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This paper develops a type of dynamic semantics in which contexts include not only information, but also questions, whose answers are ranked by strength. The questions can be local to the restrictor of a quantifier, and the quantifier can bind into them. The proposed framework satisfies several desiderata arising from quantificational expressions involving exclusives (e.g. only, just, mere and sole), allowing: (i) presupposed questions; (ii) presuppositional constraints on the strength ranking over the answers to the question under discussion; (iii) quantificational binding into such presupposed questions; and (iv) compositional derivation of logical forms for sentences.