Yes, knowing that ~P and not knowing P are clearly and fundamentally different things in the world of classical logic. (I'm not an expert, but I know this much.

Yes, knowing that ~P and not knowing P are clearly and fundamentally different things in the world of classical logic. (I'm not an expert, but I know this much.) It's hacky computing systems like Prolog and the relational model and/or SQL which erase the distinction. https://en.wikipedia.org/wiki/Closed-world_assumption https://en.wikipedia.org/wiki/Closed-world_assumption The law of the excluded middle only says that at least one of P and ~P must be true, and doesn't at all promise that we will necessarily be able to conclude which one.