I'll put what I understand by "optionality" in OO terms:
[This Thing] 0..1 -------- 1..* [That Thing]
Look at [This Thing]. The 0 says that the
association is optional. ie. You can have an Object or not. If you do, then that Object can have this particular kind of association or not.
Now [That Thing]. If you have such an object, then you must have one of these
associations.
ie. the notation refers to the optionality of the
Association, and not of the Object, but a side effect of the 1..* (or 1..1) rule of association is that the Object becomes not-optional.
Am I right? Or am I on completely the wrong track? This feels to me like a bit of insight, but many's the time when "insight" is none other than completely losing the plot.