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In this paper I argue for a new constraint on questions, namely that a question denotation (a set of propositions) must map to a partition of a Stalnakerian Context-Set by point-wise exhaustification (point-wise application of the function Exh). The presupposition that Dayal attributes to an Answer operator follows from this constraint, if we assume a fairly standard definition of Exh (Krifka, 1995). But the constraint is more restrictive thereby deriving the sensitivity of higher order quantification to negative islands (Spector, 2008).
Moreover, when combined with recent proposals about the nature of Exh - designed primarily to account for the conjunctive interpretation of disjunction (e.g. Bar-Lev and Fox, 2017) - Dayal’s presupposition follows only in certain environments. This observation allows for an account of the "mention-some" interpretation of questions that makes specific distributional predictions.
We present an experiment which tests children’s comprehension of the requirements of use of pronouns and definites. An adult-like use of definites and pronouns imposes different but related requirements. In the case of definites, a unique referent is required in the context, whereas in the case of a pronoun, the referent in the context has to be salient. In this experiment, we use a novel word task to test three-year-olds’ sensitivity to these requirements. Our results show that children are adult-like in their sensitivity to salience in their comprehension of pronouns, compared to definites. However, they failed to show sensitivity to the uniqueness requirement on the use of definites.