Recent work shows that downward entailment (DE) cannot be the right semantic domain that licenses negative polarity items (NPIs). Zwarts (1995), Giannakidou (1998), among others, argue that NPIs are licensed in non-veridical domains, those that do not entail or presuppose the truth of the propositions they embed. In this paper, based on empirical facts, I argue that DE theory is the right analysis for Jordanian Arabic. I propose an analysis of NPI licensing in which three components of grammar interface: syntax, semantics and pragmatics. Semantics defines the class of NPI licensors, pragmatics forces quantificational closure of NPIs, and syntax executes the licensing via AGREE between a phasal head and the NPI. The analysis contributes to the debate on what components of grammar are responsible for NPI licensing and provides a new perspective on the interface between different components of grammar.