This note shows no extension of bi-intuitionistic logic is structurally complete, indicating significant limits for passive completeness.
In this note we show that no extension of bi-intuitionistic logic, except for classical logic, is structurally complete; indeed, none of them are passively structurally complete. A direct proof of active structural completeness is given for some simple systems.
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Almeida et al. (2025) studied this question.
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