PP-2023-07: Herbrand Schemes for First-order Logic

PP-2023-07: Afshari, Bahareh and Enqvist, Sebastian and Leigh, Graham E. (2023) Herbrand Schemes for First-order Logic. [Pre-print] (Submitted)

[thumbnail of FOL_ILLC preprint_2023.pdf] Text
FOL_ILLC preprint_2023.pdf

Download (712kB)


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’.

Item Type: Pre-print
Report Nr: PP-2023-07
Series Name: Prepublication (PP) Series
Year: 2023
Uncontrolled Keywords: Sequent Calculus, First-order Logic, Herbrand’s Theorem, Cut Elimination, Multicut, Higher-order Recursion Schemes, Computational Content
Subjects: Computation
Depositing User: dr Bahareh Afshari
Date Deposited: 04 Dec 2023 20:22
Last Modified: 04 Dec 2023 20:22
URI: https://eprints.illc.uva.nl/id/eprint/2286

Actions (login required)

View Item View Item