5) It should be a boolean arithmetic
The linked three valued logic failes because it is no boolean arithmetic which is impossible with only three states. You need at least four: true, false, contradictory and ambigous. With these you can not only solve the liar paradox but also the proposition "This proposition is true" which is ambigous. And no, that does not mean it would be false because it states it where true while it actually is ambigous. It is simply ambigous.
As a funny side note, I think that is where Gödel erred. His incompleteness theorem probably rests on a two valued logic. But I'm not a mathematician and can't proof that.
What do you do with "This sentence is contradictory"?
Graham Priest discusses The Liar's Paradox for a NY Times blog. It seems that one way of solving the Liar's Paradox is defining dialethei, a true contradiction. Less Wrong, can you do what modern philosophers have failed to do and solve or successfully dissolve the Liar's Paradox? This doesn't seem nearly as hard as solving free will.
This post is a practice problem for what may become a sequence on unsolved problems in philosophy.