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LINK: A Proof Environment Based on Proof Nets

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Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2381))

Abstract

LINK is a proof environment including proof nets-based provers for multiplicative linear logics: mixed linear logic, or recently called non-commutative logic (MNL) [1], commutative linear logic (MLL) and non-commutative (or cyclic) linear logic (MCyLL). Its main characteristic is the provability analysis through automatic proof nets construction. A proof net is a particular graph-theoretic representation of proofs that appears appropriate for proof-search in MLL and MCyLL [4,5]. It is a powerful alternative to deal with proof search and its problems about non-permutability and resource management [3]. In the context of system verification, such a semantical and graphical representation of proof can be useful from a software engineering point of view. It allows to analyse provability (through proof nets) or non-provability (through proof structures that can be seen as counter-models).

École Normale Supérieure Ulm, Paris, France, in a training period at LORIA.

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References

  1. M. Abrusci and P. Ruet. Non-commutative logic I: the multiplicative fragment. Annals of Pure and Applied Logic, 101:29–64, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  2. J.M. Andreoli and R. Maieli. Focusing and proof-nets in linear and non-commutative logic. In Int. Conf. on Logic for Programming and Automated Reasoning, LPAR’99, LNCS 1705, pages 320–333, Tbilisi, Georgia, September 1999.

    Chapter  Google Scholar 

  3. I. Cervesato, J. Hodas, and F. Pfenning. Efficient resource management for linear logic proof search. Theoretical Computer Science, 232(1–2):133–163, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  4. D. Galmiche. Connection Methods in Linear Logic and Proof nets Construction. Theoretical Computer Science, 232(1–2):231–272, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  5. D. Galmiche and B. Martin. Proof nets construction and automated deduction in non-commutative linear logic-extended abstract. Electronic Notes in Theoretical Computer Science, 17, 1998.

    Google Scholar 

  6. D. Galmiche and J.M. Notin. Proof-search and proof nets in mixed linear logic. Electronic Notes in Theoretical Computer Science, 37, 2000.

    Google Scholar 

  7. D. Galmiche and J.M. Notin. Calculi with dependency relations for mixed linear logic. In International Workshop on Logic and Complexity in Computer Science, LCCS’2001, pages 81–102, Créteil, France, 2001.

    Google Scholar 

  8. D. Galmiche and G. Perrier. A procedure for automatic proof nets construction. In LPAR’92, International Conference on Logic Programming and Automated Reasoning, LNAI 624, pages 42–53, St. Petersburg, Russia, July 1992.

    Google Scholar 

  9. D. Gray, G. Hamilton, J. Power, and D. Sinclair. Specifying and verifying TCP/IP using Mixed Intuitionistic Linear Logic. Technical report, Dublin City Univ., 2001.

    Google Scholar 

  10. C. Kreitz, H. Mantel, J. Otten, and S. Schmitt. Connection-based proof construction in linear logic. In 14th Int. Conference on Automated Deduction, pages 207–221, Townsville, North Queensland, Australia, 1997.

    Google Scholar 

  11. V. Mogbil. Quadratic correctness criterion for non commutative logic. In 15th Int. Workshop on Computer Science Logic, CSL 2001, LNCS 2142, pages 69–83, Paris, France, 2001.

    Google Scholar 

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© 2002 Springer-Verlag Berlin Heidelberg

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Habert, L., Notin, JM., Galmiche, D. (2002). LINK: A Proof Environment Based on Proof Nets. In: Egly, U., Fermüller, C.G. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2002. Lecture Notes in Computer Science(), vol 2381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45616-3_23

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  • DOI: https://doi.org/10.1007/3-540-45616-3_23

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  • Print ISBN: 978-3-540-43929-5

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