At the extreme of abstractionist play would be a mechanic where you roll d4
before you declare some interaction with the gameworld. On a 4, you describe something really good for your PC, on a 3 you describe a net positive, on a 2 it works out for no benefit or loss, and on a 1 you describe a net loss. In this model, the resolution mechanic doesn't abstract any real world event; it limits how the player gets to describe what is about to unfold.
But it's still "abstract" (as opposed to "concrete"), precisely because the resolution mechanic is not trying to tie itself to the world model.
Of course, this is also not much of a "game" in a competitive sense, in that the resolution mechanics don't really interact with each other or give much scope for play. The "play" takes place entirely in the story.
D&D 4E is nowhere near this extreme. Its resolution mechanics form an interesting game in and of themselves. But they are also designed to evoke and support a story, without necessarily telling that story of themselves.
Andor said:
In other words there was no pretense that the rules covered all situations and yet the PCs could attempt actions outside the rules. The attitude I seem to see in the 4e rules, and the 4e fans, is the opposite. "Can I do X?" "Do you have a power for X on your sheet?" "No. " "Then no."
From what I've seen, this misses the point of abstract mechanics. At the core of the abstract mechanics are a small number of calibrated resolution mechanisms. Whenever a player wants their PC to do something, you pick the most appropriate mechanism and use it.
They key point is that there does not
need to be a mapping from story to mechanism. It's good to have guidance that says "when the PC does activity X, resolve it using mechanism Y". But since Y does not try to model or represent X, only resolve it, it gives a lot of flexibility when you encounter a novel X. You simply skim through your available resolution mechanisms and pick whichever one looks most appropriate for the situation at hand.
Of course, previous editions could do this too. They just muddied the waters with quite detailed resolution models for a bunch of things written into the rules. Alternatively, the rules can be set up so you have a fun story and a fun game running at the same time, and every so often each wanders over to see what the other is up to.
Note that I'm not making a global value judgement, here. Both styles of rules have their place. One of my favourite games is Star Fleet Battles, and their "fiction guidelines" include a warning there is a guy on staff who will take any SFB battle portrayed in submitted fiction and try to play it out on the gametable to make sure it obeys the game rules. That's simulationism / concretism at its finest. 3E seemed to have the problem that it didn't really know which design principles it was using, which frequently resulted in an inelegant mix.