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A complete semantic back chaining proof system

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10th International Conference on Automated Deduction (CADE 1990)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 449))

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Abstract

We discuss a sequent style clause-based proof system that supports several important strategies in automatic theorem proving. The system has a goal-subgoal structure and supports back chaining with caching; it permits semantic deletion, sometimes using multiple models; it is also a genuine set of support strategy; and it is complete for first order logic in clause form.

This work was supported in part by the National Science Foundation under grant DCR-8516243.

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References

  1. Ballantyne, A. and W.W. Bledsoe, "On Generating and Using Examples in Proof Discovery", Machine Intelligence, V 10, pp. 3–39, Harwood, Chichester 1982.

    Google Scholar 

  2. Bibel, W., "Automated Theorem Proving", Friedr. Vieweg & Sohn Verlagsgesellschaft MbH, Braunschweig 1982.

    Google Scholar 

  3. Bledsoe, W.W., "Using Examples to Generate Instantiations for Set Variables", Technical Report No. ATP-67, Department of Computer Science, University of Texas at Austin, July 1982.

    Google Scholar 

  4. Boyer, R., "Locking: A Restriction of Resolution", Ph.D. dissertation, University of Texas at Austin, Austin, TX, 1970.

    Google Scholar 

  5. Gelernter, H., "Realization of a Geometry Theorem-Proving Machine", Proc. ICIP, pp. 273–282, Paris UNESCO House, 1959.

    Google Scholar 

  6. Loveland, D.W., "A Simplified Format for the Model Elimination Theorem-Proving Procedure", J. ACM, Vol. 16, No. 3, pp. 349–363, July 1969.

    Google Scholar 

  7. Luckham, D., "Refinement Theorems in Resolution Theory", Proc. IRIA Symp. Automatic Demonstration, Versailles, France, 1968, Springer-Verlag, New York, pp. 163–190, 1970.

    Google Scholar 

  8. Plaisted, D.A., "Non-Horn Clause Logic Programming Without Contrapositives", Journal of Automated Reasoning, Vol. 4, Nov. 3, September 1988.

    Google Scholar 

  9. Reiter, R., "A Semantically Guided Deductive System for Automatic Theorem Proving", IEEE Transaction on Computers, Vol. C-25, No. 4, pp. 328–334, April 1976.

    Google Scholar 

  10. Robinson, J.A., "A Machine-oriented Logic Based on the Resolution Principles", JACM 12, pp. 23–41, 1965.

    Google Scholar 

  11. Sandford, D.M., "Using Sophisticated Models in Resolution Theorem Proving", Lecture Notes in Computer Science, No. 90, G. Goos and J. Hartmanis eds, Springer-Verlag, 1980.

    Google Scholar 

  12. Slagle, J.R., "Automatic Theorem Proving with Renamable and Semantics Resolution", JACM, Vol. 14, No. 4, pp. 687–697, October 1967.

    Google Scholar 

  13. Stickel, M.E., "A PROLOG Technology Theorem Prover", Journal of Automated Reasoning, Vol. 4, No. 4, pp. 353–380, 1988.

    Google Scholar 

  14. Walther, C., "A Mechanical Solution of Schubert's Steamroller by Manysorted Resolution", Proc. 8th AAAI, pp. 330–334, 1984.

    Google Scholar 

  15. Wang, T.C., "Designing Examples for Semantically Guided Hierarchical Deduction", Proc. of IJCAI, pp. 1201–1207, 1985.

    Google Scholar 

  16. Wang, T.C. and W.W. Bledsoe, "Hierarchical Deduction", Journal of Automated Reasoning, Vol. 3, No. 1, 1987.

    Google Scholar 

  17. Wos, L.T., G.A. Robinson and D.F. Carson, "Efficiency and Completeness of the Set of Support Strategy in Theorem Proving", J. of ACM, Vol. 12, No. 4, October 1965.

    Google Scholar 

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Mark E. Stickel

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© 1990 Springer-Verlag Berlin Heidelberg

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Nie, X., Plaisted, D.A. (1990). A complete semantic back chaining proof system. In: Stickel, M.E. (eds) 10th International Conference on Automated Deduction. CADE 1990. Lecture Notes in Computer Science, vol 449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52885-7_76

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  • DOI: https://doi.org/10.1007/3-540-52885-7_76

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52885-2

  • Online ISBN: 978-3-540-47171-4

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