To interpret NPs on non-subject position one extends the domain of type <1 > quantifiers: they are treated as reducers of arity of their arguments, that is as functions which when applied to n-ary relations give (n-1)ary relations.
when they apply to binary relations (denotations of transitive VPs) they give sets (considered as unary relations) as result (and sets are denotations of intransitive VPs).