Universal quantification as iterated conjunction

I analyze distributive universal quantifiers like ‘each’ and ‘every’ in terms of iterated dynamic update. I argue that this minor adjustment to standard dynamic setups has at least two empirical advantages. First, because information flows forward through the universal computation, anaphoric elements can assume “quantifier-internal” interpretations [1]. Second, because conjunction is usually analyzed as relation composition over input and output structures, the emerging representations are in a sort of disjunctive normal form that facilitates “functional” readings of indefinites. Following [13], I suggest that these two phenomena are closely related, and argue that the current approach which generates the two readings via the same compositional mechanism is simpler, more general, and more empirically adequate than the alternatives.