Skip to main content
Log in

Schubert's Steamroller problem: Formulations and solutions

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

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.

Institutional subscriptions

References

  1. Antoniou, G. and Ohlbach, H. J., ‘Terminator’, Proceedings of the Eighth International Joint Conference on Artificial Intelligence, Karlsruhe, West Germany, 1983, pp. 916–919.

  2. Bläsius, K., Eisinger, N., Siekman, J., Smolka, G., Herold, A., and Walther, C., ‘The Markgraf Karl Refutation Procedure (Fall 1981)’, Proceedings of the Seventh International Joint Conference on Artificial Intelligence, Vancouver, BC, Canada, 1981, pp. 511–518.

  3. Boyer, R. S., ‘Locking: a restriction of resolution’, PhD dissertation, University of Texas, Austin, Texas, 1971.

  4. De Champeaux, D., ‘A theorem prover dating a semantic network’, Proceedings of the AISB/GI Conference on Artificial Intelligence, Hamburg, West Germany, 1978, pp. 82–92.

  5. Cohn, A. G., ‘Mechanizing a particularly expressive many sorted logic’, PhD dissertation, University of Essex, Essex, England, 1983.

  6. Cohn, A. G., ‘On the solution of Schubert's steamroller in many sorted logic’, Proceedings of the Ninth International Joint Conference on Artificial Intelligence, Los Angeles, California, 1985, pp. 1169–1174.

  7. Dahl, V., ‘Translating Spanish into logic through logic’, American Journal of Computational Linguistics 7, 149–164 (1981).

    Google Scholar 

  8. Frisch, A. M., ‘An investigation into inference with restricted quantification and a taxonomic representation’, Technical Report CSRP 041, Cognitive Studies Programmme, The University of Sussex, Brighton, England.

  9. Henschen, L. J., ‘N-sorted logic for automatic theorem-proving in higher-order logic’, Proceedings of the ACM Annual Conference, Boston, Massachusetts, 1972, pp. 71–81.

  10. Kowalski, R., ‘A proof procedure using connection graphs’, Journal of the ACM 22, 572–595 (1975).

    Google Scholar 

  11. Lusk, E. L., McCune, W. W., and Overbeek, R. A., ‘Logic Machine Architecture: kernel functions’, Proceedings of the 6th Conference on Automated Deduction, New York, New York, 1982, pp. 70–84.

  12. Lusk, E. L., McCune, W. W., and Overbeek, R. A., ‘Logic Machine Architecture: inference mechanisms’, Proceedings of the 6th Conference on Automated Deduction, New York, New York, 1982, 85–108.

  13. Lusk, E. L. and Overbeek, R. A., ‘A portable environment for research in automated reasoning’, Proceedings of the 7th Conference on Automated Deduction, Napa, California, 1984, pp. 43–52.

  14. McCune, W. W., ‘Schubert's steamroller problem with linked UR-resolution’, Association of Automated Reasoning Newsletter No. 4 (Spring 1985), pp. 4–6.

  15. Pelletier, J. F., ‘Completely non-clausal, completely heuristically driven automatic theorem proving’, MSc Thesis, University of Alberta, Edmonton, Alberta, Canada, 1982.

  16. Schmidt-Schauss, M. A., ‘A many-sorted calculus with polymorphic functions based on resolution and paramodulation’, Proceedings of the Ninth International Joint Conference on Artificial Intelligence, Los Angeles, California, 1985, pp. 1162–1168.

  17. Stickel, M. E., ‘A nonclausal connection-graph resolution theorem-proving program’, Proceedings of the AAAI-82 National Conference on Artificial Intelligence, Pittsburgh, Pennsylvania, 1982, pp. 229–233.

  18. Stickel, M. E., ‘A PROLOG technology theorem prover’, New Generation Computing 2 371–383 (1984).

    Google Scholar 

  19. Stickel, M. E., ‘Automated deduction by theory resolution’, Journal of Automated Reasoning 1, 333–355 (1985).

    Google Scholar 

  20. Walther, C., ‘A many-sorted calculus based on resolution and paramodulation’, Proceedings of the Eighth International Joint Conference on Artificial Intelligence, Karlsruhe, West Germany, 1983, pp. 882–891.

  21. Walther, C., ‘A mechanical solution of Schubert's steamroller by many-sorted resolution’, Proceedings of the AAAI-84 National Conference on Artificial Intelligence, Austin, Texas, 1984, pp. 330–334. Revised version appeared in Artificial Intelligence 26, 217–224 (1985).

  22. Winker, S., ‘An evaluation of an implementation of qualified hyperresolution’, IEEE Transactions on Computers C 25, 835–843 (1976).

    Google Scholar 

  23. Wos, L., Veroff, R., Smith, B., and McCune, W., ‘The linked inference principle, II: the user's viewpoint’, Proceedings of the 7th International Conference on Automated Deduction, Napa, California, 1984, pp. 316–332.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Preparation of this paper was supported, in part, by the Defense Advanced Research Projects Agency under Contract N00039-84-K-0078 with the Naval Electronic Systems Command. The views and conclusions contained herein are those of the author and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the Defense Advanced Research Projects Agency or the United States Government. Approved for public release. Distribution unlimited.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stickel, M.E. Schubert's Steamroller problem: Formulations and solutions. J Autom Reasoning 2, 89–101 (1986). https://doi.org/10.1007/BF00246025

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00246025

Keywords

Navigation