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Theory links in semantic graphs

  • Neil V. Murray
  • Erik Rosenthal
Graph Based Deduction
Part of the Lecture Notes in Computer Science book series (LNCS, volume 230)

Abstract

Recently, Stickel developed Theory Resolution, a theorem proving technique in which inferences use an existing ‘black box’ to implement a theory. In this paper we examine the black box and expand his results. The analysis of the black box is accomplished with the introduction of a generalization of link which we call theory link. We demonstrate that theorem proving techniques developed for ordinary links are applicable to theory links.

Keywords

Theorem Prove Ground Theory Automate Deduction Theory Resolution Theory Link 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Andrews, P.B. Theorem proving via general matings. JACM 28,2 (April 1981), 193–214.CrossRefGoogle Scholar
  2. 2.
    Bibel, W. On matrices with connections. JACM 28,4 (Oct. 1981), 633–645.CrossRefGoogle Scholar
  3. 3.
    Brachman, R.J., Gilbert, V. Pigman, and Levesque, H.J. An essential hybrid reasoning system: Knowledge and symbol level accounts of KRYPTON. Proceedings of The 9th International Joint Conference on Artificial Intelligence, Los Angeles, CA, August 18–24, 1985, 532–539.Google Scholar
  4. 4.
    Cohn, A.G. On the solution of Schubert's Steamroller in many sorted logic. Proceedings of the 9th International Joint Conference on Artificial Intelligence, Los Angeles, CA, August 1985, 1169–1174.Google Scholar
  5. 5.
    Haas, N. and Hendrix, G.G. An approach to acquiring and applying knowledge. Proceedings of the AAAI-80 National Conference on Artificial Intelligence, Stanford, CA, August 1980, 235–239.Google Scholar
  6. 6.
    Kowalski, R. A proof procedure using connection graphs. J.ACM 22,4 (Oct. 1975), 572–595.CrossRefGoogle Scholar
  7. 7.
    Manna, Z. and Waldinger, R. Special relations in automated deduction. J.ACM 33,1 (Jan. 1986), 1–59.CrossRefGoogle Scholar
  8. 8.
    Murray, N.V., and Rosenthal, E. Path resolution and semantic graphs. Proceedings of EUROCAL '85, Linz Austria, April 1–3, 1985. In Lecture Notes in Computer Science, Springer-Verlag, vol. 204, 50–63.Google Scholar
  9. 9.
    Murray, N.V., and Rosenthal, E. Inference with path resolution and semantic graphs. Submitted, June 1985.Google Scholar
  10. 10.
    Murray, N.V., and Rosenthal, E. On deleting links in semantic graphs. To appear in the proceedings of The Third International Conference on Applied Algebra, Algebraic algorithms, Symbolic Computation and Error Correcting Codes, Grenoble, France, July 15–19, 1985.Google Scholar
  11. 11.
    Murray, N.V., and Rosenthal, E. Improved link deletion and inference: proper path resolution. Submitted, August 1985.Google Scholar
  12. 12.
    Murray, N.V., and Rosenthal, E. Theory links: applications to automated theorem proving. Submitted, March 1986.Google Scholar
  13. 13.
    Nilsson, N.J. A production system for automatic deduction. Technical Note 148, SRI International, 1977.Google Scholar
  14. 14.
    Pigman, V. The interaction between assertional and terminological knowledge in KRYPTON. Proceedings of the IEEE Workshop on Principles of Knowledge-Based Systems, Denver, Colorado, December 1984.Google Scholar
  15. 15.
    Prawitz, D. An improved proof procedure. Theoria 26 (1960), 102–139.Google Scholar
  16. 16.
    Robinson, J.A. A machine oriented logic based on the resolution principle. J.ACM 12,1 (1965), 23–41.CrossRefGoogle Scholar
  17. 17.
    Robinson, J.A. An overview of mechanical theorem proving. Theoretical Approaches to Non-Numerical Problem Solving, Springer-Verlag, New York, Inc., 1970, 2–20.Google Scholar
  18. 18.
    Shostak, R.E. DEciding combinations of theories. Proc. Sixth Conf. on Automated Deduction, New York, New York, June 1982, 209–222.Google Scholar
  19. 19.
    Stickel, M.E. Theory resolution: building in nonequational theories. Proc. of the Nat. Conf. on A.I., Washington, D.C., Aug. 1983.Google Scholar
  20. 20.
    Stickel, M.E. Automated deduction by theory resolution. Technical Note 340, SRI International, Oct. 1984.Google Scholar
  21. 21.
    Stickel, M.E. Automated deduction by theory resolution. Proc. of the 9th International Joint Conf. on Artificial Intelligence, Los Angeles, CA, August 18–24, 1985, 1181–1186.Google Scholar
  22. 22.
    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, August 1984, 330–334.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Neil V. Murray
    • 1
  • Erik Rosenthal
    • 2
  1. 1.Department of Computer ScienceState University of N.Y. at AlbanyAlbany
  2. 2.Department of Computer ScienceWellesley CollegeWellesley

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