Question: Request for information.
It is an interesting fact that natural languages distinguish between statements and questions. The main distinction is along the line that a statement is used to give information and a question is used to ask for information. The distinction is easy enough to understand, but even so it is interesting that all natural languages (to my knowledge) have both statements and questions in grammatically distinct ways.
The simplest explanation seems to be that questions as a grammatical kind arise from attempts to simplify statements that request information: The statement "I would like to know whether it rains is true" is much more complicated than "Does it rain?"
There are a number of logical problems involved with questions, of which I mention two kinds.
1. Logic of questions: It is not at all clear or self-evident that there is a logic of questions as there is a logic of statements. There have been some attempts to set up logics of questions that are analogous to propositional logic, but they only arise in the 20th Century after logic was formalized.
The main reason that a logic of questions was not thought of by Aristotle or the Stoics, who had quite subtle and sensible ideas about the logic of statements, seems to be that questions are not used in chains of inferences. And this is so because inferences proceed in terms of premisses that are supposed to be true, which is a characteristic questions do not have, and statements may have.
Even so, supposing there is no real logic of questions in the sense that there is a logic of statements, there are interesting logical problems connected with questions.
One is that questions often involve assumptions, as in "Did you stop beating your wife?". This example shows that not all questions can be fairly answered with "yes" or "no", since either answer involves the admission that at one time you did beat your wife, and you may never have done so.
A somewhat interesting example for philosophers is the sort of question Charles II - a smart man, educated by Hobbes - liked to ask would-be savants "Why are fishes lighter in water?". Those who started given an explanation were dismissed as stupid or as frauds, since they accepted a tacit assumption. (Moral: First check whether purported facts are facts before you start explaining them.)
Another is the relation between questions and heuristics: What can one say about what sort of questions are helpful in certain kinds of problems to help one solve these problems? (See the mathematician Polya's excellent "How to solve it" and "Plausible Reasoning".)
A third, that also relates to heuristics, is that there are good and bad questions, profitable and unprofitable questions, and questions that can and cannot be answered, either for logical reasons, or because of the information one has or situation one is in.
2. Ultimate questions: Many questions - of the "Why?" kind - ask for explanations or reasons, and grammatically speaking one may immediately ask "Why?" about the answers that are given. Here immediately arise two points.
First, if a question is a request for information, a request to explain one's explanation or to give reasons for one's reasons may be quite justified, especially if the explanations or reasons were not clear or are doubtful, but usually changes the subject, often also in a radical way.
Second, there are questions which are ultimate in the sense that to question the answers to these asks for information that cannot be given. Examples are: "Why does the universe exist?" and "Why is there anything at all?" and "What is the cause of the first cause?"
The first two questions seem variations on one theme, and seem to request that one can step outside or beyond everything there is, as if there is room to do so - which there isn't. The third contradicts one or the other of common implicit assumptions about causes made in the question, namely that there is a first cause or that nothing is its own cause. (These assumptions may well be false - see God - but the question seems to involve the assumptions.)
In any case, two important insights about why-questions are that (1) one can only answer questions in terms of assumptions and (2) one can test assumptions by their logical consequences, but often not profitably by asking why: The reason for an assumption - that answers the "Why?" about it - is that the assumption helps to explain something one wants to explain. That is why one made it, and not to explain a further question about the assumption.
Hence the right answer to many questions for explanations is not a further explanation of one's given explanation, but a statement why one believes that the given explanation does what it is supposed to do (because it entails what one wants to explain) and why one believes it is credible (because it is not known to be false and can be supported with evidence).