abstract:In mathematics, a Heyting algebra, named after Arend Heyting, is a bounded lattice (with join and meet operations written ∨ and ∧ and with least element 0 and greatest element 1) equipped with a binary operation a→b of implication such that (a→b)∧a ≤ b, and moreover a→b is the greatest such in the sense that if c∧a ≤ b then c ≤ a→b. From a logical standpoint, A→B is by this definition the weakest proposition for which modus ponens, the inference rule A→B, A ⊢ B, is sound.