# 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]
1. ^ a b Shoham, Y. (1987), "Nonmonotonic logics: Meaning and utility", Proc. of the 10th Int. Joint Conf. on Artificial Intelligence (IJCAI’87) (PDF), pp. 388–392 line feed character in |contribution= at position 33 (help).