Cancelling and overshadowing: two types of defeasibility in defeasible deontic logic

In this paper we give a general analysis of dyadic deontic logics that were introduced in the early seventies to formalize deontic reasoning about subideal behavior. Recently it was observed that they are closely related to non-monotonic logics, theories of diagnosis and decision theories. In particular, we argue that two types of defeasibility must be distinguished in a defeasible deontic logic: overridden defeasibility that formalizes cancelling of an obligation by other conditional obligations and factual defeasibility that formalizes overshadowing of an obligation by a violation. We also show that this distinction is essential for an adequate analysis of notorious `paradoxes' of deontic logic such as the Chisholm and Forrester `Paradoxes'.