Commuting conversions vs. the standard conversions of the “good” connectives

Studia Logica 92 (1):63 - 84 (2009)
Abstract
Commuting conversions were introduced in the natural deduction calculus as ad hoc devices for the purpose of guaranteeing the subformula property in normal proofs. In a well known book, Jean-Yves Girard commented harshly on these conversions, saying that ‘one tends to think that natural deduction should be modified to correct such atrocities.’ We present an embedding of the intuitionistic predicate calculus into a second-order predicative system for which there is no need for commuting conversions. Furthermore, we show that the redex and the conversum of a commuting conversion of the original calculus translate into equivalent derivations by means of a series of bidirectional applications of standard conversions.
Keywords Natural deduction  commuting conversions  predicative quantifiers
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References found in this work BETA
Fernando Ferreira (2006). Comments on Predicative Logic. Journal of Philosophical Logic 35 (1):1 - 8.
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