propositional logic , don't know the answer Is the assertion "This statement is false" a proposition?

I think that it is a proposition because this("This Statement is false") may have truth values. the statement may be true or maybe false. therefore its proposition. but i don't know if i am correct. please correct me , if i'm wrong.

please explain the answer.
In modern logic, the predicate $True(\quad)$ is of &quot;difficult usage&quot;, because in using it in a formal language we will encouter the problems connected with Self-Reference.
You can see in SEP the entry about the Liar Paradox ; it gives a review of most of philosophical and logical debates about this paradox.
Regarding &quot;standard&quot; logical approach to the Liar, see :

4.2.1 Tarski's hierarchy of languages
Traditionally, the main avenue for resolving the paradox within classical logic is Tarski's hierarchy of languages and metalanguages. Tarski concluded from the paradox that no language could contain its own truth predicate (in his terminology, no language can be ‘semantically closed’).
Instead, Tarski proposed that the truth predicate for a language is to be found only in an expanded metalanguage. For instance, one starts with an interpreted language $L_0$ that contains no truth predicate. One then ‘steps up’ to an expanded language $L_1$, which contains a truth predicate, but one that only applies to sentences of $L_0$. With this restriction, it is easy enough to define a truth predicate which completely accurately states the truth values of every sentence in $L_0$ and yields no paradox. Of course, this process does not stop. If we want to describe truth in $L_1$, we need to step up to $L_2$ to get a truth predicate for $L_1$. And so on. The process goes on indefinitely. At each stage, a new classical interpreted language is produced, which expresses truth for languages below it.
Why is there no Liar paradox in this sort of hierarchy of languages? Because the restriction that no truth predicate can apply to sentences of its own language is enforced as a syntactic one. Any sentence $\varphi$ equivalent to $\lnot Tr(\ulcorner \varphi \urcorner)$ is not syntactically well-formed. There is no Liar paradox because there is no Liar sentence. See the entries on Tarski and Tarski's truth definitions for more on Tarski's views of truth.
Statements such as "this statement is false" and "Window is half open" are those which cannot have fixed truth values. Hence these are not propositions.
Reference:
http://mathworld.wolfram.com/Proposition.html

P.S. By not fixed truth values I mean its debatable. The glass is half full ;)