Browsing by Author "Hetzl, Stefan"

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    Herbrand's Theorem as Higher Order Recursion
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2018) Afshari, Bahareh; Hetzl, Stefan; Leigh, Graham E.
    We provide a means to compute Herbrand disjunctions directly from sequent calculus proofs with cuts. Our approach associates to a first-order classical proof π + ∃vF, where F is quantifier free, an acyclic higher order recursion scheme H whose language is finite and yields a Herbrand disjunction for ∃vF. More generally, we show that the language of H contains the Herbrand disjunction implicit in any cut-free proof obtained from π via a sequence of Gentzen-style cut reductions that always reduce the weak side of a cut before the strong side.