Preferential entailment

Preferential entailment is a non-monotonic logic based on selecting only models that are considered the most plausible. The plausibility of models is expressed by an ordering among models called a preference relation, hence the name preference entailment.
Formally, given a propositional formula formula_1 and an ordering over propositional models formula_2, preferential entailment selects only the models of formula_1 that are minimal according to formula_2. This selection leads to a non-monotonic inference relation: formula_5 holds if and only if all minimal models of formula_1 according to formula_2 are also models of formula_8.
Circumscription can be seen as the particular case of preferential entailment when the ordering is based on containment of the sets of variables assigned to true (in the propositional case) or containment of the extensions of predicates (in the first-order logic case).