Modular Cut-Elimination: Finding Proofs or Counterexamples

  • Agata Ciabattoni
  • Kazushige Terui
Conference paper

DOI: 10.1007/11916277_10

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4246)
Cite this paper as:
Ciabattoni A., Terui K. (2006) Modular Cut-Elimination: Finding Proofs or Counterexamples. In: Hermann M., Voronkov A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2006. Lecture Notes in Computer Science, vol 4246. Springer, Berlin, Heidelberg

Abstract

Modular cut-elimination is a particular notion of ”cut-elimination in the presence of non-logical axioms” that is preserved under the addition of suitable rules. We introduce syntactic necessary and sufficient conditions for modular cut-elimination for standard calculi, a wide class of (possibly) multiple-conclusion sequent calculi with generalized quantifiers. We provide a ”universal” modular cut-elimination procedure that works uniformly for any standard calculus satisfying our conditions. The failure of these conditions generates counterexamples for modular cut-elimination and, in certain cases, for cut-elimination.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Agata Ciabattoni
    • 1
  • Kazushige Terui
    • 2
  1. 1.Institute für Diskrete Mathematik und GeometrieTU Wien 
  2. 2.National Institute of InformaticsTokyoJapan

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