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Decidability, Introduction Rules and Automata

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Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2015)

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Abstract

We present a method to prove the decidability of provability in several well-known inference systems. This method generalizes both cut-elimination and the construction of an automaton recognizing the provable propositions.

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References

  1. Basin, D., Ganzinger, H.: Automated complexity analysis based on ordered resolution. J. ACM 48(1), 70–109 (2001)

    Article  MathSciNet  Google Scholar 

  2. Bouajjani, A., Esparza, J., Maler, O.: Reachability analysis of pushdown automata: application to model-checking. In: Mazurkiewicz, A.W., Winkowski, J. (eds.) Concurrency Theory. LNCS, vol. 1243, pp. 135–150. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  3. Dowek, G., Jiang, Y.: Cut-elimination and the decidability of reachability in alternating pushdown systems (2014). arXiv:1410.8470 [cs.LO]

  4. Dyckhoff, R.: Contraction-free sequent calculi for intuitionistic logic. J. Symb. Log. 57(3), 795–807 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  5. Dyckhoff, R., Lengrand, S.: LJQ: a strongly focused calculus for intuitionistic logic. In: Beckmann, A., Berger, U., Löwe, B., Tucker, J.V. (eds.) CiE 2006. LNCS, vol. 3988, pp. 173–185. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  6. Dyckhoff, R., Negri, S.: Admissibility of structural rules for contraction-free systems of intuitionistic logic. J. Symb. Log. 65, 1499–1518 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  7. Girard, J.-Y.: Locus solum. Math. Struct. Comput. Sci. 11, 301–506 (2001)

    MATH  MathSciNet  Google Scholar 

  8. Girard, J.-Y., Lafont, Y., Taylor, P.: Proofs and Types. Cambridge University Press, Cambridge (1989)

    MATH  Google Scholar 

  9. Frühwirth, T., Shapiro, E., Vardi, M., Yardeni, E.: Logic programs as types for logic programs. In: Logic in Computer Science, pp. 300–309 (1991)

    Google Scholar 

  10. Goubault-Larrecq, J.: Deciding H\(_1\) by resolution. Inf. Process. Lett. 95(3), 401–408 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  11. Hudelmaier, J.: An \(O(n \log n)\)-space decision procedure for intuitionistic propositional logic. J. Log. Comput. 3, 63–76 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  12. Kleene, S.C.: Introduction to Metamathematics. North-Holland, Amsterdam (1952)

    MATH  Google Scholar 

  13. McAllester, D.A.: Automatic recognition of tractability in inference relations. J. ACM 40(2), 284–303 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  14. Prawitz, D.: Natural Deduction. Almqvist & Wiksell, Stockholm (1965)

    MATH  Google Scholar 

  15. Vorob’ev, N.N.: A new algorithm for derivability in the constructive propositional calculus. Am. Math. Soc. Transl. 2(94), 37–71 (1970)

    Google Scholar 

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Acknowledgements

This work is supported by the ANR-NSFC project LOCALI (NSFC 61161130530 and ANR 11 IS02 002 01) and the Chinese National Basic Research Program (973) Grant No. 2014CB340302.

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Authors and Affiliations

  1. Inria, 23 Avenue d’Italie, CS 81321, 75214, Paris Cedex 13, France

    Gilles Dowek

  2. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China

    Ying Jiang

Authors
  1. Gilles Dowek
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  2. Ying Jiang
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Corresponding author

Correspondence to Gilles Dowek .

Editor information

Editors and Affiliations

  1. New York University, New York, New York, USA

    Martin Davis

  2. University of the South Pacific, Suva, Fiji

    Ansgar Fehnker

  3. Macquarie University, Sydney, New South Wales, Australia

    Annabelle McIver

  4. The University of Manchester, Manchester, United Kingdom

    Andrei Voronkov

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Dowek, G., Jiang, Y. (2015). Decidability, Introduction Rules and Automata. In: Davis, M., Fehnker, A., McIver, A., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2015. Lecture Notes in Computer Science(), vol 9450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48899-7_8

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  • DOI: https://doi.org/10.1007/978-3-662-48899-7_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48898-0

  • Online ISBN: 978-3-662-48899-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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