Is there a paper that formalizes questions from a mathematical perspective?

Solution 1:

I think that, per the comments above, the answer is definitely yes. Indeed, a quick glance suggests that there is a fair amount of work on the topic which cannot be summarized in an MSE-fitting answer. However, I can mention a couple good starting sources:

• The Stanford Encyclopedia article "Questions" has a lot on the topic as usual (and more broadly the term "erotetic logic" is also a fruitfully searchable phrase).

• Wisniewski has a book The posing of questions in the Synthese library which seems very on topic.

So that's a freely-available survey article with a rich bibliography, a key term, and a monograph in a respected book series - probably a decent starting point!