Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

OTTER experiments in a system of combinatory logic

  • 26 Accesses

  • 4 Citations

Abstract

This paper describes some experiments involving the automated theorem-proving program OTTER in the system TRC of illative combinatory logic. We show how OTTER can be steered to find a contradiction in an inconsistent variant of TRC, and present some experimentally discovered identities in TRC.

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

References

  1. 1.

    Barendregt, H. P.:The Lambda Calculus, North-Holland, Amsterdam, 1984.

  2. 2.

    Curry, H. B. and Feys, R.:Combinatory Logic I, North-Holland, Amsterdam, 1958.

  3. 3.

    Holmes, M. R.: System of combinatory logic related to Quine's New Foundations,Annals Pure Appl. Logic 53 (1991), 103–133.

  4. 4.

    Kunen, K.: Single axioms for groups,J. Automated Reasoning 9 (1992), 291–308.

  5. 5.

    McCune, W. W.:OTTER 3.0 Reference Manual and Guide, ANL 96/6 Argonne National Laboratory, 1994.

  6. 6.

    McCune, W. W.: Automated discovery of new axiomatizations of the left group and right group calculi,J. Automated Reasoning 9 (1992) 1–24.

  7. 7.

    McCune, W. W.: Single axioms for groups and Abelian groups with various operations,J. Automated Reasoning 10 (1993) 1–13.

  8. 8.

    Wos, L.: Automated reasoning answers open questions,Notices Amer. Math. Society 40 (1993), 15–26.

  9. 9.

    Wos, L.: The kernel strategy and its use for the study of combinatory logic,J. Automated Reasoning 10 (1993), 287–343.

Download references

Author information

Additional information

This work was supported by the Office of Scientific Computing U.S. Department of Energy, under the Summer 1994 Faculty Research Participation Program at Argonne National Laboratory.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Jech, T. OTTER experiments in a system of combinatory logic. J Autom Reasoning 14, 413–426 (1995). https://doi.org/10.1007/BF00881715

Download citation

Key words

  • combinatory logic
  • OTTER
  • TRC

AMS Subject Classification

  • 03B40
  • 68T15