Kuroda's Translation for Higher-Order Logic

Thomas Traversié (1, 2)

1 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes
2 DEDUCTEAM - Deduction modulo, interopérabilité et démonstration automatique

In 1951, Kuroda defined an embedding of classical first-order logic into intuitionistic logic, such that a formula and its translation are equivalent in classical logic. Recently, Brown and Rizkallah extended this translation to higher-order logic, but did not prove the classical equivalence, and showed that the embedding fails in the presence of functional extensionality. We prove that functional extensionality and propositional extensionality are sufficient to derive the classical equivalence between a higher-order formula and its translation. We emphasize a condition under which Kuroda's translation works with functional extensionality.

Mots clés: Kuroda's translation; higher-order logic; functional extensionality

Domaines: Logique en informatique [cs.LO]

Thomas Traversié. Kuroda's Translation for Higher-Order Logic. 2024. ⟨hal-04561757⟩