, Volume 6, Issue 3, pp 219-273

Quantifiers, Anaphora, and Intensionality

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Abstract

The relationship between Lexical-Functional Grammar (LFG) functional structures (f-structures) for sentences and their semanticinterpretations can be formalized in linear logic in a way thatcorrectly explains the observed interactions between quantifier scopeambiguity, bound anaphora and intensionality.

Our linear-logic formalization of the compositional properties ofquantifying expressions in natural language obviates the need forspecial mechanisms, such as Cooper storage, in representing thescoping possibilities of quantifying expressions. Instead, thesemantic contribution of a quantifier is recorded as a linear-logicformula whose use in a proof will establish the scope of thequantifier. Different proofs can lead to different scopes. In eachcomplete proof, the properties of linear logic ensure thatquantifiers are properly scoped.

The interactions between quantified NPs and intensional verbs such as’’seek‘‘ are also accounted for in this deductive setting. A singlespecification in linear logic of the argument requirements ofintensional verbs is sufficient to derive the correct readingpredictions for intensional-verb clauses both with nonquantified andwith quantified direct objects. In particular, both de dictoand de re readings are derived for quantified objects. Theeffects of type-raising or quantifying-in rules in other frameworksjust follow here as linear-logic theorems.

While our approach resembles current categorial approaches inimportant ways (Moortgat, 1988, 1992a; Carpenter, 1993; Morrill, 1994)it differs from them in allowing the greater compositional flexibility ofcategorial semantics (van Benthem, 1991)while maintaining a precise connection to syntax. As a result, we areable to provide derivations for certain readings of sentences withintensional verbs and complex direct objects whose derivation inpurely categorial accounts of the syntax-semantics interface appearsto require otherwise unnecessary semantic decompositions of lexicalentries.