Modified numerals, such as at least three and more than five, are known to sometimes give rise to ignorance inferences. However, there is disagreement in the literature regarding the nature of these inferences, their context dependence, and differences between at least and more than. We present a series of experiments which sheds new light on these issues. Our results show that (a) the ignorance inferences of at least are more robust than those of more than, (b) the presence and strength of the ignorance inferences triggered by both at least and more than depends on the question under discussion (QUD), and (c) whether ignorance inferences are detected in a given experimental setting depends partly on the task that participants are asked to perform (e.g., an acceptability task versus an inference task). We offer an Optimality Theoretic account of these findings. In particular, the task effect is captured by assuming that in performing an acceptability task, participants take the speaker’s perspective in order to determine whether an expression is optimal given a certain epistemic state, while in performing an inference task they take the addressee’s perspective in order to determine what the most likely epistemic state of the speaker is given a certain expression. To execute the latter task in a fully rational manner, participants have to perform higher-order reasoning about alternative expressions the speaker could have used. Under the assumption that participants do not always perform such higher-order reasoning but also often resort to so-called unidirectional optimization, the task effect finds a natural explanation. This also allows us to relate our finding to asymmetries between comprehension and production that have been found in language acquisition.

已知修改后的数字，例如至少 3和超过 5，有时会引起无知的推论。然而，关于这些推论的性质、它们的上下文依赖性以及至少和超过之间的差异，文献中存在分歧。我们提出了一系列实验，为这些问题提供了新的思路。我们的结果表明，（a）所述的无知推论至少比的更健壮超过，（b）该无知推论的存在和强度双方触发至少和多于取决于所讨论的问题 (QUD)，以及 (c) 在给定的实验环境中是否检测到无知推理部分取决于参与者被要求执行的任务（例如，可接受性任务与推理任务）。我们提供了这些发现的最优理论解释。特别地，任务效果是通过假设在执行可接受性任务时，参与者采取说话者的观点来确定给定某种认知状态的表达是否最优，而在执行推理任务时，他们采取收件人的观点以确定说话者最可能的认知状态是什么，给出了某种表达。为了以完全理性的方式执行后一项任务，参与者必须对说话者可能使用的替代表达进行高阶推理。假设参与者并不总是执行这种高阶推理，但也经常求助于所谓的单向优化，任务效果找到了一个自然的解释。这也使我们能够将我们的发现与语言习得中发现的理解和产生之间的不对称联系起来。