Deontic and Epistemic Modals in Suppositional [Inquisitive] Semantics

In Groenendijk and Roelofsen (2015) a suppositional semantics for implication is proposed within the general framework of inquisitive semantics. Our aim is to extend this semantic approach to epistemic and deontic modals, but, for the purposes of this short paper, we bracketed off inquisitive aspects of meaning. To illustrate the semantics we discuss a semantic solution to a Jackson  inspired puzzle which involves the interaction of implication and both types of modals.