2005
DOI: 10.2201/niipi.2005.2.4
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Second order permutative conversions with Prawitz's strong validity

Abstract: Permutative conversions transform a proof with a disjunction or existential quantification elimination rule followed by an elimination rule into a proof with the second rule in the minor deduction of the first rule [14,21]. Permutative conversions are indispensable for normalizing a proof in a natural deduction system with disjunction or existential quantification. Without permutative conversions, a normal proof fails to have the subformula property, because there may exist an introduction rule of a logical sy… Show more

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Cited by 4 publications
(3 citation statements)
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“…Different proofs of strong normalization of several variants of these calculi occur in the literature cf. [1,5,7,9,10]. It is however surprising that it is quite hard to find one covering the full set of connectives, applying to all the permutative conversions (in the polymorphic case none of the cited works does so) and given by a simple and straightforward argument.…”
Section: Introductionmentioning
confidence: 99%
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“…Different proofs of strong normalization of several variants of these calculi occur in the literature cf. [1,5,7,9,10]. It is however surprising that it is quite hard to find one covering the full set of connectives, applying to all the permutative conversions (in the polymorphic case none of the cited works does so) and given by a simple and straightforward argument.…”
Section: Introductionmentioning
confidence: 99%
“…Girard: I didn't find a proof really nice, and taking little space [4, p. 130]. For instance, many proofs, like these in [7,9,10] are based on the computability method, or (in the polymorphic case) candidates of reducibility. This requires re-doing each time the same argument, but in a more complex way, due to the increased complexity of the language.…”
Section: Introductionmentioning
confidence: 99%
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