Basic Constructive Connectives, Determinism and Matrix-Based Semantics

  • Agata Ciabattoni
  • Ori Lahav
  • Anna Zamansky
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6793)


(Non-)deterministic Kripke-style semantics is used to characterize two syntactic properties of single-conclusion canonical sequent calculi: invertibility of rules and axiom-expansion. An alternative matrix-based formulation of such semantics is introduced, which provides an algorithm for checking these properties, and also new insights into basic constructive connectives.


Atomic Formula Intuitionistic Logic Structural Rule Sequent Calculus Canonical System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Avron, A., Lev, I.: Non-deterministic Multi-valued Structures. Journal of Logic and Computation 15, 241–261 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Avron, A., Ciabattoni, A., Zamansky, A.: Canonical calculi: Invertibility, axiom expansion and (Non)-determinism. In: Frid, A., Morozov, A., Rybalchenko, A., Wagner, K.W. (eds.) CSR 2009. LNCS, vol. 5675, pp. 26–37. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Avron, A., Lahav, O.: On Constructive Connectives and Systems. Logical Methods in Computer Science 6(4:12) (2010)Google Scholar
  4. 4.
    Avron, A., Zamansky, A.: Non-deterministic Semantics for Logical Systems - A Survey. In: Gabbay, D., Guenther, F. (eds.) Handbook of Philosophical Logic. Kluwer, Dordrecht (to appear, 2011)Google Scholar
  5. 5.
    Bowen, K.A.: An extension of the intuitionistic propositional calculus. Indagationes Mathematicae 33, 287–294 (1971)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Ciabattoni, A., Terui, K.: Towards a semantic characterization of cut-elimination. Studia Logica 82(1), 95–119 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Gurevich, Y., Neeman, I.: The logic of Infons. Bulletin of European Association for Theoretical Computer Science 98 (June 2009)Google Scholar
  8. 8.
    Kripke, S.: Semantical analysis of intuitionistic logic I. In: Crossly, J., Dummett, M. (eds.) Formal Systems and Recursive Functions, pp. 92–129 (1965)Google Scholar
  9. 9.
    McCullough, D.P.: Logical connectives for intuitionistic propositional logic. Journal of Symbolic Logic 36(1), 15–20 (1971)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Mints, G.: A Short Introduction to Intuitionistic Logic. Plenum Publishers, New York (2000)zbMATHGoogle Scholar
  11. 11.
    Urquhart, A.: Many-valued Logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. 2, pp. 249–295. Kluwer Academic Publishers, Boston (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Agata Ciabattoni
    • 1
  • Ori Lahav
    • 2
  • Anna Zamansky
    • 1
  1. 1.Vienna University of TechnologyAustria
  2. 2.Tel Aviv UniversityIsrael

Personalised recommendations