In my experience, the best way to understand this is to understand that IN NO LIMIT (the rules for limit are different), any incomplete raise is best understood as not really "part of the game" but rather as "additional action" (think of it as a side bet, not to be confused with a side pot).
So, let's say it is after the flop (just for the sake of example, to avoid having to talk about the blinds) and the following scenario occurs:
Player A bets $20
Player B calls $20
Player C goes all-in for $30
The question that was asked here earlier, "can player A raise?" is easily answered if you understand that player C's incomplete "raise" (of the extra $10) is NOT to be intepreted as part of the game, but rather an additional side-action bet. In effect the player has only called, but also proposed (outside of the game, if you want to think of it this way) an additional $10 side bet (except that if you want to continue playing, you MUST accept this bet, so it's not really "outside of the game").
Given this, player A cannot raise, because all that has happened behind him are calls, there has been no raise. There has been a call by B, and a call by C but with that extra $10 side-bet that needs to be accepted as well.
Now take a different scenario:
Player A bets $20
Player B goes all-in for $30
Player C wants to raise
What is the minimum valid total amount for player C's raise? $40? $50? $60?
Again, this is easily understood if you understand the incomplete all-in as "a call plus additional action".
Given that player B "called" (with $10 of additional action, that we can ignore for a moment), the minimum amount that C can raise to is $40. Of course, C is obligated (by the rules of the game) to also participate in the additional $10 action proffered by B.
Therefore the minimum legal raise for player C is to $50 total, which is to be understood as a raise of $20 on top of the $20 bet from A and B, plus matching the $10 of additional side action on B's all-in.
Now if A wants to reraise, *his* minimum bet (for a reraise) would be to $70. Again this is because C's raise was to $40 (which is $20 more than the A bet), so the raise increment is still $20. Thus A can reraise to $60 but also still has to include the $10 side action for B's all-in.
Sounds complex but it is actually quite simple: an all-in that itself is not a legal raise is really just a call plus an entirely separate side-bet for the additional amount. That side-bet has to be included in all other subsequent bets, but otherwise does not affect the state of the bet/raise/call amounts dictated by the normal rules.
It is certainly possible for any given house to have its own interpretation of this situation; however, this is the rule as described (not very well) in Robert's Rules.