Quantifiers, Anaphora, and Intensionality

Abstract

The relationship between Lexical-Functional Grammar (LFG) functional structures (f-structures) for sentences and their semantic interpretations can be formalized in linear logic in a way that correctly explains the observed interactions between quantifier scope ambiguity, bound anaphora and intensionality. Our linear-logic formalization of the compositional properties of quantifying expressions in natural language obviates the need for special mechanisms, such as Cooper storage, in representing the scoping possibilities of quantifying expressions. Instead, the semantic contribution of a quantifier is recorded as a linear-logic formula whose use in a proof will establish the scope of the quantifier. Different proofs can lead to different scopes. In each complete proof, the properties of linear logic ensure that quantifiers are properly scoped. The interactions between quantified NPs and intensional verbs such as ’’seek‘‘ are also accounted for in this deductive setting. A single specification in linear logic of the argument requirements of intensional verbs is sufficient to derive the correct reading predictions for intensional-verb clauses both with nonquantified and with quantified direct objects. In particular, both de dicto and de re readings are derived for quantified objects. The effects of type-raising or quantifying-in rules in other frameworks just follow here as linear-logic theorems. While our approach resembles current categorial approaches in important ways (Moortgat, 1988, 1992a; Carpenter, 1993; Morrill, 1994) it differs from them in allowing the greater compositional flexibility of categorial semantics (van Benthem, 1991) while maintaining a precise connection to syntax. As a result, we are able to provide derivations for certain readings of sentences with intensional verbs and complex direct objects whose derivation in purely categorial accounts of the syntax-semantics interface appears to require otherwise unnecessary semantic decompositions of lexical entries.