I haven't tried enforcing Law of Excluded Middle along with Principle of Non-Contradiction (i.e., "It's either one or the other and it can't be both, pick one"), but I'm fairly certain that this would lead to argument too...

I KNOW that there is something systematic going on here, I can tell from the contexts in which she does this, but by the time she can articulate what the system is, she'll have enough words to no longer use this construction, which is a bit sad.