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Canonical Constructive Systems

  • Conference paper
Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5607))

Abstract

We define the notions of a canonical inference rule and a canonical constructive system in the framework of strict single-conclusion Gentzen-type systems (or, equivalently, natural deduction systems), and develop a corresponding general non-deterministic Kripke-style semantics. We show that every constructive canonical system induces a class of non-deterministic Kripke-style frames, for which it is strongly sound and complete. This non-deterministic semantics is used to show that such a system always admits a strong form of the cut-elimination theorem, and for providing a decision procedure for such systems.

This research was supported by THE ISRAEL SCIENCE FOUNDATION (grant No 809-06).

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References

  1. Avron, A.: Simple Consequence Relations. Information and Computation 92, 105–139 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  2. Avron, A.: Gentzen-Type Systems, Resolution and Tableaux. Journal of Automated Reasoning 10, 265–281 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  3. Avron, A.: A Nondeterministic View on Nonclassical Negations. Studia Logica 80, 159–194 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Avron, A.: Non-deterministic Semantics for Families of Paraconsistent Logics. In: Beziau, J.-Y., Carnielli, W., Gabbay, D.M. (eds.) Handbook of Paraconsistency. Studies in Logic, vol. 9, pp. 285–320. College Publications (2007)

    Google Scholar 

  5. Avron, A., Lev, I.: Canonical Propositional Gentzen-Type Systems. In: Goré, R., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, pp. 529–544. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  6. Avron, A., Lev, I.: Non-deterministic Multiple-valued Structures. Journal of Logic and Computation 15, 24–261 (2005)

    Article  MathSciNet  Google Scholar 

  7. Belnap, N.D.: Tonk, Plonk and Plink. Analysis 22, 130–134 (1962)

    Article  Google Scholar 

  8. Ciabattoni, A., Terui, K.: Towards a Semantic Characterization of Cut-Elimination. Studia Logica 82, 95–119 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  9. Fernandez, D.: Non-deterministic Semantics for Dynamic Topological Logic. Annals of Pure and Applied Logic 157, 110–121 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  10. Gentzen, G.: Investigations into Logical Deduction. In: Szabo, M.E. (ed.) The Collected Works of Gerhard Gentzen, pp. 68–131. North Holland, Amsterdam (1969)

    Google Scholar 

  11. Gurevich, Y., Neeman, I.: The Logic of Infons, Microsoft Research Tech Report MSR-TR-2009-10 (January 2009)

    Google Scholar 

  12. Kripke, S.: Semantical Analysis of Intuitionistic Logic I. In: Crossly, J., Dummett, M. (eds.) Formal Systems and Recursive Functions, pp. 92–129. North-Holland, Amsterdam (1965)

    Chapter  Google Scholar 

  13. Prior, A.N.: The Runabout Inference Ticket. Analysis 21, 38–39 (1960)

    Article  Google Scholar 

  14. Sundholm, G.: Proof theory and Meaning. In: Gabbay, D.M., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. 9, pp. 165–198 (2002)

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Computer Science, Tel-Aviv University, Israel

    Arnon Avron & Ori Lahav

Authors
  1. Arnon Avron
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  2. Ori Lahav
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Oslo, Blindern, P.O. Box 1080, 0316, Oslo, Norway

    Martin Giese  & Arild Waaler  & 

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Avron, A., Lahav, O. (2009). Canonical Constructive Systems. In: Giese, M., Waaler, A. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2009. Lecture Notes in Computer Science(), vol 5607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02716-1_6

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  • DOI: https://doi.org/10.1007/978-3-642-02716-1_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02715-4

  • Online ISBN: 978-3-642-02716-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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