 However, there is no S5 model where \(A \wedge \neg A\) holds at some world. So an inference of the form \(\{A \wedge \neg A\} \vDash B\) is valid in discussive logic. This means that, in discussive logic, adjunction \((\{A, \neg A\} \vDash A \wedge \neg A)\) fails. But one can define a discussive conjunction, \(\wedge_d\), as \(A \wedge \Diamond B\) (or \(\Diamond A \wedge B)\). Then adjunction holds for \(\wedge_d\) (Jaśkowski 1949).