On Permuting Cut with Contraction

Details On Permuting Cut with Contraction On Permuting Cut with Contraction

1999-11-10

arxiv.org/abs/math/9911065v1

Mathematics

Logic

32 pages, to appear in Mathematical Structures in Computer Science

Scientific paper

The paper presents a cut-elimination procedure for intuitionistic propositional logic in which cut is eliminated directly, without introducing the multiple-cut rule mix, and in which pushing cut above contraction is one of the reduction steps. The presentation of this procedure is preceded by an analysis of Gentzen's mix-elimination procedure, made in the perspective of permuting cut with contraction. It is also shown that in the absence of implication, pushing cut above contraction doesn't pose problems for directly eliminating cut.

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