[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to main content

Proof normalization for resolution and paramodulation

  • Regular Papers
  • Conference paper
  • First Online:
Rewriting Techniques and Applications (RTA 1989)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 355))

Included in the following conference series:

Abstract

We prove the refutation completeness of restricted versions of resolution and paramodulation for first-order predicate logic with equality. Furthermore, we show that these inference rules can be combined with various deletion and simplification rules, such as rewriting, without compromising refutation completeness. The techniques employed in the completeness proofs are based on proof normalization and proof orderings.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Bachmair, L. 1987. Proof methods for equational theories. Ph.D. diss., University of Illinois, Urbana-Champaign.

    Google Scholar 

  2. Bachmair, L., Dershowitz, N., and Hsiang, J. 1986. Orderings for equational proofs. In Proc. Symp. Logic in Computer Science, Boston, Massachusetts, 346–357.

    Google Scholar 

  3. Brand, D. 1975. Proving theorems with the modification method. SIAM J. Comput.4:412–430.

    Google Scholar 

  4. Brown, T. 1975. A structured design-method for specialized proof procedures. Ph.D. diss., California Institute of Technology, Pasadena.

    Google Scholar 

  5. Chang, C., and Lee, R. C. 1973. Symbolic logic and mechanical theorem proving. New York, Academic Press.

    Google Scholar 

  6. Dershowitz, N. 1982. Orderings for term-rewriting systems. Theor. Comput. Sci.17:279–301.

    Google Scholar 

  7. Dershowitz, N. 1987. Termination of rewriting. J. Symbolic Computation3:69–116.

    Google Scholar 

  8. Dershowitz, N., and Manna, Z. 1979. Proving termination with multiset orderings. Commun. ACM22:465–476.

    Google Scholar 

  9. Ganzinger, H. 1988. A completion procedure for conditional equations. To appear in J. Symbolic Computation.

    Google Scholar 

  10. Hsiang, J., and Rusinowitch, M. 1986. A new method for establishing refutational completeness in theorem proving. In Proc. 8th Int. Conf. on Automated Deduction, ed. J. H. Siekmann, Lect. Notes in Comput. Sci., vol. 230, Berlin, Springer-Verlag, 141–152.

    Google Scholar 

  11. Hsiang, J., and Rusinowitch, M. 1988. Proving refutational completeness of theorem proving strategies, Part I: The transfinite semantic tree method. Submitted for publication.

    Google Scholar 

  12. Joyner, W. 1976. Resolution strategies as decision procedures. J. ACM23:398–417.

    Google Scholar 

  13. Knuth, D., and Bendix, P. 1970. simple word problems in universal algebras. In Computational Problems in Abstract Algebra, ed. J. Leech, Oxford, Pergamon Press, 263–297.

    Google Scholar 

  14. Lankford, D. 1975. Canonical inference. Tech. Rep. ATP-32, Dept. of Mathematics and Computer Science, University of Texas, Austin.

    Google Scholar 

  15. Peterson, G. 1983. A technique for establishing completeness results in theorem proving with equality. SIAM J. Comput.12:82–100.

    Google Scholar 

  16. Robinson, G., and Wos, L. T. 1969. Paramodulation and theorem proving in first order theories with equality. In Machine Intelligence 4, ed. B. Meltzer and D. Michie, New York, American Elsevier, 133–150.

    Google Scholar 

  17. Robinson, J. A. 1965. A machine-oriented logic based on the resolution principle. J. ACM12:23–41.

    Google Scholar 

  18. Rusinowitch, M. 1988. Theorem proving with resolution and superposition: An extension of the Knuth and Bendix procedure as a complete set of inference rules.

    Google Scholar 

  19. Slagle, J. R. 1974. Automated theorem proving for theories with simplifiers, commutativity, and associativity. J. ACM21:622–642.

    Google Scholar 

  20. Wos, L. T., and Robinson, G. 1973. Maximal models and refutation completeness: Semidecision procedures in automatic theorem proving. In Word Problems, ed. W.W. Boone et al., Amsterdam, North-Holland, 609–639.

    Google Scholar 

  21. Wos, L. T., Robinson, G. A., Carson, D. F., and Shalla, L. 1967. The concept of demodulation in theorem proving. J. ACM14:698–709.

    Google Scholar 

  22. Zhang, H., and Kapur, D. 1988. First-order theorem proving using conditional rewrite rules. In Proc. 9th Conf. Automated Deduction, Let. Notes in Comput. Sci. Berlin, Springer-Verlag, 1–20.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Nachum Dershowitz

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bachmair, L. (1989). Proof normalization for resolution and paramodulation. In: Dershowitz, N. (eds) Rewriting Techniques and Applications. RTA 1989. Lecture Notes in Computer Science, vol 355. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51081-8_97

Download citation

  • DOI: https://doi.org/10.1007/3-540-51081-8_97

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51081-9

  • Online ISBN: 978-3-540-46149-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics