Do modals take propositions or sets of propositions? Evidence from Japanese `darou'

The Japanese modal particle darou can take either a declarative or an interrogative prejacent (Hara 2006; Hara & Davis 2013). We point out, however, that its interrogative-embedding use cannot be reduced to its declarative-embedding use. This is problematic under the standard assumption that modal operators always apply to propositions, but not under more recent proposals which take modal op- erators to apply to sets of propositions. We develop a detailed account of darou, capturing its non-reductive nature as well as its puzzling interaction with intonation (Hara 2015).