One of those capabilities is inverting existing conditions. Sequel uses this feature extensively.
For example, if you want to specify a not equals condition in Sequel, you just specify an equals condition and invert it.
This keeps the internals and API simple, and gives you power to take an existing dataset and invert it to return all rows except the rows currently filtered.
Let's say you want to to use this to determine which characters are not allowed. You just apply the tilde to the BooleanExpression, which returns a BooleanExpression representing the inversion of the condition.