Nothing Special   »   [go: up one dir, main page]

Skip to main content

Guiding program development systems by a connection based proof strategy

  • Conference paper
  • First Online:
Logic Program Synthesis and Transformation (LOPSTR 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1048))

Abstract

We present an automated proof method for constructive logic based on Wallen's matrix characterization for intuitionistic validity. The proof search strategy extends Bibel's connection method for classical predicate logic. It generates a matrix proof which will then be transformed into a proof within a standard sequent calculus. Thus we can use an efficient proof method to guide the development of constructive proofs in interactive proof/program development systems.

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. E. W. Beth. The foundations of mathematics. North-Holland, 1959.

    Google Scholar 

  2. W. Bibel, S. Brüning, U. Egly, T. Rath. Komet. In Proceedings of the 12th CADE, LNAI 814, pp. 783–787. Springer Verlag, 1994.

    Google Scholar 

  3. W. Bibel. On matrices with connections. Jour, of the ACM, 28, p. 633–645, 1981.

    Google Scholar 

  4. W. Bibel. Automated Theorem Proving. Vieweg Verlag, 1987.

    Google Scholar 

  5. A. Bundy, F. van Harmelen, C. Horn, A. Smaill. The Oyster-Clam system. In Proceedings of the 10th CADE, LNCS 449, pp. 647–648. Springer Verlag, 1990.

    Google Scholar 

  6. R. L. Constable et. al. Implementing Mathematics with the NuPRL proof development system. Prentice Hall, 1986.

    Google Scholar 

  7. M. C. Fitting. Intuitionistic logic, model theory and forcing. North-Holland, 1969.

    Google Scholar 

  8. G. Gentzen. Untersuchungen über das logische Schließen. Mathematische Zeitschrift, 39:176–210, 405–431, 1935.

    Google Scholar 

  9. R. Letz, J. Schumann, S. Bayerl, W. Bibel Setheo: A high-performance theorem prover. Journal of Automated Reasoning, 8:183–212, 1992.

    Google Scholar 

  10. H. J. Ohlbach. A resolution calculus for modal logics. Ph.D. Thesis (SEKI Report SR-88-08), Universität Kaiserslautern, 1988.

    Google Scholar 

  11. J. Otten, C. Kreitz A connection based proof method for intuitionistic logic. In Proceedings of the 4th Workshop on Theorem Proving with Analytic Tableaux and Related Methods, LNAI 918, pp. 122–137, Springer Verlag, 1995.

    Google Scholar 

  12. J. Otten, C. Kreitz T-String-Unification: Unifying Prefixes in Non-Classical Proof Methods. Report AIDA-95-09, FG Intellektik, TH Darmstadt, 1995.

    Google Scholar 

  13. J. Otten. Ein konnektionenorientiertes Beweisverfahren für intuitionistische Logik. Master's thesis, TH Darmstadt, 1995.

    Google Scholar 

  14. L. Paulson. Isabelle: The next 700 theorem provers. In Piergiorgio Odifreddi, editor, Logic and Computer Science, pp. 361–386. Academic Press, 1990.

    Google Scholar 

  15. R. Pollack. The theory of LEGO — a proof checker for the extendend calculus of constructions. PhD thesis, University of Edinburgh, 1994.

    Google Scholar 

  16. S. Schmitt, C. Kreitz. On transforming intuitionistic matrix proofs into standardsequent proofs. In Proceedings of the 4th Workshop on Theorem Proving with Analytic Tableaux and Related Methods, LNAI 918, pp. 106–121, Springer, 1995.

    Google Scholar 

  17. S. Schmitt. Ein erweiterter intuitionistischer Sequenzenkalkül und dessen Anwendung im intuitionistischen Konnektionsbeweisen. Master's thesis, TH Darmstadt, 1994.

    Google Scholar 

  18. G. Takeuti. Proof Theory. North-Holland, 1975.

    Google Scholar 

  19. L. Wallen. Automated deduction in nonclassical logic. MIT Press, 1990.

    Google Scholar 

  20. L. Wos et. al. Automated reasoning contributes to mathematics and logic. In Proceedings of the 10th CADE, LNCS 449, p. 485–499. Springer Verlag 1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Maurizio Proietti

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kreitz, C., Otten, J., Schmitt, S. (1996). Guiding program development systems by a connection based proof strategy. In: Proietti, M. (eds) Logic Program Synthesis and Transformation. LOPSTR 1995. Lecture Notes in Computer Science, vol 1048. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60939-3_10

Download citation

  • DOI: https://doi.org/10.1007/3-540-60939-3_10

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60939-1

  • Online ISBN: 978-3-540-49745-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics