 Such a consequence relation can equivalently be expressed semantically in terms of a preferential semantics (see Section  Selection semantics).  Given an LLL-model \(M\) we can identify its abnormal part \(Ab(M) = \{\mathsf{ab} \in \Omega \mid M \models \mathsf{ab}\}\) to be the set of all abnormalities that hold in \(M\). The selection semantics for minimal abnormality can be phrased as follows. We order the LLL-models by \(M \prec M'\) if and only if \(Ab(M) \subset Ab(M')\). Then we define that \(\phi\) is a semantic consequence of \(\Gamma\) if and only if for all \(\prec\)-minimal LLL-models \(M\) of \(\Gamma\), \(M\models \phi\). (We omit selection semantics for other strategies.) 