A Deductive Account of Scope

this paper, we argue that the grammatical scopings of quantifiers should be treated by deductive methods. To this end, we propose a type-theoretic, categorial logic. This logic captures the broad range of allowable scopings, as well as correctly imposing constraints on impossible ones. It is particularly simple, being built out of dual introduction (proof) and elimination (use) schemes for complementation, unbounded dependencies, boolean coordination and scoping. The second theme of this paper is an argument that a number of previously proposed grammatical operations are best seen as approximations of the logical approach. Here we consider the quantificational rules of Montague's quantifying-in and type raising, and Cooper's realization of these rules by means of storage in a phrase structure setting. Montague's rules are very similar to a sequent-based presentation of our logic, whereas Cooper's storage method appears to be an approximation of the same logic in natural deduction format. We also explicate th