 An action \((A,e)\) operates on an initial situation \((M,w)\) satisfying \(M,w\models\pre^A(e)\) via the action-priority update to produce the resultant situation \((M[A],(w,e))\). Note that we may write the plausibility relation \(\mathrel{{\geq}[A]_a}\) for agent a after the action-priority update by A simply as \(\geq_a\) when the meaning is clear from context.