For instance there are ideas from OWL where you could define a category instead of other categories and their attributes, for instance tag D could be the union of tag A and tag B and the complement of tag C.

Implication is also useful both as a way to implement subclassing but also containment relationships. For instance on Danbooru a character that has several forms would have the various forms of the character imply that character and the character would imply the media property that the character comes from.

I am looking at what a tagging system looks like in the transformer age and one key idea is a kind of three value logic around tags which can be in a “positive”, “indeterminant” and “negative” state. If you are training a machine learning system to auto tag you will need (1) a number of examples where a tag does not apply (the tag not being applied is not evidence that the tag doesn’t apply, poor coverage of negative examples is one reason why YouTube recommendation is worse than TikTok) and (2) to deal with cases where the ML model tags something incorrectly. If the model tagging something puts it in an indeterminant polarity and that result can later be switched to negative or positive that is a great way to manage the situation.