Negative Inquisitiveness and Alternatives-Based Negation

We propose some fundamental requirements for the treatment of negative particles, positive/negative polar questions, and negative propositions, as they occur in dialogue with questions. We offer a view of negation that combines aspects of alternative semantics, intuitionist negation, and situation semantics. We formalize the account in TTR (a version of type theory with records) [6, 8]. Central to our claim is that negative and positive propositions should be distinguished and that in order to do this they should be defined in terms of types rather than possible worlds. This is in contrast to [10] where negative propositions are identified in terms of the syntactic or morphological properties of the sentences which introduce them.