Falsification, natural deduction and bi-intuitionistic logic
Heinrich Wansing · Journal of Logic and Computation · 2013
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.