A theory of focus with negative quantifiers

A J Sanford, L M Moxey and E J Dawydiak
University of Glasgow

In expressing quantitative statements, like "contains 10% fat", or "90% fat free", the perspectives introduced by any kind of statement have great practical implications. We shall describe a theory of how perspectives occur in quantified statements. Earlier work has shown that negative quantifiers give a different pattern of focus from positive ones (Moxey & Sanford, 1987). In (1), "they" refers to the people who went to match;in (2) "they "refers to people who didn't:

(1) Nearly all of the fans went to the match. They wanted to see it live.
(2) Not quite all of the fans went to the match. They watched it on TV instead.

These patterns are observed in continuations and reading times (Sanford et al, 1996).

We present a theory that explains the phenomena in terms of some negative quantifiers producing mental representations that correspond to S-negation (sentential negation, exemplified by

Not quite all of the fans did X -> It is not the case that (all of the fans did X).

This idea can readily explain why some negative (monotone decreasing) quantifiers do not lead to complement reference, such as "At most 10 of the (x)".

In four experiments, we compared the likelihood of participants scoring linguistic tests of S-negation as showing s-negation to have taken place, such as.

Not quite all of the fans went to the match, and *so/neither did the commentators.

Here, checking "neither" indicates s-negation (Horn, 1989).

We compared this likelihood with the probability of obtaining complement set reference patterns, indexed by the following task:

Not many of the fans went to the match, including John. Did John go to the match?

We explored a very wide range of quantifiers, and demonstrated a tight linear relation between S-negation, and complement set attachment. Both simple judgements, and reading time data show that a model based on S-negation exactly (r = .98) explains the data. A full model, based on the association of S-negation to a psychologically-motivated process of denial, will be described. The model links types of continuation as well as patterns of focus
to S-negation through a mechanism based on denial of presupposition.

References

Horn, Horn, L. R. (1989). A Natural History of Negation. Chicago: University of Chicago Press.

Moxey, L M and Sanford, A J (1987). Quantifiers and Focus, Journal of Semantics, 5, 189 - 206.

Sanford, A. J., Moxey, L. M. and Paterson, K. B. (1996) Attentional focussing with quantifiers in production and comprehension. Memory and Cognition, 24, 144-155.