Ignorance inferences and roundness effects with modified numerals
Modified numerals like "at least four" or "more than three" are notorious for a number of puzzles they pose to the theory of implicatures. I will first present experimental results that clarify the ignorance implicatures of 'at least' and 'more than' and their dependence on the Question under Discussion (QUD), and demonstrate a task effect that has led to seemingly contradicting results in the previous empirical literature: in a truth-value judgment task, a clear difference is observed between 'at least' and 'more than', while an inference task shows no such contrast. I will then present a new account of modified numerals based on a classic semantics and a pragmatics formalized in Optimality Theory. The task effect can be captured under the assumptions that participants in the inference task behave as sub-rational listeners (who do not draw Bayesian inferences from the speaker's utterance but adopt the simpler strategy of flipping the OT tableaux). Most importantly, the basic model captures all standard properties of modified numerals with minimal assumptions: obligatory ignorance with 'at least' but not with 'more than', QUD effects, roundness sensitivity of 'more than' but not 'at least', and the PPI behavior of 'at least'. The account can be extended to partial orders ("at least Ann and Bill passed the exam") and can capture upper-bound readings of 'more than' ("more than 80" ~> no more than 100).
