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<p>This article provides a language-theoretic rendering of Herbrand’s theorem. To each first-order proof is associated a higher-order recursion scheme that abstracts the computation of Herbrand sets obtained through Gentzen-style multicut elimination. The representation extends previous results in this area by lifting the prenex restriction on cut formulas and relaxing the cut-elimination strategies. Features of the new approach are the interpretation of cut as simple composition and contraction as ‘call with current continuation’.</p>

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Herbrand schemes for first-order logic

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月14日

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  • Bahareh Afshari,
  • Sebastian Enqvist,
  • Graham E. Leigh

摘要

This article provides a language-theoretic rendering of Herbrand’s theorem. To each first-order proof is associated a higher-order recursion scheme that abstracts the computation of Herbrand sets obtained through Gentzen-style multicut elimination. The representation extends previous results in this area by lifting the prenex restriction on cut formulas and relaxing the cut-elimination strategies. Features of the new approach are the interpretation of cut as simple composition and contraction as ‘call with current continuation’.