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Cut Elimination In Situ

In: Gentzen's Centenary

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  • Sam Buss

    (University of California, San Diego, Department of Mathematics)

Abstract

We present methods for removing top-level cuts from a sequent calculus or Tait-style proof without significantly increasing the space used for storing the proof. For propositional logic, this requires converting a proof from tree-like to dag-like form, but at most doubles the number of lines in the proof. For first-order logic, the proof size can grow exponentially, but the proof has a succinct description and is polynomial time uniform. We use direct, global constructions that give polynomial time methods for removing all top-level cuts from proofs. By exploiting prenex representations, this extends to removing all cuts, with final proof size near-optimally bounded superexponentially in the alternation of quantifiers in cut formulas.

Suggested Citation

  • Sam Buss, 2015. "Cut Elimination In Situ," Springer Books, in: Reinhard Kahle & Michael Rathjen (ed.), Gentzen's Centenary, edition 1, pages 245-277, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-10103-3_10
    DOI: 10.1007/978-3-319-10103-3_10
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