An Inconsistency-Adaptive Deontic Logic for Normative Conflicts

We present the inconsistency-adaptive deontic logic DPr, a nonmonotonic logic for dealing with conflicts between normative statements. On the one hand, this logic does not lead to explosion in view of normative conflicts such as OA ∧ O ∼A, OA ∧ P ∼A or even OA ∧ ∼OA. On the other hand, DPr still verifies all intuitively reliable inferences valid in Standard Deontic Logic (SDL). DPr interprets a given premise set ‘as normally as possible’ with respect to SDL. Whereas some SDL-rules are verified unconditionally by DPr, others are verified conditionally. The latter are applicable unless they rely on formulas that turn out to behave inconsistently in view of the premises. This dynamic process is mirrored by the proof theory of DPr.