Asymmetries in the scope behavior of quantifiers: A Synchronous Tree-Adjoining Grammar approach

Mike Freedman, Yale University

Abstract

It is well known that quantifiers in English, and many other languages, are not always interpreted with surface scope; with respect to other quantifiers and scopal elements that linearly precede or are hierarchically superior, quantifiers often can take wider scope. But it is equally well known that the different quantifiers of English differ in how they interact with other scope taking operators, with some quantifiers being able to take inverse scope and others not. This paper aims to primarily look at three different environments where there are scope asymmetries: (1) asymmetries between quantifiers in subject and object position; (2) asymmetries when a quantifier is in object position and there is sentential negation; and (3) asymmetries when there is a quantifier in subject position and sentential negation.

    1. A student read every paper.
      (∀ > ∃, ∃ > ∀)

    2. Every student read a/2 paper(s).
      (∀ > 2/∃, 2/∃ > ∀ )

    3. Every student read more than 2 papers.
      (∀ > 2+, *2+ > ∀ )

    1. John didn’t read every/each paper.
      (*∀ > ¬, ¬> ∀ )

    2. John didn’t read a/2 paper(s).
      (∃/2 > ¬, ¬ > ∃/2)

    3. John didn’t read more than 2 papers.
      (*2+ > ¬, ¬ > 2+)

    1. Every student didn’t read Huckleberry Finn.
      (¬ > ∀ , *∀ > ¬)

    2. A student didn’t read Huckleberry Finn.
      (∃ > ¬, ?¬ > ∃)

    3. Two students didn’t read Huckleberry Finn.
      (2 > ¬, ¬ > 2)

    4. More than 2 students didn’t read Huckleberry Finn.
      (2+ > ¬, ¬ > 2+)

I will show that two general principles can account for the data in (1), (2), (3) and extensions thereof. First, I assume that classes of quantifiers differ in the flexibility of their derivationally-constructed syntax-semantics mapping. Second, I assume that interpretive possibilities can be made unavailable because of competition from alternative derivations that provide the same interpretation, but are more simply derived. I implement these principles in synchronous tree adjoining grammar, a version of TAG where the derivation of semantic trees parallels the syntactic derivation.