An Andersonian Deontic Logic with Contextualized Sanctions

We present a refinement of Anderson’s reduction of deontic logic to modal logic with only alethic modalities. The refined proposal contextualizes the Andersonian sanction constant s by replacing it with a unary sanction operator S that is dependent on the concrete normative requirement that is violated. A formula SB is then for instance interpreted as “B causes a sanction” or as “B provides a reason for (the applicability of) a sanction”. Due to its modified sanction operator, the resulting logic DSL invalidates some instances of the inheritance principle. This gives rise to new interesting features. For instance, DSL consistently allows for the presence of conflicting obligations. Moreover, it provides novel insights in various central ‘paradoxes’ in deontic logic such as the Ross paradox, the paradox of the good Samaritan, and Forrester’s ‘gentle murderer’ paradox.