Bilattices and the semantics of natural language questions

In this paper we reexamine the question of whether questions are inherently intensional entities. We do so by proposing a novel extensional theory of questions, based on a re-interpretation of the domain of type t as a bilattice rather than the usual boolean interpretation. We discuss the adequacy of our theory with respect to the adequacy criteria imposed on the semantics of questions by (Groenendijk and Stokhof 1997). We show that the theory is able to account in a straightforward manner for some complex issues in the semantics of questions including coordinated questions, combined indicative and interrogative sentences, questions with quantifiers, and the impossibility of negating questions.