Many syntactic and semantic studies have focused on the distribution of closed-class lexical noun phrases (NPs) such as "her, herself, and each other." Recent work has demonstrated that many other NPs are also referentially dependent. A model-theoretic semantic analysis of a number of such referentially dependent NPs is presented. These NPs are interpreted as functions that map two-place relations onto predicates that are true or false of sets of individuals. The analysis allows NPs to be classified according to their degree of dependency as specified by four semantic conditions on higher-order functions. Furthermore, distinctions made by these semantic conditions correlate with differences in syntactic distribution. It is also shown that properties associated with bound variable pronouns generalize to the full class of referentially dependent NPs. For example, referentially dependent NPs do not have a bound reading in weak crossover contexts. However, unlike pronouns, these higher-order NPs appear to discriminate between crossover environments at surface structure and logical form. (MSE)