An improper Treatment of Quantification in Ordinary English

In the currently standard ways of representing quantification in logical form, this sentence has 120 different readings, or quantifier scopings. Moreover, they are truly distinct, in the sense that for any two readings, there is a model that satisfies one and not the other. With the standard logical forms produced by the syntactic and semantic translation components of current theoretical frameworks and implemented systems, it would seem that an inferencing component must process each of these 120 readings in turn in order to produce a best reading. Yet it is obvious that people do not entertain all 120 possibilities, and people really do understand the sentence. The problem is not Just that inferencing is required for disamblguation. It is that people never do dlsambiguate completely. A single quantifier scoping is never chosen. (Van Lehn [1978] and Bobrow and Webber [1980] have also made this point.) In the currently standard logical notations, it is not clear how this vagueness can be represented. 1