Cut Elimination In Situ

Sam Buss ()
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Sam Buss: University of California, San Diego, Department of Mathematics

A chapter in Gentzen's Centenary, 2015, pp 245-277 from Springer

Abstract: 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.

Keywords: Proof Size; Outermost Connectives; Lower Cedar; Quantifier Alternation Depth; Tree-like Proofs (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-10103-3_10

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DOI: 10.1007/978-3-319-10103-3_10

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