OBLIGATION AS WEAKEST PERMISSION: A STRONGLY COMPLETE AXIOMATIZATION
Frederik Van De Putte · The Review of Symbolic Logic · 2016
Abstract In (Anglbergeret al., 2015, Section 4.1), a deontic logic is proposed which explicates the idea that a formulaφis 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 Anglbergeret 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.