Quantifiers, anaphora, and intensionality

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.
Keywords Quantification   anaphora   intensional verbs   lexical-functionalgrammar   linear logic   syntax-interface
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DOI 10.1023/A:1008224124336
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Eric McCready (2008). What Man Does. Linguistics and Philosophy 31 (6):671-724.
Miltiadis Kokkonidis (2008). First-Order Glue. Journal of Logic, Language and Information 17 (1):43-68.

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