From the Universality of Mathematical Truth to the Interoperability of Proof Systems - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Communication Dans Un Congrès Année : 2022

From the Universality of Mathematical Truth to the Interoperability of Proof Systems

Résumé

The development of computerized proof systems, such as Coq, Matita, Agda, Lean, HOL 4, HOL Light, Isabelle/HOL, Mizar, etc. is a major step forward in the never ending quest of mathematical rigor. But it jeopardizes the universality of mathematical truth [5]: we used to have proofs of Fermat's little theorem, we now have Coq proofs of Fermat's little theorem, Isabelle/HOL proofs of Fermat's little theorem, PVS proofs of Fermat's little theorem, etc. Each proof system: Coq, Isabelle/HOL, PVS, etc. defining its own language for mathematical statements and its own truth conditions for these statements. This crisis can be compared to previous ones, when mathematicians have disagreed on the truth of some mathematical statements: the discovery of the incommensurability of the diagonal and side of a square, the introduction of infinite series, the non-Euclidean geometries, the discovery of the independence of the axiom of choice, and the emergence of constructivity. All these past crises have been resolved.
Fichier principal
Vignette du fichier
universalityinteroperability.pdf (141.89 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03959359 , version 1 (27-01-2023)

Identifiants

Citer

Gilles Dowek. From the Universality of Mathematical Truth to the Interoperability of Proof Systems. IJCAR 2022 - International Joint Conference on Automated Reasoning, Aug 2022, Haifa, Israel. ⟨10.1007/978-3-031-10769-6_2⟩. ⟨hal-03959359⟩
63 Consultations
18 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More