Skip to main content

A model elimination calculus with built-in theories

  • Technical Papers
  • Conference paper
  • First Online:
GWAI-92: Advances in Artificial Intelligence

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 671))

Abstract

The model elimination calculus is a linear, refulationally complete calculus for first order clause logic. We show how to extend this calculus with a framework for theory reasoning. Theory reasoning means to separate the knowledge of a given domain or theory and treat it by special purpose inference rules. We present two versions of theory model elimination: the one is called total theory model elimination (which allows e.g. to treat equality in a rigid E-resolution style), and the other is called partial theory model elimination (which allows e.g. to treat equality in a paramodulation style).

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.

References

  1. R. Anderson and W. Bledsoe. A linear format for resolution with merging and a new technique for establishing completeness. J. of the ACM, 17:525–534, 1970.

    Article  Google Scholar 

  2. P. Baumgartner. A Model Elimination Calculus with Built-in Theories. Fachbericht Informatik 7/91, Universität Koblenz, 1991.

    Google Scholar 

  3. P. Baumgartner. An Ordered Theory Resolution Calculus. In Proc. LPAR '92, 1992. (To appear).

    Google Scholar 

  4. P. Baumgartner. Completion for Linear Deductions. (in preparation), 1992.

    Google Scholar 

  5. P. Baumgartner and U. Furbach. Consolution as a Framework for Comparing Calculi. (in preparation), 1992.

    Google Scholar 

  6. R. Brachman, V. Gilbert, and H. Levesque. An Essential Hybrid Reasoning System: Knowledge and Symbol Level Accounts of Krypton. In Proc. IJCAI, 1985.

    Google Scholar 

  7. W. Bibel. Automated Theorem Proving. Vieweg, 2nd edition, 1987.

    Google Scholar 

  8. C. Chang and R. Lee. Symbolic Logic and Mechanical Theorem Proving. Academic Press, 1973.

    Google Scholar 

  9. Ulrich Furbach, Steffen Hölldobler, and Joachim Schreiber. Horn equational theories and paramodulation. Journal of Automated Reasoning, 3:309–337, 1989.

    Article  Google Scholar 

  10. M. Fitting. First Order Logic and Automated Theorem Proving. Texts and Monographs in Computer Science. Springer, 1990.

    Google Scholar 

  11. J. Gallier, P. Narendran, D. Plaisted, and W. Snyder. Rigid E-unification: NP-Completeness and Applications to Equational Matings. Information and Computation, pages 129–195, 1990.

    Google Scholar 

  12. D. Loveland. Automated Theorem Proving — A Logical Basis. North Holland, 1978.

    Google Scholar 

  13. D. W. Loveland. Mechanical Theorem Proving by Model Elimination. JACM, 15(2), 1978.

    Google Scholar 

  14. R. Letz, J. Schumann, S. Bayerl, and W. Bibel. SETHEO: A High<-Performace Theorem Prover. Journal of Automated Reasoning, 1992.

    Google Scholar 

  15. N. Murray and E. Rosenthal. Theory Links: Applications to Automated Theorem Proving. J. of Symbolic Computation, 4:173–190, 1987.

    Google Scholar 

  16. Hans Jürgen Ohlbach. The Semantic Clause Graph Procedure — A First Overview. In Proc GWAI '86, pages 218–229. Springer, 1986. Informatik Fachberichte 124.

    Google Scholar 

  17. Hans Jürgen Ohlbach. Link Inheritance in Abstract Clause Graphs. Journal of Automated Reasoning, 3(1):1–34, 1987.

    Article  Google Scholar 

  18. U. Petermann. Towards a connection procedure with built in theories. In JELIA 90. European Workshop on Logic in AI, Springer, LNCS. 1990.

    Google Scholar 

  19. Jörg H. Siekmann. Unification Theory. Journal of Symbolic Computation, 7(1):207–274, January 1989.

    Google Scholar 

  20. M.E. Slickel. Theory Resolution: Building in Nonequational Theories. SRI International Research Report Technical Note 286, Artificial Intelligence Center, 1983.

    Google Scholar 

  21. M. E. Stickel. Automated deduction by theory resolution. Journal of Automated Reasoning, pages 333–356, 1985.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Hans Jürgen Ohlbach

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Baumgartner, P. (1993). A model elimination calculus with built-in theories. In: Jürgen Ohlbach, H. (eds) GWAI-92: Advances in Artificial Intelligence. Lecture Notes in Computer Science, vol 671. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0018990

Download citation

  • DOI: https://doi.org/10.1007/BFb0018990

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56667-0

  • Online ISBN: 978-3-540-47626-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics