K. and H. propose a formal semantics for questions and answers which enables them to explain in what sense a question like 'Did it surprise the professors that every student passed?' carries a presupposition like 'Every student passed'. The question-answer relation is treated as a new sort of logical relation. It is shown that the presuppositions of questions are definable in terms of the presuppositions of the question-answer pairs, which are said to carry truth values so that the old definition of presupposition (in terms of truth values) obtains.