Dag Prawitz on Proofs and Meaning pp 163-187

Part of the Outstanding Contributions to Logic book series (OCTR, volume 7) | Cite as

Cut Elimination, Substitution and Normalisation

Chapter

Abstract

We present a proof (of the main parts of which there is a formal version, checked with the Isabelle proof assistant) that, for a G3-style calculus covering all of intuitionistic zero-order logic, with an associated term calculus, and with a particular strongly normalising and confluent system of cut-reduction rules, every reduction step has, as its natural deduction translation, a sequence of zero or more reduction steps (detour reductions, permutation reductions or simplifications). This complements and (we believe) clarifies earlier work by (e.g.) Zucker and Pottinger on a question raised in 1971 by Kreisel.

Keywords

Intuitionistic logic Minimal logic Sequent calculus Natural deduction Cut-elimination Substitution Normalisation 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.School of Computer ScienceSt Andrews UniversityScotlandUK

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