Questions as information types

This paper argues that there is an important role to be played by questions in logic, both semantically and proof-theoretically. Semantically, we show that, by generalizing the classical notion of entailment to questions, we can capture not only the standard relation of logical consequence, which concerns specific pieces of information, but also the relation of logical dependency, which concerns information types. Proof-theoretically, we show that questions may be used in inferences as placeholders for generic information of a given type; by manipulating such placeholders, we may construct formal proofs of dependencies. Finally, we show that such proofs have a specific kind of constructive content: they do not just witness the existence of a certain dependency, but actually encode a method for computing it.