 The so-called standard system of deontic logic KD is defined as PC supplemented with 1-4 (except that ! is usually written as O: see the entry on  deontic logic),  so the new system is at least as strong as KD. It is not difficult to see that it is in fact identical with KD supplemented with OU (Mally’s Axiom IV) and the following definition of f : A f B = O(A → B). In modern deontic logic, the notion of commitment is sometimes defined in this way.