Skip to main content
Log in

A sequent-style model elimination strategy and a positive refinement

  • Published:
Journal of Automated Reasoning Aims and scope Submit manuscript

Abstract

We present a sequent style proof system related to the MESON procedure, which is itself based on the model elimination strategy for mechanical theorem proving. The MESON procedure is attractive because it is a problem reduction format, that is, it has a goal-subgoal structure. The sequent style system based on it shares this advantage, and also has a simple declarative semantics and soundness proof. A refinement of the sequent style system tends to produce shorter sequents and may facilitate the use of the MESON procedure with caching of solutions to subgoals to avoid repeated work on the same subgoal. In the MESON procedure, a goal is marked ‘contradicted’ and considered to be solved, if an ancestor goal is complementary to it. In the positive refinement, only the positive goals need to be checked for contradiction in this way. This means that if a list of ancestor goals is kept with each goal, it is only necessary to store the negative ancestor goals, since these are the only ones that need to be examined in testing if a positive goal is contradicted. Similar restrictions on the reduction operation of model elimination are possible.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Chang C. and Lee R., Symbolic Logic and Mechanical Theorem Proving, Academic Press, New York, 1973.

    Google Scholar 

  2. Clocksin W. F. and Mellish C. S., Programming in Prolog, Springer-Verlag, New York, 1981.

    Google Scholar 

  3. Gallier J., Logic for Computer Science: Foundations of Automatic Theorem Proving, Harper and Row, Philadelphia, 1986.

    Google Scholar 

  4. Loveland D. W., ‘A simplified format for the model elimination procedure’, JACM 16 (1969) 349–363.

    Google Scholar 

  5. Loveland D., Automated Theorem Proving: A Logical Basis, North-Holland, New York, 1978.

    Google Scholar 

  6. Loveland, D. W., ‘Near-Horn prolog’, Proceedings of the Fourth International Conference on Logic Programming, Melbourne, Australia, 1987, pp. 456–469.

  7. Plaisted, D., Theorem Proving and Semantic Trees, Ph.D. thesis, Stanford University, 1976.

  8. Plaisted D., ‘A simplified problem reduction format’, Artificial Intelligence 18 (1982) 227–261.

    Google Scholar 

  9. Plaisted D., ‘Non-Horn clause logic programming without contrapositives’, J. Automated Reasoning 4 (1988) 287–325.

    Google Scholar 

  10. Stickel M. E., ‘A PROLOG technology theorem prover: implementation by an extended PROLOG compiler’, J. Automated Reasoning 4 (1988) 353–380.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

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

Rights and permissions

Reprints and permissions

About this article

Cite this article

Plaisted, D.A. A sequent-style model elimination strategy and a positive refinement. J Autom Reasoning 6, 389–402 (1990). https://doi.org/10.1007/BF00244355

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00244355

Key words

Navigation