In
proof theory, a discipline within
mathematical logic,
double-negation translation, sometimes called
negative translation, is a general approach for embedding
classical logic into
intuitionistic logic, typically by translating formulas to formulas which are classically equivalent but intuitionistically inequivalent. Particular instances of double-negation translation include
Glivenko's translation for
propositional logic, and the
Gödel–Gentzen translation and
Kuroda's translation for
first-order logic.