 To capture this implication of Gap formally, and to axiomatize the logic of strict actualism (under Gap) generally, Prior makes basically two changes to the language \(\scrL_\Box\)—call this language \(\scrL_{Q}\). First, for reasons that will become evident shortly, he takes \(\Diamond\) rather than \(\Box\) as a primitive operator. Secondly, he adds a new sentential operator \(\text S\) for necessary statability (“n-statability”) to \(\scrL_\Box\).  It is also useful to think of impossible falsehood as a sort of weak necessity signified by its own operator: