Which Alice?

Looking-Glass Logic
"That's easy," replied Humpty Dumpty. "Take, for example, the
statement that the Red King is asleep. Its opposite is that the Red
King is awake. Clearly one of them is true and the other false. The
Looking-Glass logician believes only the one which is false, hence he
can't believe each of them separately. Yet the single statement that
the Red King is both asleep and awake is a false statement, hence
the Looking-Glass logician must believe this false statement.
"And now that you have the key, the answers to my ten questions
should all be obvious."
Here are the answers that Humpty Dumpty gave to his ten
questions:
1—Since the Looking-Glass logician believes the Red King is
asleep, then the Red King must actually be awake. Therefore the
Red King is not dreaming of Alice. (By dreaming, I don't mean
daydreaming!) Since the King is not dreaming of Alice, then the
Looking-Glass logician must believe that he is dreaming of Alice.
2—Since he (the Looking-Glass logician) believes that either the
Red King or the Red Queen is asleep, then it is false that either the
Red King or the Red Queen is asleep. This means that both of them
are actually awake. Since the Red Queen is awake, then he must
believe that she is asleep. (By the same token he must also believe
that the Red King is asleep.)
3—He believes the Red King is asleep, which merely means that
the Red King is awake. This tells us nothing about whether the Red
Queen is asleep or not, so we have no way of knowing whether he
believes she is asleep.
4—This is a different story! Since he believes that the Red King is
asleep, then it is false that the Red King is asleep. Hence it is
certainly false that the Red King and Queen are both asleep!
Therefore he must believe that they are both asleep.
So the curious thing is that he doesn't necessarily believe that the
Red Queen is asleep, yet he does believe that the Red King and the
Red Queen are both asleep!
5—He believes they are both asleep, from which only follows that
at least one is awake. We don't know which one, hence we cannot
determine whether or not the Looking-Glass logician believes the
King is asleep.
6—Since he believes that they are either both asleep or both
125