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)

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Abstract

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 Logic
Depositing User:	dr Bahareh Afshari
Date Deposited:	04 Dec 2023 20:22
Last Modified:	17 Sep 2024 18:11
URI:	https://eprints.illc.uva.nl/id/eprint/2286

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