This SpringerBrief proposes a general framework for reasoning about inconsistency in a wide variety of logics, including inconsistency resolution methods that have not yet been studied. The proposed framework allows s to specify preferences on how to resolve inconsistency when there are multiple ways to do so. This empowers s to resolve inconsistency in data leveraging both their detailed knowledge of the data as well as their application needs. The brief shows that the framework is well-suited to handle inconsistency in several logics, and provides algorithms to compute preferred options. Finally, the brief shows that the framework not only captures several existing works, but also s reasoning about inconsistency in several logics for which no such methods exist today.