ABSTRACT. In pursuit of a canonistic logic comprised of dualized proof rules, we introduce a sequent calculus system, 2Intx, that is inspired by Wansing's bi-intuitionistic propositional logic 2Int. Though 2Int has canonicity and duality, it defines only natural deduction proof rules and employs an unintuitive Kripke semantics that allows atomic formulas to be both true and false. In addition to defining the sequent calculus rules of 2Intx, we also define a Kripke semantics that only admits models in which atomic formulas are either true or false but not both. Finally, we prove soundness of 2Intx.