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In this paper we show that cut-free derivations in the epsilon format of sequent calculus provide for a non-elementary speed-up w.r.t. cut-free proofs in usual sequent calculi in first-order language. In addition, a non-elementary speed-up is shown w.r.t. cut-free proofs in calculi with relaxed eigenvariable conditions which proved a speed-up themselves w.r.t. \({\mathbf {LK}}\) .

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Epsilon Calculus Provides Shorter Cut-Free Proofs

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  • 发表日期：

    2025年

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  • Matthias Baaz,
  • Anela Lolić

摘要

In this paper we show that cut-free derivations in the epsilon format of sequent calculus provide for a non-elementary speed-up w.r.t. cut-free proofs in usual sequent calculi in first-order language. In addition, a non-elementary speed-up is shown w.r.t. cut-free proofs in calculi with relaxed eigenvariable conditions which proved a speed-up themselves w.r.t. \({\mathbf {LK}}\) .