What is the difference between Applicative Universal Grammar and Combinatory Categorial Grammar? They both use type inference rules to define their grammars. Is it simply that CCG uses combinatory calculus instead of lambda calculus? Does it have more to do with AUG focusing on being universal? Other than the addition of composition and type-raising in CCG they seem almost identical. But those seem implicit in AUG too, so what am I missing here?