Quantifier scope ambiguity is one of the most challenging problems in deep language understanding systems. As a result, most deep understanding systems use a constraint-based scope-underspecified model to represent the output of the syntax/semantics interface, where constraints on the relative order of quantifiers can be further added to the representation at the deeper processing levels (e.g. discourse or pragmatics) in order to rule out unwanted readings. A major algorithmic problem to be solved for such a representation is the satisfiability problem, that is whether there exists any solution satisfying all the constraints. We present the first tractable underspecification framework, broad enough to provably cover all coherent natural language sentences under a linguistically justified notion of coherence.
In the second part of the talk, I discuss automatic scope disambiguation. We have built the first scope-disambiguated corpus of English text, in which every pair of scope-bearing elements in a sentence (including all noun phrases and scopal adverbials) are examined for possible scope interactions. I present the challenges we faced in building this corpus and our solutions to address those. Given the scope-disambiguated corpus, we define learning to disambiguate quantifier scoping, as learning to build partial orders. We achieve a relatively high F-score on retrieving the scope preferences on our corpus using a preliminary supervised model. The early results are promising, encouraging further studies in this area.