Preferential entailment

Formally, given a propositional formula ${\displaystyle F}$ and an ordering over propositional models ${\displaystyle \leq }$, preferential entailment selects only the models of ${\displaystyle F}$ that are minimal according to ${\displaystyle \leq }$. This selection leads to a non-monotonic inference relation: ${\displaystyle F\models _{\text{pref}}G}$ holds if and only if all minimal models of ${\displaystyle F}$ according to ${\displaystyle \leq }$ are also models of ${\displaystyle G}$.[1]