A dynamic logic for reasoning about sub-ideal states

In this paper, we will show how dynamic logic can be used to reason about so-called sub-ideal states, i.e. states in which some deontic constraint is violated. For this purpose we have to extend the defonition of the deontic operators. Instead of only giving a post-condition with respect to violations for each action we will consider the complete state transition. In order to distinguish between different states of violation we will also index the violation predicates. The introduction of these two extensions makes it possible to reason in a flexible and natural way about sub-ideal states.