A logic of interrogation should be internalized in a modal logic for knowledge

We propose a new, modal interpretation of questions. The idea of interpreting questions via modal logic goes back to Hintikka (1976) and Åqvist (1965), who interpret a question as a request for knowledge: “bring it about that I know whether . . . ”. Such a request is composed of an imperative part and an epistemic part. Focusing on the latter, we interpret a question as the knowledge condition required in order to answer it completely. We will reduce the epistemic part of the meaning of both yes-no questions and wh-questions to statements of the form “it is known whether” or “it is in the common ground that . . . ”. For instance, for a yes-no question such as Is Alice quitting?, the meaning is “it is known that Alice is quitting or it is known that Alice is not quitting”. Several different approaches have been suggested in linguistic semantics for modeling questions.