In today’s NYT, the headline
AirAsia Jet That Crashed Had Lacked All Clearances to Fly, Regulators Say
This is a classical case of scope ambiguity, involving negation and universal quantification:
in the domain J of jets and C of clearances C for jets to fly, for some specific j ∈ J, the contrast is between
NEG-Q: ¬ (∀x ∈ C)) j(x) — it’s not the case that j has every C; there are clearances that j doesn’t have
and
Q-NEG: (∀x ∈ C) ¬ j(x) — for any C, j does not have C; j has no clearance at all
I am strongly inclined to read the headline as Q-NEG, but given context either interpretation is possible.
[Amendment 1/7/14: It’s clear in the story that the intended interpretation of the headline is NEG-Q: there were clearances the jet didn’t have, so it should not have been allowed to take off.]
I’m no semanticist, but it seems clear to me that the choice of lexical items biases the interpretation considerably: lack all tilts things to Q-NEG, not have all to NEG-Q. No doubt there is significant technical literature on the matter, but, as I said, I’m not a semanticist.