Violated obligations in a defeasible deontic logic
Deontic logic is characterized by the distinction between the actual and the ideal. In this article we discuss the situation where the actual deviates from the ideal, where obligations are violated. Nonmonotonic logics can be very helpful for the formalization of deontic reasoning, in particular to infer moral cues. It has been argued that the problems related to violated obligations, e.g. the Chisholm `Paradox', are just instances of problems of defeasible reasoning. We disagree with this claim since we will argue that there is a fundamental difference between a violated and a defeated obligation. In this article, we analyze violated obligations in Horty's nonmonotonic framework. We extend his definition of deontic consequence in such a way that it covers violated obligations and we give a solution to deal with conflicts between violability and defeasibility.