I would like to ask if anyone has seen elsewhere this variation on the standard truth tellers/liars kind of puzzle.
In the usual repertoire it is assumed that every person questioned knows the answer to every question asked. We now assume that this need not be the case; and that if a truth-teller is asked a question to which he does not know the answer, he will truthfully reply "I don't know", while a liar will never admit to not knowing.
This can still be formulated in various ways: here is a specific example and a puzzle.
(But please note: my question is not to solve the puzzle but to ask if anyone has seen anything like it before.)
In a certain town each of the inhabitants is either a truth-teller or a liar; however this does not mean that everyone is actually able to answer every question they are asked. If a truth-teller is absolutely certain of the answer to a question, he will give that answer; if not, he will say, "I don't know." On the other hand, a liar will never truthfully admit to not knowing something: he will give an answer that he knows is false, if any, but if there is nothing that he is certain is false then he will give a randomly chosen answer (possibly even, by accident, the true answer). Moreover, everyone in this town can instantly deduce the logical consequences of any facts they know.
I meet four inhabitants of this town and ask them, "How many of you four are truth-tellers?"
Kevin says, "I don't know"; then Laura says, "One"; then Mike says, "None." Noela, however, is asleep. Fortunately I don't need to wake her up, since I can already tell whether she is a truth-teller or a liar. Which?