Partition by exhaustification: comments on Dayal 1996

In this paper I argue for a new constraint on questions, namely that a questiondenotation (a set of propositions) must map to a partition of a Stalnakerian Context-Set bypoint-wise exhaustification (point-wise application of the function Exh). The presuppositionthat Dayal attributes to an Answer operator follows from this constraint, if we assume a fairlystandard definition of Exh (Krifka, 1995). But the constraint is more restrictive therebyderiving the sensitivity of higher order quantification to negative islands (Spector, 2008).Moreover, when combined with recent proposals about the nature of Exh – designedprimarily to account for the conjunctive interpretation of disjunction (e.g. Bar-Lev and Fox,2017) – Dayal’s presupposition follows only in certain environments. This observationallows for an account of the “mention-some” interpretation of questions that makes specificdistributional predictions.Keywords: exhaustivity, Free Choice, maximality, higher-order quantification, mentionsome,negative-islands, partition, scalar implicatures, uniqueness.