 One difficulty is a formulation of a conditional. In S5, the inference from \(\Diamond p\) and \(\Diamond(p \supset q)\) to \(\Diamond q\) fails. Jaśkowski chose to introduce a connective which he called discussive implication, \(\supset_d\), defined as \(\Diamond A \supset B\). This connective can be understood to mean that “if some participant states that \(A\), then \(B\)”. As the inference from \(\Diamond A \supset B\) and \(\Diamond A\) to \(\Diamond B\) is valid in S5, modus ponens for \(\supset_d\) holds in discussive logic. A discussive bi-implication, \(\equiv_d\), can also be defined as \((\Diamond A \supset B) \wedge \Diamond(\Diamond B \supset A)\) (or \(\Diamond(\Diamond A \supset B) \wedge (\Diamond B \supset A))\). For some history of work on Jaśkowski’s logic and axiomatizations thereof, see Omori and Alama (2018).