A Calculus for Semantic Composition and Scoping

Certain restrictions on possible scopings of quantified noun phrases in natural language are usually expressed in terms of formal constraints on binding at a level of logical form. Such reliance on the form rather than the content of semantic interpretations goes against the spirit of compositionality. I will show that those scoping restrictions follow from simple and fundamental facts about functional application and abstraction, and can be expressed as constraints on the derivation of possible meanings for sentences rather than constraints of the alleged forms of those meanings. 1 A n O b v i o u s C o n s t r a i n t ? Treatments of quantifier scope in Montague grammar (Montague, 1973; Dowty et al., 1981; Cooper, 1983), transformational grammar (Reinhart, 1983; May, 1985; Helm, 1982; Roberts, 1987) and computational linguistics (Hobbs and Shieber, 1987; Moran, 1988) have depended implicitly or explicitly on a constraint on possible logical forms to explain why examples 1 such as (1) * A woman who saw every man disliked him are ungrammatical, and why in examples such as (2) Every man saw a friend of his (3) Every admirer of a picture of himself is vain the every.., noun phrase must have wider scope than the a... noun phrase if the pronoun in each example is assumed to be bound by its antecedent. What exactly counts as bound anaphora varies between different accounts of the phenomena, but the rough intuition is that semantically a bound pronoun plays the role of a variable bound by the logical form (a quantifier) of its antecedent. Example (1) above is then "explained" by noting that l I n all the examples t ha t follow, the pronoun and its intended antecedent are italicized. As usual, s tarred exampies are supposed to be u n g r m t i c a L its logical form would be something like 3W.WOMAN(W)~ (Vm.MAN(rn) ::~ SAW(W, rn))~