A Multiple-Conclusion Calculus for First-Order Gödel Logic

  • Arnon Avron
  • Ori Lahav
Conference paper

DOI: 10.1007/978-3-642-20712-9_36

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6651)
Cite this paper as:
Avron A., Lahav O. (2011) A Multiple-Conclusion Calculus for First-Order Gödel Logic. In: Kulikov A., Vereshchagin N. (eds) Computer Science – Theory and Applications. CSR 2011. Lecture Notes in Computer Science, vol 6651. Springer, Berlin, Heidelberg

Abstract

We present a multiple-conclusion hypersequent system for the standard first-order Gödel logic. We provide a constructive, direct, and simple proof of the completeness of the cut-free part of this system, thereby proving both completeness for its standard semantics, and the admissibility of the cut rule in the full system. The results also apply to derivations from assumptions (or “non-logical axioms”), showing that such derivations can be confined to those in which cuts are made only on formulas which occur in the assumptions. Finally, the results about the multiple-conclusion system are used to show that the usual single-conclusion system for the standard first-order Gödel logic also admits (strong) cut-admissibility.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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