  In this paper I will show the problems that are encountered when dealing with
uniqueness of connectives in a bilateralist setting within the larger framework
of proof-theoretic semantics and suggest a solution. Therefore, the logic 2Int
is suitable, for which I introduce a sequent calculus system, displaying - just
like the corresponding natural deduction system - a consequence relation for
provability as well as one dual to provability. I will propose a modified
characterization of uniqueness incorporating such a duality of consequence
relations, with which we can maintain uniqueness in a bilateralist setting.
