Downward monotonicity in questions

I show that the hypothesis that downward monotonicity is required for the licensing of negative polarity items (Fauconnier 1975, 1979, Ladusaw 1979) can account for why they appear in interrogatives. In particular, I show that strong exhaustive answers to questions with negative polarity items are downward monotone using three ingredients: (i) interrogatives denote sets of propositions (Hamblin 1973, Karttunen 1977), (ii) negative polarity items introduce alternatives and thereby enrich this denotation, and (iii) an answer operator (Heim 1994, Beck and Rullmann 1999) delivers the strong exhaustive answer. Among other things this accounts for Guerzoni and Sharvit’s 2007 observation that only interrogatives embedded under predicates allowing for a strong exhaustive interpretation of that question license negative polarity items.