Comment by ColinWright

I read statement "All my hats are green" as meaning:

For every hat H that I have, H is green.

If I have no hats, this statement is true, just as

* the empty sum is 0,

* the empty product is 1,

* the empty AND is True, and

* the empty OR is False.

So with this interpretation, the liar having no hats would make the statement true.