Institut de Mathématiques de Marseille, UMR 7373


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The true concurrency of Herbrand’s theorem

Jeudi 14 juin 11:00-12:30 - Pierre CLAIRAMBAULT - LIP, ÉNS Lyon

The true concurrency of Herbrand’s theorem

Résumé : Herbrand’s theorem, widely regarded as a cornerstone of proof theory, exposes some of the constructive content of classical logic. In its simplest form, it reduces the validity of a first-order purely existential formula to that of a finite disjunction. In the general case, it reduces first-order validity to propositional validity, by understanding the structure of the assignment of first-order terms to existential quantifiers, and the causal dependency between quantifiers.
In this paper, we show that Herbrand’s theorem in its general form can be elegantly stated and proved as a theorem in the framework of concurrent games, a denotational semantics designed to faithfully represent causality and independence in concurrent systems, thereby exposing the concurrency underlying the computational content of classical proofs. The causal structure of concurrent strategies, paired with annotations by first-order terms, is used to specify the dependency between quantifiers implicit in proofs. Furthermore concurrent strategies can be composed, yielding a compositional proof of Herbrand’s theorem, simply by interpreting classical sequent proofs in a well-chosen denotational model.
This is joint work with Aurore Alcolei, Martin Hyland, and Glynn Winskel.

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Lieu : Salle des séminaires 304-306 (3ème étage) - Institut de Mathématiques de Marseille (UMR 7373)
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Pour en savoir plus sur cet événement, consultez l'article Séminaire Logique et Interactions