Computing Quantifier Scope for Natural Language using Natural Logic
Ambiguities arising from alternations of scope in interpretations for multiply quantified sentences appear to require grammatical operations that compromise the strong assumptions of syntactic/semantic transparency and monotonicity underlying the Frege-Montague approach to the theory of grammar. Examples that have been proposed include covert movement at the level of logical form, abstraction or storage mechanisms, and proliferating type-changing operations.
The paper examines some interactions of scope alternation with syntactic phenomena including coordination, binding, and relativization. Using Combinatory Categorial Grammar (CCG) as a grammatical framework, and a "natural" logic that eliminates most quantifiers, the talk presents an account of quantifier scope ambiguities according to which the available readings are projected directly from the lexicon by the combinatorics of the syntactic derivation, without any independent manipulation of logical form and without recourse to otherwise unmotivated type-changing operations.
As a direct result, scope ambiguity can be efficiently processed computationally using packed representations, from which all and only the available readings can be simply enumerated for purposes of natural language processing.
M. Steedman (2012) Taking Scope: The Natural Semantics of Quantifiers. MIT Press: Cambridge MA (to appear).