The definition of a proposition is as follows
A proposition is a declarative statement that is either true or false but not both
Let us categorize declarative statement in to four types
Type 1: True declarative statements
Ex: 2 + 3 = 5
Type 2: False declarative statement
Ex: 2 * 3 = 5
Type 3: Dual declarative statement (both true and false)
Ex: x + 2 = 5
Type 4: Declarative statement that is neither true nor false
My doubt is whether type 4 exists or not? Does type 4 comes under paradox? Are both(type 4 and paradox) same? Are the following paradoxes come under type 4?
This statement is false.
I know that i know nothing
If not, provide an example for type 4?
There are many examples of such statements. Generally, ill-defined statements fall under the category of: 'neither true nor false'.
For example, consider this statement: $$\text{This ice-cream is tasty} $$ This cannot be true or false without an appropriate definition of "tasty" as applied to "the icecream." And yes, your first example statement also falls under this category.
Also, see here, and these previous MSE questions:
Link 1
Link 2