Forum:Harry and Ginny's children = Half-bloods?

Something in the current FA, Potter, struck me as odd. It is stated that Harry's three children are Half-bloods. But then on the Half-blood article page, it says that a Half-blood is a witch/wizard with at least one Muggle grandparent/parent. The thing is, James II, Albus and Lily Luna do have Muggles in their family, but they're their great-grandparents. Isn't this a bit contradictory? We need to change either the Half-blood article, or otherwise the Potter article (if we changed this one it would be to say that Harry and Ginny's kids are Pure-bloods). There is another problem to factor in too: the Pure-blood article says that Pure-bloods have no Muggles in their family at all. What should we do? --Margiechocoholic.