Permutability of Proofs in Intuitionistic Sequent Calculi

Roy Dyckhoff, L Pinto

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


We prove a folklore theorem, that two derivations in a cut-free sequent calculus for intuitionistic propositional logic (based on Kleene's G3) are inter-permutable (using a set of basic "permutation reduction rules" derived from Kleene's work in 1952) iff they determine the same natural deduction. The basic rules form a confluent and weakly normalising rewriting system. We refer to Schwichtenberg's proof elsewhere that a modification of this system is strongly normalising. (C) 1999-Elsevier Science B.V. All rights reserved.

Original languageEnglish
Pages (from-to)141-155
Number of pages15
JournalTheoretical Computer Science
Issue number1-2
Publication statusPublished - 6 Feb 1999


  • intuitionistic logic
  • proof theory
  • natural deduction
  • sequent calculus


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