Disjunctions in the scope of possibility modals give rise to a conjunctive inference, generally referred to as ‘free choice.’ For example, Emma can take Spanish or Calculus suggests that Emma can take Spanish and can take Calculus. This inference is not valid on standard semantics for modals in combination with a Boolean semantics for disjunction. Hence free choice has sparked a whole industry of theories in philosophy of language and semantics. This paper investigates free choice in sentences involving a non-monotonic modified numeral, under which we embed a possibility modal scoping over disjunction. One example is Exactly one student can(not) take Spanish or Calculus. As we point out, the presence (or absence) of certain readings of these sentences is a key test for a prominent approach, which analyzes free choice as a kind of scalar implicature. We report on two experiments investigating the readings of such sentences, using an inferential task. Our results are challenging for the implicature approach. We sketch two possible solutions within this approach, either adopting a different recent implicature algorithm, or exploring a different meaning for modified numerals with exactly. Both of them suffer from a variety of problems. We then discuss a third solution, which exploits a recent account of free choice based on homogeneity. This approach can account for our results, in combination with plausible assumptions about homogeneity projection, though it too has open issues with related cases. Regardless of which solution is chosen, non-monotonic contexts turn out to be an important test case for theories of free choice, implicature, and modified numerals.

中文翻译：

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非单调情况下的选择和禁止

可能性模态范围内的析取引起合取推断，通常被称为“自由选择”。例如，艾玛（Emma）可以学习西班牙语，或者微积分暗示艾玛（Emma）可以学习西班牙语并且可以接受微积分。该推论在模态的标准语义与布尔逻辑用于析取的结合上无效。因此，自由选择激发了语言哲学和语义学的整个理论领域。本文研究了涉及非单调修饰数字的句子中的自由选择，在此之下我们嵌入了析取的可能性模态范围。一个例子是，恰好一位学生可以（不可以）学习西班牙语或微积分。正如我们所指出的那样，这些句子的某些读物的存在（或不存在）是对一种突出方法的关键测试，该方法将自由选择分析为一种标量含义。我们报告了一项使用推理任务调查此类句子阅读的两个实验。对于隐式方法，我们的结果具有挑战性。我们在此方法中勾勒出两种可能的解决方案，要么采用不同的最新隐式算法，要么探索具有精确含义的修饰数字的不同含义。。他们两个都遭受各种各样的问题。然后，我们讨论第三种解决方案，该解决方案利用了最近基于同质性的自由选择的描述。这种方法可以结合同质性预测的合理假设来解释我们的结果，尽管它在相关案例中也存在未解决的问题。无论选择哪种解决方案，非单调上下文都成为自由选择，隐含和修饰数字理论的重要测试案例。