  In the style of Lindstr\"om's theorem for classical first-order logic, this
article characterizes propositional bi-intuitionistic logic as the maximal
(with respect to expressive power) abstract logic satisfying a certain form of
compactness, the Tarski union property and preservation under bi-asimulations.
Since bi-intuitionistic logic introduces new complexities in the intuitionistic
setting by adding the analogue of a backwards looking modality, the present
paper constitutes a non-trivial modification of previous work done by the
authors for intuitionistic logic in: G. Badia and G. Olkhovikov. A Lindstr\"om
theorem for intuitionistic propositional logic. Notre Dame Journal of Formal
Logic, 61 (1): 11-30 (2020).
