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


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.

4 Responses to “Scoping”

  1. Emily M. Bender Says:

    Actually, my current best understanding of how English compositional semantics works would allow only Q-NEG for ‘lack’, since the negation is expressed as a verb and not as a negative operator. If there’s discussion out there that supports the view that this particular sentence is ambiguous, I’d be really interested to see it!

    • arnold zwicky Says:

      I should have been clearer. The intended interpretation in this case was clearly NEG-Q: the jet didn’t have all of its clearances. That called me up short.

      • Emily M. Bender Says:

        Then I’m even more curious, because I would have thought NEG-Q isn’t possible there…

  2. Robert Coren Says:

    The Boston Globe did the same thing (slightly different wording), and as I noted on Facebook, to me “lacked all” means “had none”. The context makes it clear that that’s not what they meant, but I maintain that it is what the headline said.

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