The semantics of minimal requirements

The sentence in (1) is predicted to be true by the theory of von Fintel and Iatridou 2005. In their account, need receives the standard analysis of a universal quantifier over worlds. To p, need to q is true in w iff q is true all the worlds in the modal base of w where p is true: !to p, need to q"w = 1 ⇔ ∀w′[w′ ∈ ∩f(w) & p(w′) → q(w′)]. Given what we know about the productivity of the workers, we come to expect that worlds in which the project is finished in 4 days are worlds in which 18 workers are involved. Now consider, (2).