Considered generally, though, if I ask a true/false question then read your answer from a single bit, it may be the case that there is no possible way for you to not lie to me.
Then you are not asking a binary question. If there is, for example, the possibility that I might not know the answer, then you are actually asking two dependent questions - do you know the answer and if so, what is the answer.
That question is obviously made as a trap because you can defend both answers. Yes, I am not beating her and actually never have, focusing on the current state. No, I did not stop because I never started, focusing on the state change. And the other party can do the same. No, so you did not stop beating your wife, so you are beating her. Yes, so you stopped beating your wife, then must have beaten here in the past.
The correct response is of course that the question is not applicable because it assumes a state - the wife has been beaten in the past - that does not match reality. And not applicable is not a third answer to the question, it is a statement about the question itself. So in contexts where non-applicable binary question might occur, you have to first determine whether the question is applicable before proceeding to answer the question.
It is reasonable to map the world in binary logic. but the map logic must be correct and raising an error when it is not is important.