According to formal sementics propositions (semantic term for "sentences", "clauses") have truth value. The truth value shows whether sentence is true or false and it is denoted as 1 or 0. What about sentences that have failed in presupposition? Do they have truth value? Ex: The king of USA lives in NY. Here, the interlocutor presupposes that the USA is ruled by the king, and s/he fails in his/her presupposition. So what be the truth value of this proposition? I think that it is impossible for proposition that has failed in presupposition to have a truth value but I am not sure.
Note: here I am talking about the direct meaning of the word "king", not possible metaphoric.