Quantifiers, Anaphora, and Intensionality
 Mary Dalrymple,
 John Lamping,
 Fernando Pereira,
 Vijay Saraswat
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Abstract
The relationship between LexicalFunctional Grammar (LFG) functional structures (fstructures) 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 linearlogic 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 linearlogicformula 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 intensionalverb clauses both with nonquantified andwith quantified direct objects. In particular, both de dictoand de re readings are derived for quantified objects. Theeffects of typeraising or quantifyingin rules in other frameworksjust follow here as linearlogic 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 syntaxsemantics interface appearsto require otherwise unnecessary semantic decompositions of lexicalentries.
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 Title
 Quantifiers, Anaphora, and Intensionality
 Journal

Journal of Logic, Language and Information
Volume 6, Issue 3 , pp 219273
 Cover Date
 19970701
 DOI
 10.1023/A:1008224124336
 Print ISSN
 09258531
 Online ISSN
 15729583
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Quantification
 anaphora
 intensional verbs
 syntaxinterface
 lexicalfunctionalgrammar
 linear logic
 Authors

 Mary Dalrymple ^{(1)}
 John Lamping ^{(1)}
 Fernando Pereira ^{(2)}
 Vijay Saraswat ^{(2)}
 Author Affiliations

 1. Xerox PARC, Palo Alto, CA, 94304, U.S.A.
 2. AT&T Research, Murray Hill, NJ, 07974, U.S.A.