Dynamic generalised quantifiers and hypothetical contexts

We shall consider a formulation of generalised quantifiers using type theory with records (TTR). TTR follows closely the development of record types in Martin-L¨of or constructive type theory but differs in that the type theory is defined on a classical set theoretic basis. This means that the classical set-theoretic approach to generalised quantifiers can be imported into the type theoretic framework. The result is, I believe, equivalent to the proposal for dynamic generalised quantifiers in Chierchia (1995). The use of dependent types provides us with an elegant approach to the formulation of dynamic quantifiers. We use a notion of hypothetical context which we have used elsewhere to give accounts of intentional identity, answers to questions and information state updates in dialogue management. We suggest that this points towards a general theory of hypothetical context in natural language. We suspect also that our analysis using records will support analyses of common noun phrase and verb-phrase anaphora and also facilitate representations which are underspecified with respect to quantifier scope, though we leave the investigation of this to future research.
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