Obligation as weakest permission : a strongly complete axiomatization

In (Anglberger et al., 2015, Section 4.1), a deontic logic is proposed which explicates the idea that a formula phi is obligatory if and only if it is (semantically speaking) the weakest permission. We give a sound and strongly complete, Hilbert style axiomatization for this logic. As a corollary, it is compact, contradicting earlier claims from Anglberger et al. (2015). In addition, we prove that our axiomatization is equivalent to Anglberger et al.'s infinitary proof system, and show that our results are robust w.r.t. certain changes in the underlying semantics