  The consequence relations of classical logics are monotonic. That is, if a set Γ of formulas implies a consequence C then a larger set Γ ∪ A will also imply C. A logic is nonmonotonic if its consequence relation lacks this property. Preferred models provide a general way to induce a nonmonotonic consequence relation. Invoke a function that for each Γ produces a subset  MΓ of the models of Γ; in general, we will expect  MΓ to be a proper subset of these models. We then say that Γ implies C if C is satisfied by every model in  MΓ. As long as we do not suppose that  MΓ∪{A} ⊆  MΓ, we can easily have an implication relation between Γ and C without imposing this relation on supersets of  Γ.[14]