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Special relations in automated deduction

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Automata, Languages and Programming (ICALP 1985)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 194))

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Abstract

Two deduction rules are introduced to give streamlined treatment to relations of special importance in an automated theorem-proving system. These rules, the relation replacement and relation matching rules, generalize to an arbitrary binary relation the paramodulation and E-resolution rules, respectively, for equality, and may operate within a nonclausal or clausal system. The new rules depend on an extension of the notion of polarity to apply to subterms as well as to subsentences, with respect to a given binary relation. The rules allow us to eliminate troublesome axioms, such as transitivity and monotonicity, from the system; proofs are shorter and more comprehensible, and the search space is correspondingly deflated.

This research was supported in part by the National Science Foundation under grants MCS-82-14523 and MCS-81-05565, by the Defense Advanced Research Projects Agency under contract N00039-84-C-0211, by the United States Air Force Office of Scientific Research under contract AFOSR-81-0014, by the Office of Naval Research under contract N00014-84-C-0706, and by a contract from the International Business Machines Corporation.

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References

  1. R. Anderson, Completeness results for E-resolution, AFIPS Spring Joint Computer Conference, 1970, pp. 652–656.

    Google Scholar 

  2. R. S. Boyer and J S. Moore, A Computational Logic, Academic Press, New York, N.Y., 1979.

    Google Scholar 

  3. D. Brand, Proving theorems with the modification method, SIAM Journal of Computing, Vol. 4, No. 2, 1975, pp. 412–430.

    Article  Google Scholar 

  4. V. Digricoli, Resolution By Unification and Equality, Ph.D. thesis, New York University, New York, N.Y., 1983.

    Google Scholar 

  5. R. Kowalski, Logic for Problem Solving, North Holland, New York, N.Y., 1979.

    Google Scholar 

  6. Z. Manna and R. Waldinger, A deductive approach to program synthesis, ACM Transactions on Programming Languages and Systems, Vol. 2, No. 1, January 1980, pp. 90–121.

    Article  Google Scholar 

  7. Z. Manna and R. Waldinger, Deductive synthesis of the unification algorithm, Science of Computer Programming, Vol. 1, 1981, pp. 5–48.

    Article  Google Scholar 

  8. Z. Manna and R. Waldinger, Special relations in program-synthetic deduction, Technical Report, Computer Science Department, Stanford University, Stanford, Calif., March 1982.

    Google Scholar 

  9. Z. Manna and R. Waldinger, Special relations in automated deduction, Journal of the ACM (to appear).

    Google Scholar 

  10. Z. Manna and R. Waldinger, Origin of the binary search paradigm, in the Proceedings of IJCAI-85, Los Angeles, August 1985.

    Google Scholar 

  11. J. B. Morris, E-resolution: extension of resolution to include the equality relation, International Joint Conference on Artificial Intelligence, Washington, D.C., May 1969, pp. 287–294.

    Google Scholar 

  12. N. V. Murray, Completely nonclausal theorem proving, Artificial Intelligence, Vol. 18, No. 1, 1982, pp. 67–85.

    Article  Google Scholar 

  13. J. A. Robinson, A machine-oriented logic based on the resolution principle, Journal of the ACM, Vol. 12, No. 1, January 1965, pp. 23–41.

    Article  Google Scholar 

  14. J. A. Robinson, Logic: Form and Function, North-Holland, New York, N.Y., 1979.

    Google Scholar 

  15. M. E. Stickel, A nonclausal connection-graph resolution theorem-proving program. National Conference on AI, Pittsburgh, Pa., 1982, pp. 229–233.

    Google Scholar 

  16. J. Traugott, Deductive synthesis of sorting algorithms, Technical Report, Computer Science Department, Stanford University, Stanford, Calif. (forthcoming).

    Google Scholar 

  17. L. Wos and G. Robinson, Paramodulation and theorem proving in first order theories with equality, in Machine Intelligence 4 (B. Meltzer and D. Michie, editors) American Elsevier, New York, N.Y., 1969, pp. 135–150.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Computer Science Department, Stanford University, USA

    Zohar Manna

  2. Artificial Intelligence Center SRI International, USA

    Richard Waldinger

Authors
  1. Zohar Manna
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  2. Richard Waldinger
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Wilfried Brauer

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© 1985 Springer-Verlag Berlin Heidelberg

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Manna, Z., Waldinger, R. (1985). Special relations in automated deduction. In: Brauer, W. (eds) Automata, Languages and Programming. ICALP 1985. Lecture Notes in Computer Science, vol 194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015767

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  • DOI: https://doi.org/10.1007/BFb0015767

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15650-5

  • Online ISBN: 978-3-540-39557-7

  • eBook Packages: Springer Book Archive

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