E.g. you can't say "Imagine (song) 'is a' John Lennon (solo career)", or "I Am The Walrus 'is a' John Lennon (Beatles
career)", or
"Imagine (song) 'is a' British rock musicians".
That's because you haven't quite gotten what I'm getting at yet. The category wouldn't be called "John Lennon", because nothing is a John Lennon (other than, presumably, John Lennon, who would be rather lonely). Rather, under "things related to Beatles", you would have "things related to John Lennon" or something. Inelegant, I know, but I think you see where I'm going with this?
OK, but how's that any different than what we have now, except with more words involved, and more potential for confusion?
I.e. you can still say Imagine (song) is a thing related to John Lennon, which is a thing related to The Beatles. The relationship between the Beatles and Imagine (song) is somewhat tenuous, I think.
Also it leads to things like saying "Jesus is related somehow to Waves", to use the original loop example. I'm just not sure that it tells you anything useful.
The main problem is the terminology. I mean, it works logically, but I don't think people will go for saying "No, things-related-to-the-Beatles isn't a supercategory of things-related-to-John-Lennon, things-related-to-the-Beatles is only related to things-related-to-John-Lennon!" But that's the fault of the English language. I leave it to the wordsmiths to improve upon my terminology. :P
So you're saying that supercategories should not imply any transitive relationship whatsoever? But isn't that worse than the current situation, which at least tries for some vague ill-defined type of relationship? Granted, it seems to fail, but at least it tries.
But what if when you specified a category, if you could say what the relationship was?
That's Wikidata. We're still waiting.
Ah, ok. I've just quickly read through the Wikidata page on meta, and while it sounds interesting, it's trying to do much more than just store a relationship type between categories ... possibly too much more.
Hmm... can anybody morph this http://web.archive.org/web/20010604173556/www.jimmywales.com/jimmy.jpg with this http://en.wikipedia.org/wiki/Image:The_Hunt_for_Red_October_movie_poster.JPG
[[Sailing Yacht]] -- is a --> [[sailing ship]] -- is a --> [[Category:Ship types]] ^ | is a | [[The Hunt for Red October]] -- is about a --> [[submarine]]
... or is it a trick question?
All the best, Nick.