Ignorance in context: The interaction of modified numerals and QUDs

We argue for a purely pragmatic account of the ignorance inferences associated with superlative but not comparative modifiers (at least vs. more than). Ignorance inferences for both modifiers are triggered when the question under discussion (QUD) requires an exact answer, but when these modifiers are used out of the blue the QUD is implicitly reconstructed based on the way these modifiers are typically used, and on the fact that "at least n", but not "more than n", mentions and does not exclude the lower bound "exactly n". The paper presents new experimental evidence for the context-sensitivity of ignorance inferences, and also for the hypothesis that the higher processing cost reported in the literature for superlative modifiers is context-dependent in the exact same way.Keywords: superlative vs. comparative modifiers, ignorance inferences, questions under discussion, experimental semantics and pragmatic