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Linear logic with isabelle: Pruning the proof search tree

  • Linear Logic
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Theorem Proving with Analytic Tableaux and Related Methods (TABLEAUX 1995)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 918))

Abstract

This paper introduces a general backward proof search strategy for multiplicative additive linear logic. This strategy, which is based on Isabelle's basic tactics and tacticals, has been implemented and appears to be rather efficient. Its efficiency derives from several heuristics that we introduce in the paper. We prove that these heuristics preserve completeness.

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References

  1. P. Bradford, J.-Y. Marion, and L. Moss. The additive fragment of linear logic is nc 1-complete. In D. Leivant, editor, Logic complexity and computation, page 30, October 1994.

    Google Scholar 

  2. G. Perrier D. Galmiche. Automated deduction in additive and multiplicative linear logic. In A. Nerode and M. Taitslin, editors, Proceedings of the Second International Symposium on Logical Foundations of Computer Science — Tver'92, pages 151–162. Lecture Notes in Computer Science, 620, Springer Verlag, 1992.

    Google Scholar 

  3. Jean Gallier. Constructive logic part II: Linear logic and proof nets. Technical Report 9, Digital Equipment Corporation, Paris, 1991.

    Google Scholar 

  4. D. Galmiche and G. Perrier. On proof normalisation in linear logic. Theoretical Computer Science, 1994. to appear in december 1994.

    Google Scholar 

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

    Article  Google Scholar 

  6. J.-Y. Girard. Quantifiers in linear logic II. Technical Report 19, Equipe de Logique Mathématique, Université de Paris VII, 1991.

    Google Scholar 

  7. P. Lincoln, J. Mitchell, A. Scedrov, and N. Shankar. Decision problems for propositional linear logic. Annals of Pure ans Applied Logic, 56:239–311, 1992.

    Article  Google Scholar 

  8. L. C. Paulson. Isabelle, a generic theorem prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, 1994.

    Google Scholar 

  9. L.C. Paulson. Isabelle: The next 700 theorem provers. In P. Odifreddi, editor, Logic and Computer Science, pages 361–386. Academic Press, 1990.

    Google Scholar 

  10. T. Tammet. Proof search strategies in linear logic. Technical Report 70, Department of Computer Science, Chalmers University of Technology, Göteborg, Sweden, 1993.

    Google Scholar 

  11. Anne Troelstra. Lectures on Linear Logic, volume 29 of CSLI Lecture Notes. Center for the Study of Language and Information, 1992.

    Google Scholar 

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Authors and Affiliations

  1. INRIA-Lorraine-CRIN-CNRS, 615 rue du Jardin Botanique, B.P. 101, F 54602, Villers-lès-Nancy Cedex, France

    Philippe de Groote

Authors
  1. Philippe de Groote
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Editor information

Peter Baumgartner Reiner Hähnle Joachim Possega

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© 1995 Springer-Verlag Berlin Heidelberg

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de Groote, P. (1995). Linear logic with isabelle: Pruning the proof search tree. In: Baumgartner, P., Hähnle, R., Possega, J. (eds) Theorem Proving with Analytic Tableaux and Related Methods. TABLEAUX 1995. Lecture Notes in Computer Science, vol 918. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59338-1_41

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  • DOI: https://doi.org/10.1007/3-540-59338-1_41

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59338-6

  • Online ISBN: 978-3-540-49235-1

  • eBook Packages: Springer Book Archive

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