I've never used Protege before, but I can talk about the Processing side of things:
Before Processing 3, each sketch could be treated as a component, because the
PApplet class extended Java's
Applet class. That allowed you to do things like add a sketch to a Swing window, just like you would add any other
But since Processing 3,
PApplet no longer extends
Applet. This means you can no longer treat a Processing sketch as a component.
It sounds like this is more a Protege question than it is a Processing question. If you can embed a
Applet inside Protege, then Processing 2 should work for you. If you can use arbitrary Java classes and library (and are okay with your Processing sketch being in a different window than the Protege window), then Processing 3 should work for you.
So if I were you, I'd try asking in a Protege forum about those two options. If you have an example that does either one (uses an
Applet or uses an arbitrary Java class and library), then I'll be able to help with the Processing half of things.
Sounds like an interesting project. Good luck!