Falsification, natural deduction and bi-intuitionistic logic

A kind of a bi-intuitionistic propositional logic is introduced that combines verification and its dual. This logic, 2Int, is motivated by a certain dualization of the natural deduction rules for intuitionistic propositional logic, Int. It is shown that 2Int can be faithfully embedded into Int with respect to validity. Moreover, 2Int can be faithfully embedded into dual intuitionistic logic, DualInt, with respect to a notion of dual validity. In 2Int, from a falsificationist perspective, intuitionistic negation internalizes support of truth, whereas from a verificationist perspective, co-negation internalizes support of falsity.