Nothing Special   »   [go: up one dir, main page]

Skip to main content

Experiments in automated deduction with condensed detachment

  • Conference paper
  • First Online:
Automated Deduction—CADE-11 (CADE 1992)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 607))

Included in the following conference series:

Abstract

This paper contains the results of experiments with several search strategies on 112 problems involving condensed detachment. The problems are taken from nine different logic calculi: three versions of the two-valued sentential calculus, the many-valued sentential calculus, the implicational calculus, the equivalential calculus, the R calculus, the left group calculus, and the right group calculus. Each problem was given to the theorem prover Otter and was run with at least three strategies: (1) a basic strategy, (2) a strategy with a more refined method for selecting clauses on which to focus, and (3) a strategy that uses the refined selection mechanism and deletes deduced formulas according to some simple rules. Two new features of Otter are also presented: the refined method for selecting the next formula on which to focus, and a method for controlling memory usage.

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.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. A. Church. Introduction to Mathematical Logic, volume I. Princeton University Press, 1956.

    Google Scholar 

  2. J. A. Kalman. Axiomatizations of logics with values in groups. Journal of the London Math. Society, 2(14):193–199, 1975.

    Google Scholar 

  3. J. A. Kalman. Computer studies of T→-W-I. Relevance Logic Newsletter, 1:181–188, 1976.

    Google Scholar 

  4. J. A. Kalman. A shortest single axiom for the classical equivalential calculus. Notre Dame Journal of Formal Logic, 19:141–144, 1978.

    Google Scholar 

  5. J. A. Kalman. Condensed detachment as a rule of inference. Studia Logica, LXII(4):443–451, 1983.

    Google Scholar 

  6. E. J. Lemmon, C. A. Meredith, D. Meredith, A. N. Prior, and I. Thomas. Calculi of pure strict implication. Technical report, Canterbury University College, Christchurch, 1957. Reprinted in Philosophical Logic, Reidel, 1970.

    Google Scholar 

  7. J. Łukasiewicz. Elements of Mathematical Logic. Pergamon Press, 1963. English translation of the second edition (1958) of Elementy logiki matematycznej, PWN, Warsaw.

    Google Scholar 

  8. J. Łukasiewicz. Selected Works. North-Holland, 1970. Edited by L. Borkowski.

    Google Scholar 

  9. W. McCune. Otter 2.0 Users Guide. Tech. Report ANL-90/9, Argonne National Laboratory, Argonne, IL, March 1990.

    Google Scholar 

  10. W. McCune. Automated discovery of new axiomatizations of the left group and right group calculi. Preprint MCS-P220-0391, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, 1991.

    Google Scholar 

  11. W. McCune. Single axioms for the left group and right group calculi. Preprint MCS-P219-0391, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, 1991.

    Google Scholar 

  12. C. A. Meredith. Single axioms for the systems (C,N), (C,0), and (A,N) of the two-valued propositional calculus. Journal of Computing Systems, 1:155–164, 1953.

    Google Scholar 

  13. C. A. Meredith and A. N. Prior. Equational logic. Notre Dame Journal of Formal Logic, 9:212–226, 1968.

    Google Scholar 

  14. D. Meredith. In memoriam Carew Arthur Meredith (1904–1976). Notre Dame Journal of Formal Logic, 18:513–516, 1977.

    Google Scholar 

  15. J. G. Peterson. Shortest single axioms for the classical equivalential calculus. Notre Dame Journal of Formal Logic, 17(2):267–271, 1976.

    Google Scholar 

  16. J. G. Peterson. The possible shortest single axioms for EC-tautologies. Report 105, Dept. of Mathematics, University of Auckland, 1977.

    Google Scholar 

  17. F. Pfenning. Single axioms in the implicational propositional calculus. In E. Lusk and R. Overbeek, editors, Proceedings of the 9th International Conference on Automated Deduction, Lecture Notes in Computer Science, Vol. 310, pages 710–713, New York, 1988. Springer-Verlag.

    Google Scholar 

  18. L. Wos. Meeting the challenge of fifty years of logic. Journal of Automated Reasoning, 6(2):213–232, 1990.

    Google Scholar 

  19. L. Wos. Automated reasoning and Bledsoe's dream for the field. In R. S. Boyer, editor, Automated Reasoning: Essays in Honor of Woody Bledsoe, chapter 15, pages 297–342. Kluwer Academic Publishers, 1991.

    Google Scholar 

  20. L. Wos and W. McCune. The application of automated reasoning to proof translation and to finding proofs with specified properties: A case study in many-valued sentential calculus. Tech. Report ANL-91/19, Argonne National Laboratory, Argonne, IL, 1991. In preparation.

    Google Scholar 

  21. L. Wos, S. Winker, W. McCune, R. Overbeek, E. Lusk, R. Stevens, and R. Butler. Automated reasoning contributes to mathematics and logic. In M. Stickel, editor, Proceedings of the 10th International Conference on Automated Deduction, Lecture Notes in Artificial Intelligence, Vol. 449, pages 485–499, New York, July 1990. Springer-Verlag.

    Google Scholar 

  22. L. Wos, S. Winker, B. Smith, R. Veroff, and L. Henschen. A new use of an automated reasoning assistant: Open questions in equivalential calculus and the study of infinite domains. Artificial Intelligence, 22:303–356, 1984.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Deepak Kapur

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

McCune, W., Wos, L. (1992). Experiments in automated deduction with condensed detachment. In: Kapur, D. (eds) Automated Deduction—CADE-11. CADE 1992. Lecture Notes in Computer Science, vol 607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55602-8_167

Download citation

  • DOI: https://doi.org/10.1007/3-540-55602-8_167

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55602-2

  • Online ISBN: 978-3-540-47252-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics