Effective Finite-Valued Semantics for Labelled Calculi

  • Matthias Baaz
  • Ori Lahav
  • Anna Zamansky
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7364)

Abstract

We provide a systematic and modular method to define non-deterministic finite-valued semantics for a natural and very general family of canonical labelled calculi, of which many previously studied sequent and labelled calculi are particular instances. This semantics is effective, in the sense that it naturally leads to a decision procedure for these calculi. It is then applied to provide simple decidable semantic criteria for crucial syntactic properties of these calculi, namely (strong) analyticity and cut-admissibility.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A.A.: Multi-valued Semantics: Why and How. Studia Logica 92, 163–182 (2009)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Avron, A., Lev, I.: Non-deterministic Multiple-valued Structures. Journal of Logic and Computation 15 (2005)Google Scholar
  3. 3.
    Avron, A., Zamansky, A.: Non-deterministic Semantics for Logical Systems. Handbook of Philosophical Logic 16, 227–304 (2011)CrossRefGoogle Scholar
  4. 4.
    Avron, A., Zamansky, A.: Canonical Signed Calculi, Non-deterministic Matrices and Cut-Elimination. In: Artemov, S., Nerode, A. (eds.) LFCS 2009. LNCS, vol. 5407, pp. 31–45. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  5. 5.
    Avron, A., Konikowska, B., Zamansky, A.: Modular Construction of Cut-Free Sequent Calculi for Paraconsistent Logics. To Appear in Proceedings of Logic in Computer Science (LICS 2012) (2012)Google Scholar
  6. 6.
    Baaz, M., Fermüller, C.G., Salzer, G., Zach, R.: Labelled Calculi and Finite-valued Logics. Studia Logica 61, 7–33 (1998)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Ciabattoni, A., Terui, K.: Towards a semantic characterization of cut elimination. Studia Logica 82(1), 95–119 (2006)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Gabbay, D.M.: Labelled Deductive Systems, Volume 1. Oxford Logic Guides, vol. 33. Clarendon Press/Oxford Science Publications, Oxford (1996)Google Scholar
  9. 9.
    Lahav, O.: Non-deterministic Matrices for Semi-canonical Deduction Systems. To Appear in Proceedings of IEEE 42nd International Symposium on Multiple-Valued Logic (ISMVL 2012) (2012)Google Scholar
  10. 10.
    Sano, K.: Sound and Complete Tree-Sequent Calculus for Inquisitive Logic. In: Ono, H., Kanazawa, M., de Queiroz, R. (eds.) WoLLIC 2009. LNCS, vol. 5514, pp. 365–378. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  11. 11.
    Stachniak, Z.: Resolution Proof Systems: An Algebraic Theory. Kluwer Academic Publishers (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Matthias Baaz
    • 1
  • Ori Lahav
    • 2
  • Anna Zamansky
    • 1
  1. 1.Vienna University of TechnologyAustria
  2. 2.Tel Aviv UniversityIsrael

Personalised recommendations