This sentence is false.

Well, I see it as similar to shrodinger's cat, in that you can not say the cat is dead or alive. You cannot say the cat is dead or alive, but you 'can' say the cat is dead and alive. You don't actually say that the cat is both dead and alive. Rather, you say that the cat is in a superposition of a live state and a dead state. Moreover, what you really say is that your best description of the cat when it is unobserved is the mathematical description of its being in a superposition of a live state an a dead state. This is not the same thing as saying that the same proposition can be both true and false. (Of course, there is the complication that there is disagreement as to whether quantum mechanics is a description of reality or instead a description of our state of knowledge about reality.) I admit I had in mind classical systems rather than quantum systems. Even in quantum systems, though, I think the most that could be said--on a realist interpretation of quantum mechanics rather than an epistemological one--is that the Law of the Excluded Middle is violated (so that it is not true that Schrodinger's cat is either in a live state or in a dead state), not that the Law of Non-Contradiction is violated. This reminds me of the Pinnochio paradox, in which Pinnochio says my nose will grow. I think the paradox is supposed to arise when Pinocchio says, "My nose grows now." Do a Google search on "the Pinocchio paradox." I thought I had a hold of the paradox, but then I thought about it, and: Even if his nose grows, he does not have to tell a lie for his nose to grow, does he? Or are we making the assumption that the only way in which Pinnochio's nose could grow was if he was telling a lie?  But that can't be true, because by the paradox his nose grew when he was telling the truth. In simple, just because Pinnochio's nose grows, it does not have to imply he has told a lie. And what does this sentence is false mean? What are we saying is false? You could say this sentence is false: the boy is cold; but what do you mean when you say 'this sentence is false' is false? What does that actually mean? What is actually false? What are you assigning the word false to? By saying this setence is false is false, what is false? Think about it for a second. The sentence 'this setence is false' has no content, how can something with no content be false? In other words without even translating this setence is false into this setence is true, into this setence is false, etc, without even going through the paradox, you already have encountered a problem by trying to assign the value false to 'this setence is false.' What is 'this sentence,' there is no sentence, which is evident when you try to assign a false value to 'this sentence is false.' Interesting, by thinking deeply you're actually not thinking at all....... The Liar Sentence and the Strengthened Liar Sentence are pathological cases. I addressed them, as you noted in a later post than this one. The Pinocchio Paradox is a form of Liar Sentence, too, except that it's indexed to the particular speaker Pinocchio. We have to accept that there are some grammatically correct sentences that do not express propositions and therefore have no truth-values. Pinocchio may say, "My nose is growing," but since his nose grows when and only when he lies, "My nose is growing" is equivalent to "I am lying," which we already know is meaningless. The reason it sounds meaningful is that lying about subject X is usually meaningful. But lying about lying while lying is logically impossible, so "I am lying," construed not as "I am lying about tigers' being polka-dotted" logically meaningful but construed as "I am lying about lying when I say right now that I am lying" is logically meaningless.

In any case, Liar Sentences would at most violate the Law of the Excluded Middle, as they are neither true nor false; they do not violate the Law of Non-Contradiction, as they are not both true and false.