 Another version of bi-intuitionistic logic, called 2Int, with a different notion of co-implication and hence co-negation has been developed in Wansing 2016a. In particular, in the semantics of 2Int a distinction is drawn between a support of truth and a support of falsity relation between states and formulas, and a state supports the truth of \(-A\) iff it supports the falsity of \(A\).