Permissibility and violable rules
From a logical point of view, permissibility can be reduced to possibility by introducing demands which can be met. The alleged reduction is circular from a philosophical perspective, however, because demands are fundamentally deontic. This paper solves this problem by replacing demands which can be met with rules which can be satisfied and violated.
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Rowbottom, D. P. (2008). Permissibility and violable rules. Philosophia, 36(3), 367-374. doi: 10.1007/s11406-007-9113-5