Skip to main content
SpringerLink
Log in

Local simplification

  • Conference paper
  • First Online:
Constraints in Computational Logics (CCL 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 845))

Included in the following conference series:

Abstract

We present a modification to the paramodulation inference system, where semantic equality and non-equality literals are stored as constraints with each clause. The constraints are created when new clauses are generated and inherited by the descendants of that clause. Then the constraints can be used to perform demodulation and unit simplification, if certain conditions are satisfied. This reduces the search space of the theorem proving procedure and the length of the proofs obtained. We show that this process is sound, complete, and compatible with deletion rules (e.g., demodulation, subsumption, unit simplification, and tautology deletion), which do not have to be modified to preserve completeness. We also show the relationship between this technique and model elimination.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. Bachmair and H. Ganzinger. Rewrite-based equational theorem proving with selection and simplification. Journal of Logic and Computation Vol. 4, No. 3 (1994) pp. 1–31.

    Google Scholar 

  2. L. Bachmair, H. Ganzinger, C. Lynch, and W. Snyder. Basic Paramodulation. In Proc. 11th Int. Conf. on Automated Deduction, Lect. Notes in Artificial Intelligence, vol. 607, pp. 462–476, Berlin, 1992. Springer-Verlag. To appear in Journal of Information and Computation.

    Google Scholar 

  3. J. Hsiang and M. Rusinowitch. Proving refutational completeness of theorem proving strategies: The transfinite semantic tree method. Journal of the Association for Computing Machinery 38 (1991) pp. 559–587.

    Google Scholar 

  4. C. Kirchner, H. Kirchner and M. Rusinowitch. Deduction with Symbolic Constraints. Revue Francaise d'Intelligence Artificielle Vol 4, no. 3 (1990) pp. 9–52.

    Google Scholar 

  5. D. Loveland. Mechanical theorem proving by model elimination. Journal of the Association for Computing Machinery 15(2) (1968) pp. 349–363.

    Google Scholar 

  6. D. Loveland. Automated Theorem Proving: A Logical Basis. North-Holland, 1978.

    Google Scholar 

  7. C. Lynch, and W. Snyder. Redundancy Criteria for Constrained Completion. In Proc. 5th Int. Conf. on Rewriting Techniques and Applications, Lect. Notes in Computer Science, vol. 690, pp. 2–16, Berlin, 1992. Springer-Verlag.

    Google Scholar 

  8. R. Nieuwenhuis and A. Rubio. Basic Superposition is Complete. In Proc. European Symposium on Programming, Rennes, France (1992).

    Google Scholar 

  9. R. Nieuwenhuis and A. Rubio. Theorem Proving with Ordering Constrained Clauses. In Proc. 11th Int. Conf. on Automated Deduction, Lect. Notes in Artificial Intelligence, vol. 607, pp. 477–491, Berlin, 1992. Springer-Verlag.

    Google Scholar 

  10. R. Niewenhuis and A. Rubio. AC-superposition with constraints: No AC-unifiers needed. In Proc. 12th Int. Conf. on Automated Deduction, Nancy, France.

    Google Scholar 

  11. G. Peterson. A technique for establishing completeness results in theorem proving with equality. SIAM Journal of Computing 12 (1983) pp. 82–100.

    Google Scholar 

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

    Google Scholar 

  13. M. Rusinowitch and L. Vigneron. Automated deduction with associative-commutative operators. Internal report 1896, INRIA, May 1993.

    Google Scholar 

  14. L. Vigneron. Associative-Commutative Deduction with Constraints. In Proc. 12th Int. Conf. on Automated Deduction, Nancy, France.

    Google Scholar 

  15. L. T. Wos, G. A. Robinson, D. F. Carson, and L. Shalla. The concept of demodulation in theorem proving. Journal of the ACM, Vol. 14, pp. 698–709, 1967.

    Google Scholar 

  16. H. Zhang. Reduction, Superposition, and Induction: Automated Reasoning in an Equational Logic. Ph.D. Thesis, Rensselaer Polytechnic Institute (1988).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Computer Science, Northeastern University, 360 Huntington Avenue #13CN, 02115, Boston, MA

    Christopher Lynch

Authors
  1. Christopher Lynch
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jean-Pierre Jouannaud

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lynch, C. (1994). Local simplification. In: Jouannaud, JP. (eds) Constraints in Computational Logics. CCL 1994. Lecture Notes in Computer Science, vol 845. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0016841

Download citation

  • DOI: https://doi.org/10.1007/BFb0016841

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58403-2

  • Online ISBN: 978-3-540-48699-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation