Hmm, no, my logic doesn't say that at all, really. If you're not doing the art, you're not doing the art. By my reasoning, the only way to say you're playing football is to be playing football. Now, if the retired footballer is playing a game with only four people a side, that's still playing football, as the core elements of the game are all there.
Sure.
In terms of what point it no longer is the art, well, that's really something individual to the art... but once one or more of the key components (whatever they are according to the system itself) is removed (not just moved past, actually removed, as in K-Man's hypothetical of the karate 4th dan removing kata), then it's no longer that art. Basically, it is until it isn't. And it isn't until it is. Clear, right?
Again, I think that it depends upon what is being removed and why. If it is removed from the curriculum (thus is not available to the student), then you have a separate circumstance from that of the student simply hasn't learned it or started it or the student is unable to do it (thus the accommodation).
In this thread, the premise is the latter. With regards to the former, you're getting into whether or not something is a variant of an existing art or a separate art altogether.
What is your reason, then?
I'm not an aikido practitioner, so take my answer for what its worth. I see ukemi as something that is done so that the art of aikido can be practiced safely. Ukemi, or whatever else you want to call it, of some kind is part of a lot of arts. If you're throwing your partner, or doing any one of a number of other things with a partner, the partner will need to practice ukemi in order to not be injured in the course of practicing the art. Aikido has core principles, not all of which are physical and which do not preordain the specific technical content of the art.
We do ukemi (though we don't call it that) in hapkido so that we can train without injury and so that we can avoid injury outside of the dojang, be it in self defense or simply breaking a fall from slipping. We also have joint locks, joint manipulation, striking (hands, feet, knees, elbows), throwing, and weapon work. None of which makes hapkido particularly unique, as some ryus of karate likely have the same features, and I'm certain that a number of CMA do as well.
But the principles of hapkido,
hwa ,
weon, and yu (harmony/nonresistance, circular motion, and flow)
, arewhat make hapkido hapkido and not simply taekwondo with joint locks, which I have experienced. So long as those principles are there, you're 'doing' hapkido whether you are doing nak beop and gureugi (falling and rolling respectively) or not.
I believe (and any aikidoka here, feel free to correct me) that aikido has similar principles.
Hmm, thought that was kinda what I was saying.
In general, it is, but your posts get very specific (which is fine) and very definitive with regards to 'this without this cannot be this.'