Mally's Deontic Logic: Reducibility and Semantics

We discuss three aspects of the intuitionistic reformulation of Mally’s deontic logic that was recently proposed (Journal of Philosophical Logic (2013) 42:635–641). First, this reformulation is more similar to Standard Deontic Logic than appears at first sight: like Standard Deontic Logic, it is Kanger reducible and Anderson reducible to alethic logic and it has a semantical interpretation that can be read in deontic terms. Second, this reformulation has an extension that provides 100% of the theorems stated by Mally himself (and that does not provide OA→ A, which Mally himself did not state either). Third, it is interesting to view Mally’s original deontic logic as an extension of this reformulation.