_Wh_-questions with the modal verb _can_ admit both mention-some (MS) and mention-all (MA) answers. This paper argues that we should treat MS as a grammatical phenomenon, primarily determined by the grammar of the _wh_-interrogative. I assume that MS and MA answers can be modeled using the same definition of answerhood (Fox in Mention-some interpretations, MIT seminar, 2013 ) and attribute the MS/MA ambiguity to structural variations within the question nucleus. The variations are: (i) the scope ambiguity of the higher-order _wh_-trace (...) and (ii) the absence/presence of an anti-exhaustification operator. However, treating MS answers as complete answers in this way contradicts the widely adopted analysis of uniqueness effects in questions of Dayal (Locality in _wh_ quantification: Questions and relative clauses in Hindi, 1996 ), according to which the uniqueness effects of singular _which_-phrases arise from an exhaustivity presupposition, namely that a question must have a unique exhaustive true answer. To solve this dilemma, I propose that question interpretations presuppose Relativized Exhaustivity: roughly, the exhaustivity in questions is evaluated relative to the accessible worlds as opposed to the anchor/utterance world. Relativized Exhaustivity preserves the merits of Dayal’s exhaustivity presupposition while permitting MS; moreover, it explains the local-uniqueness effects in modalized singular _wh_-questions. (shrink)

This paper revisits two fundamental issues in question semantics—what does a question mean, and how is this meaning compositionally derived? Drawing on observations with the distribution of wh-words in questions and free relatives as well as quantificational variability effects in question-embeddings, I argue that the nominal meanings of short answers must be derivable from question denotations, which therefore calls for a categorial approach to defining questions, including embedded questions. I provide a novel hybrid categorial approach to compose questions. This approach (...) overcomes the problems with traditional categorial approaches in defining bare wh-indefinites, composing multi-wh questions, and accounting for coordinations of questions. (shrink)