 In modern deontic logic, P A (“it is permitted that A”) is defined as P A = ¬ !¬ A. If we adopt this definition, ID provides !A ↔ P A (because IPC provides ¬ ¬ A ↔ ¬ ¬ ¬ ¬ A). Mally did not discuss permission. His approval of !A → ¬ !¬ A (which is usually regarded as characteristic for deontic logic) is clear from Mally 1926, ch. 4, sec. 10, p. 49, ad (V).