You ought to do something ! The logic of obligation as weakest permission

This paper studies the following interpretation of obligations: A person i ought to do A in a situation S just in case everything else i may (and can) do in S is consistent with A. In such case A can be called the weakest permission that i has in S. We show that, under this interpretation, obligation and permission are not dual notions, and that it gives rise to an interesting interplay between deontic and alethic notions. We also discuss the logics’ adequacy w.r.t. the paradoxes of (classic) deontic logic and provide a sound and complete axiomatization for it. We finally show that practical, rational recommendations in games provide a natural, concrete application of such understanding of obligations and permissions.