The logic of scope in natural language


Sometimes the dog wags the tail:

(1) Ann gave Bill cookies. == gave bill cookies ann

And sometimes the tail wags the dog:

(2) Ann gave everyone cookies. == everyone (λx. gave x cookies ann)

In (1), the functor gave applies to its arguments in the normal way. In (2), the argument everyone somehow manages to take control over the entire sentence that contains it, quantifying over all the people Ann may have given cookies, and substituting those individuals into the original argument position one by one. In other words, an embedded expression can take scope over a larger expression that contains it. Scope-taking is a robust and pervasive feature of English and many other natural languages. The usual account of scope-taking in linguistics is a quasi-logical rule known as Quantifier Raising, which licenses an inference from the left-hand side of (2) to the right-hand side. But Quantifier Raising is never studied as an integral part of a formal logic. In the tradition of Lambek and of Moortgat, I will present a substructural logic that characterizes scope-taking. As an example of one of the insights that can come from taking a formal logical approach, Quantifier Raising on its own does not guarantee any limit on the length of a derivation; in contrast, the logic here is decidable, leading to an effective parsing strategy. I will also explain how the logic makes explicit use of continuations, a concept from the theory of computer programming languages: roughly, the tail is the scope-taking expression, and the rest of the dog is its continuation. So what is the logic of scope? Here is my answer: reasoning about scope-taking is reasoning about continuations.

[Note from local organization: slides available here.]

Lecture date: 
Thursday, August 6, 2015 - 19:00 to 20:30
Auditori Poblenou