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arXiv · 1611.08208

The problem of Pi_2-cut-introduction

Alexander Leitsch·Michael Peter Lettmann
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Abstract

We describe an algorithmic method of proof compression based on the introduction of Pi_2-cuts into a cut-free LK-proof. The current approach is based on an inversion of Gentzen s cut-elimination method and extends former methods for introducing Pi_1-cuts. The Herbrand instances of a cut-free proof pi of a sequent S are described by a grammar G which encodes substitutions defined in the elimination of quantified cuts. We present an algorithm which, given a grammar G, constructs a Pi_2-cut formula A and a proof phi of S with one cut on A. It is shown that, by this algorithm, we can achieve an exponential proof compression.

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Alexander Leitsch, Michael Peter Lettmann. 2018-01-15. The problem of Pi_2-cut-introduction. https://doi.org/10.1016/j.tcs.2017.10.003

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