Kripke Semantics for Basic Sequent Systems

  • Arnon Avron
  • Ori Lahav
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6793)


We present a general method for providing Kripke semantics for the family of fully-structural multiple-conclusion propositional sequent systems. In particular, many well-known Kripke semantics for a variety of logics are easily obtained as special cases. This semantics is then used to obtain semantic characterizations of analytic sequent systems of this type, as well as of those admitting cut-admissibility. These characterizations serve as a uniform basis for semantic proofs of analyticity and cut-admissibility in such systems.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Avron, A.: On Modal Systems having arithmetical interpretations. Journal of Symbolic Logic 49, 935–942 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Avron, A.: Gentzen-Type Systems, Resolution and Tableaux. Journal of Automated Reasoning 10, 265–281 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Avron, A.: Classical Gentzen-type Methods in Propositional Many-Valued Logics. In: Fitting, M., Orlowska, E. (eds.) Beyond Two: Theory and Applications of Multiple-Valued Logic, Studies in Fuzziness and Soft Computing, vol. 114, pp. 117–155. Physica Verlag, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Avron, A.: A Non-Deterministic View on Non-Classical Negations. Studia Logica 80, 159–194 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Avron, A., Lahav, O.: On Constructive Connectives and Systems. Journal of Logical Methods in Computer Science 6 (2010)Google Scholar
  6. 6.
    Avron, A., Lev, I.: Non-deterministic Multiple-valued Structures. IJCAR 2001 15 (2005); Avron, A., Lev, I.: Canonical Propositional Gentzen-Type Systems. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, p. 529. Springer, Heidelberg (2001) Google Scholar
  7. 7.
    Ciabattoni, A., Terui, K.: Towards a Semantic Characterization of Cut-Elimination. Studia Logica 82, 95–119 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Crolard, T.: Subtractive Logic. Theoretical Computer Science 254, 151–185 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Goré, R., Postniece, L.: Combining Derivations and Refutations for Cut-free Completeness in Bi-intuitionistic Logic. Journal of Logic and Computation 20(1), 233–260 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Gurevich, Y., Neeman, I.: The Infon Logic: the Propositional Case. To appear in ACM Transactions on Computation Logic 12 (2011)Google Scholar
  11. 11.
    Ono, H.: On some intuitionistic modal logic, pp. 687–722. Publications of Research Institute for Mathematical Sciences, Kyoto University (1977)zbMATHGoogle Scholar
  12. 12.
    Pinto, L., Uustalu, T.: Proof Search and Counter-Model Construction for Bi-intuitionistic Propositional Logic with Labelled Sequents. In: Giese, M., Waaler, A. (eds.) TABLEAUX 2009. LNCS, vol. 5607, pp. 295–309. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  13. 13.
    Sambin, G., Valentini, S.: The modal logic of provability. The sequential approach. Journal of Philosophical Logic 11, 311–342 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Takeuti, G.: Proof Theory. North-Holland, Amsterdam (1975)zbMATHGoogle Scholar
  15. 15.
    Troelstra, A.S., Schwichtenberg, H.: Basic Proof Theory. Cambridge University Press, Cambridge (1996)zbMATHGoogle Scholar
  16. 16.
    Rineke, V.: Provability Logic. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (2010), (revision November 2010)
  17. 17.
    Wansing, H.: Sequent Systems for Modal Logics. In: Gabbay, D.M., Guenthner, F. (eds.) Handbook of Philosophical Logic, 2nd edn. vol. 8, pp. 61–145 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Arnon Avron
    • 1
  • Ori Lahav
    • 1
  1. 1.School of Computer ScienceTel Aviv UniversityIsrael

Personalised recommendations