I've sometimes heard people use rather for connecting two sentences where the second one sets counterexample to something negated in the first.
This is not a meaningful sentence. Rather, it's an example.
First, I would like to find out whether this is a proper usage of the word. Finally, if it is, I would like to find out how to properly write such sentences (the above example is likely grammatically incorrect). I am especially interested whether they can, or even should for that matter, be separated by a semicolon rather than by a period.