Consider the functions \mathbb {B}_\bot \rightarrow \mathbb {B}_\bot . Which ones are monotonic? There are a total of 27 such functions but only three significant classes.
The three classes are the nine strict functions (which map \bot to \bot ), which are all monotonic, the two non-strict constant functions (which ignore their input and return \mathit {T} and \mathit {F} respectively), which are also monotonic, and the 16 non-monotonic functions.