V. Davydov, “On the correction of unprovable formulas,” Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,4 (1967).

  44. O. F. Serebrennikov, Heuristic Principles and Logical Calculi [in Russian], Moscow (1970).

Download references

Authors

Additional information

Translated from Kibernetika, No. 4, pp. 134–144, July–August, 1975.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maslov, S.Y. Theory of deduction search and some applications of it. Cybern Syst Anal 11, 659–669 (1975). https://doi.org/10.1007/BF01070445

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01070445

Keywords

Navigation