Skip to main content
SpringerLink
Log in

Some obstacles to the automation of reasoning, and the problem of redundant information

  • Basic Research Problem
  • Published:
Journal of Automated Reasoning Aims and scope Submit manuscript

Abstract

This article is the first of a series of articles discussing various unsolved research problems in automated reasoning. We begin with an overview of some of the main obstacles that prevent reasoning programs from being even more useful than they currently are. We include a brief discussion of the basic paradigm used by those programs whose power is demonstrated by their use in answering open questions from mathematics. We then turn our attention to an unsolved research problem concerned with finding a strategy to avoid or reduce the deduction of redundant information.

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

Similar content being viewed by others

References

  1. Andrews, P., ‘Theorem proving via general matings’, Journal of the ACM 28, 193–214 (1981).

    Google Scholar 

  2. Bibel, W., ‘On matrices with connections’, Journal of the ACM 28, 633–645 (1981).

    Google Scholar 

  3. Bledsoe, W. and Bruell, P., ‘A man-machine theorem proving system’, Artificial Intelligence 5, 51–72 (1974).

    Google Scholar 

  4. Boyer, R. and Moore, J, A Computational Logic, Academic Press, New York (1979).

    Google Scholar 

  5. Guard, J., Oglesby, F., Bennett, J., and Settle, L., ‘Semi-automated mathematics’, Journal of the ACM 16, 49–62 (1969).

    Google Scholar 

  6. Knuth, D. and Bendix, P., ‘Simple word problems in universal algebras’, pp. 263–297 in Computational Problems in Abstract Algebra, J.Leech (ed.), Pergamon Press, New York (1970).

    Google Scholar 

  7. Lusk, E., McCune, W., and Overbeek, R., ‘Logic Machine Architecture: inference mechanisms’, pp. 85–108 in Proceedings of the Sixth Conference on Automated Deduction, Springer-Verlag Lecture Notes in Computer Science, Vol. 138, D.Loveland (ed.), Springer-Verlag, New York (1982).

    Google Scholar 

  8. Lusk, E., McCune, W., and Overbeek, R., ‘Logic Machine Architecture: kernel functions’, pp. 70–84 in Proceedings of the Sixth Conference on Automated Deduction, Springer-Verlag Lecture Notes in Computer Science, Vol. 138, D.Loveland (ed.), Springer-Verlag, New York (1982).

    Google Scholar 

  9. McCharen, J., Overbeek, R., and Wos, L., ‘Complexity and related enhancements for automated theorem-proving programs’, Computers and Mathematics with Applications 2, 1–16 (1976).

    Google Scholar 

  10. Murray, N., ‘Completely non-clausal theorem proving’, Artificial Intelligence 18, 67–85 (1982).

    Google Scholar 

  11. Robinson, J., ‘A machine-oriented logic based on the resolution principle’, Journal of the ACM 12, 23–41 (1965).

    Google Scholar 

  12. Robinson, J., ‘Automatic deduction with hyper-resolution’, International Journal of Computer Mathematics 1, 227–234 (1965).

    Google Scholar 

  13. Smith, B., ‘Reference manual for the environmental theorem prover, an incarnation of AURA’, to be published as Argonne National Laboratory technical report.

  14. Smullyan, R., To Mock a Mockingbird, Alfred A. Knopf, New York (1985).

    Google Scholar 

  15. Stickel, M., ‘A case study of theorem proving by the Knuth-Bendix method: discovering that x 3=x implies ring commutativity’, pp. 248–258 in Proceedings of the Seventh International Conference on Automated Deduction, Lecture Notes in Computer Science, Vol. 170, R. E.Shostak (ed.), Springer-Verlag, New York (1984).

    Google Scholar 

  16. Winker, S., ‘Generation and verification of finite models and counterexamples using an automated theorem prover answering two open questions’, Journal of the ACM 29, 273–284 (1982).

    Google Scholar 

  17. Wos, L., Robinson, G., and Carson, D., ‘Efficiency and completeness of the set of support strategy in theorem proving’, Journal of the ACM 12, 536–541 (1965).

    Google Scholar 

  18. Wos, L., Robinson, G., Carson, D., and Shalla, L., ‘The concept of demodulation in theorem proving’, Journal of the ACM 14, 698–709 (1967).

    Google Scholar 

  19. Wos, L. and Robinson, G., ‘Maximal models and refutation completeness: semidecision procedures in automatic theorem proving’, pp. 609–639 in Word Problems: Decision Problems and the Burnside Problem in Group Theory, W.Boone, F.Cannonito, and R.Lyndon (eds.), North-Holland, New York (1973).

    Google Scholar 

  20. Wos, L., Overbeek, R., Lusk, E., and Boyle, J., Automated Reasoning: Introduction and Applications, Prentice-Hall, Englewood Cliffs, NJ (1984).

    Google Scholar 

  21. Wos, L. and McCune, W., ‘Negative hyperparamodulation’, pp. 229–239 in Proceedings of the Eighth International Conference on Automated Deduction, Lecture Notes in Computer Science, Vol. 230, J.Siekmann (ed.), New York, Springer-Verlag (1986).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Argonne National Laboratory, 9700 South Cass Ave., 60439-4844, Argonne, IL, U.S.A.

    Larry Wos

Authors
  1. Larry Wos
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported by the Applied Mathematical Sciences subprogram of the office of Energy Research, U.S. Department of Energy, under contract W-31-109-Eng-38.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wos, L. Some obstacles to the automation of reasoning, and the problem of redundant information. J Autom Reasoning 3, 81–90 (1987). https://doi.org/10.1007/BF00381146

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00381146

Key words

Search

Navigation