Skip to main content

A procedure for automatic proof nets construction

  • Session 2: Non-Resolution Theorem Proving I
  • Conference paper
  • First Online:
Logic Programming and Automated Reasoning (LPAR 1992)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 624))

  • 135 Accesses

  • 9 Citations

Abstract

In this paper, we consider the multiplicative fragment of linear logic (MLL) from an automated deduction point of view. Before to use this new logic to make logic programming or to program with proofs, a better comprehension of the proof construction process in this framework is necessary. We propose a new algorithm to construct automatically a proof net for a given sequent in MLL and its proofs of termination, correctness and completeness. It can be seen as an implementation oriented way to consider automated deduction in linear logic.

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. S. Abramsky. Computational interpretations of linear logic. technical report, Department of Computing, Imperial College, London SW7 2Bz, England, 1991.

    Google Scholar 

  2. J.M. Andreoli and R. Pareschi. Logic programming with sequent systems: A linear logic approach. In Int. Workshop on Extensions of Logic Programming, LNCS 475, pages 1–30, Tübingen, Germany, December 1989.

    Google Scholar 

  3. P. Andrews. Theorem proving via general mating. Journal of ACM, 28(2):193–214, 1981.

    Article  Google Scholar 

  4. G. Bellin. Proof nets for multiplicative and additive linear logic. Technical Report ECS-LFCS 91-161, Department of Computer Science, Edinburgh University, May 1991.

    Google Scholar 

  5. W. Bibel. On matrices with connections. Journal of ACM, 28(4):633–645, 1981.

    Article  Google Scholar 

  6. V. Danos and L. Regnier. The structure of multiplicatives. Archive for Mathematical Logic, 28:181–203, 1989.

    Article  Google Scholar 

  7. D. Galmiche. Constructive system for automatic program synthesis. Theoretical Computer Science, 71(2):227–239, 1990.

    Article  Google Scholar 

  8. D. Galmiche and G. Perrier. Automated deduction in additive and multiplicative linear logic. In Logic at Tver '92, Logical Foundations of Computer Science Symposium, Tver, Russia, July 1992.

    Google Scholar 

  9. J.-Y. Girard. Linear logic. Theoretical Computer Science, 50(1):1–102, 1987.

    Article  Google Scholar 

  10. J.-Y. Girard. Towards a geometry of interaction. In J.-W. Gray and A. Scedrov, editors, AMS Conference on categories in computer science and logic, pages 69–108, Boulder-Colorado, June 1987.

    Google Scholar 

  11. J.-Y. Girard, P. Taylor, and Y. Lafont. Proofs and Types. Cambridge University Press, 1989.

    Google Scholar 

  12. J. S. Hodas and D. Miller. Logic programming in a fragment of intuitionistic linear logic. In 6th IEEE symposium Logic in Computer Science, pages 32–42, Amsterdam, July 1991.

    Google Scholar 

  13. P. Lincoln, J. Mitchell, A. Scedrov, and N. Shankar. Decision problems for prepositional linear logic. In 31st annual IEEE Symp. on Foundations of Computer Science, St-Louis, Missouri, October 1990.

    Google Scholar 

  14. M. Masseron, C. Tollu, and J. Vauzeilles. Generating plans in linear logic. In Foundations of Software Technology and Theoretical Computer Science, LNCS 472, pages 63–75, Bangalore, India, December 1990.

    Google Scholar 

  15. U. Solitro. A typed calculus based on a fragment of linear logic. Theoretical Computer Science, 68:333–342, 1989.

    Article  Google Scholar 

  16. A.-S. Troelstra and D. Van Dalen. Constructivism in Mathematics, an Introduction. North-Holland, Amsterdam, 1988.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Andrei Voronkov

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Galmiche, D., Perrier, G. (1992). A procedure for automatic proof nets construction. In: Voronkov, A. (eds) Logic Programming and Automated Reasoning. LPAR 1992. Lecture Notes in Computer Science, vol 624. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013047

Download citation

  • DOI: https://doi.org/10.1007/BFb0013047

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55727-2

  • Online ISBN: 978-3-540-47279-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics