Input/output logics with a consistency check

Norm-based semantics to deontic logic typically come in an unconstrained and constrained version, where the unconstrained version comes with a proof system, and the constraints handle phenomena such as dilemmas, contrary-to-duty reasoning, uncertaintyanddefeasibility. Thisisanalogoustotheuseofrule-basedlanguagesin non-monotonic logic such as logic programming or default logic, but in contrast to the traditional modal framework. Traditionally, for example, specific modal deontic logics have been defined that make dilemmas inconsistent, as well as other modal deontic logics representing dilemmas in a consistent way. This issue was raised recently in the input/output logic framework, and weaker unconstrained logics have been defined handling phenomena like dilemmas and contrary-to-duty reasoning. In this paper we introduce a semantics and proof theory for a system with various desirable properties. We show that our new deontic logic satisfies a criterion posed several years ago by Broersen and van der Torre, allowing deontic detachment while preventing Prakken and Sergot’s pragmatic oddities as well as Sergot’s drowning problem.