Axiomatising Questions

Accounts of the formal semantics of natural language often adopt a pre-existing framework. Such formalisations rely upon informal narrative to explain the intended interpretation of an expression - an expression that may have different interpretations in different circumstances, and may supports patterns of behaviour that exceed what is intended. This ought to make us question the sense in which such formalisations capture our intuitions about semantic behaviour. In the case of theories of questions and answers, a question might be interpreted as a set (of possible propositional answers), or as a function (that yields a proposition given a term that is intended to be interpreted as a phrasal answer), but the formal theory itself provides no means of distinguishing such sets and functions from other cases where they are not intended to represent questions, or their answers. Here we sketch an alternative approach to formalisation a theory of questions and answers that aims to be sensitive to such ontological considerations.