The semantic contribution of any in existential modal sentences, as in Mary is allowed to read any book, is famuously stronger than that of simple existential quantification. This can be captured by assuming that the existential import of any can be strengthened by exhaustification (e.g., Chierchia 2013, Crnič 2019 for different implementations). We derive new predictions from this assumption and the premise that some expressions in natural language have divisive denotations (Link 1983, Bunt 1985, Landman 1989, among others). Prospects for explaining the variation among NPIs by recourse solely to their semantic properties are discussed in light of our conclusions.

Link to the paper on Lingbuzz