[Boo. Hi, folks. :-)]
Is there a standard definition of "abstract sound design?" Smarter minds than mine can probably answer that. Personally and subjectively, I think it can refer to a few things. We talk about this a lot with our clients and sound design folks at work, since we primarily do SFX for interfaces.
Just like visual art, sound design can be representative or abstract, two ends of a spectrum. It can represent something that is meant to seem real (a sound we recognize, the sound of a real object or instrument, or real sound(s) recontextualized to represent something new, like a spaceship or creature), in which case I'd call that representative sound design.
Abstract sound design could be construed as a sound that represents something that doesn't usually have a sound (mental flashbacks or character epiphanies, for example), or a sound that itself doesn't have a real world equivalent (many button sounds found in fantasy user interfaces in films). Abstract sounds can be used to represent abstract ideas or concepts, representing both aspects of abstraction at the same time.
As to how they're created, I think this is where sound designers get to flex their creative muscles the most. I'd argue that there are no rules. Resynthesis, waveshaping, synthesis from scratch, huge plug-in or effects chains, even something as simple as playing something in a reverse boomerang loop...it all depends on how the sound matches the visuals for which they're intended, abstract or not, and how much (well, since it's abstract, more like how little) the end listener can identify the sound.
Just my take, of course, and intensely curious to hear what others think.