The “preferential entailments” considered in this text are all defined in the same way, by a binary relation, or “preference relation”. This relation can be among interpretations, or sets of interpretations, or among “states” which are copies of interpretations or copies of sets of interpretations. This provides four kinds of preferential entailments. What we do here is to provide a characterization result for these four kinds of preferential entailments. We choose properties as simple and natural as possible, and sometimes we (...) provide various characterizations for the same notion. It appears that the apparently most complicated notion possesses by far the simplest characterization result. A by-product of our results is that case is equivalent to case : we can define directly the relation among sets of interpretations, eliminating the need for “states” in this case. The paper deals mainly with propositional logic, however it describes also the situation in first order logic. Any complete theory has one model in the propositional case and many models in the first order case. This is why the simplest notion in the first order case has exactly the same syntactical characterization as the notion in the propositional case. (shrink)