Canonical Constructive Systems

  • Arnon Avron
  • Ori Lahav
Conference paper

DOI: 10.1007/978-3-642-02716-1_6

Volume 5607 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
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

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

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