The Logics of Formal Inconsistency are paraconsistent logics which internalize the notions of consistency and inconsistency by meansof connectives of their language. Based on that idea, we propose several deontic systems in which contradictory obligations are allowed, without trivializing the system. Thus, from conflicting obligations $O(A)$ and $O(-A)$ just can be derived that the sentence $A$ is deontically inconsistent. This avoids the logic collapse, and, on the other hand, this allows to "repair" or to refine the given information set. The novel systems introduce new deontic operators of "deontic consistency" and "deontic inconsistency". This approach can be used for analyzing paradoxes based on contrary-to-duty obligations. This is a joint work with Newton Peron.