Why Defeasible Deontic Logic needs a Multi Preference Semantics

There is a fundamental difference between a conditional obligation being violated by a fact, and a conditional obligation being overridden by another conditional obligation. In this paper we analyze this difference in the multi preference semantics of our defeasible deontic logic DefDiode. The semantics contains one preference relation for ideality, which can be used to formalize deontic paradoxes like the Chisholm and Forrester paradoxes, and another preference relation for normality, which can be used to formalize exceptions. The interference of the two preference orderings generates new questions about preferential semantics.