I'll go one step further:

In some cases, there may be a middle ground between A and not-A. In that case, "not not-A" is quite distinct from "A."

For example, consider "hungry" or "not hungry" - there is a middle ground where you won't miss the food if there isn't any more, but you would eat it and probably enjoy it if there were. Often that middle ground is the difference between heavy and slender...

But I'll have to leave it to the assembled multitudes to decide whether this point is applicable to the Court of AWAD or not.