Besides their ordinary cardinal and proportional meanings, many and few have been argued to allow for a ‘reverse proportional’ reading (Westerstahl in Linguist and Philos 8:387–413, 1985). This reading has later been characterised in two opposite directions: Cohen’s (Nat Lang Semant 69:41–67, 2001) reading where the proportion $$|P\cap Q|:|P|$$ matters and Herburger’s (Nat Lang Semant 5:53–78, 1997) where it does not. We develop a compositional analysis that derives the correct truth conditions for both characterisations of Westerstahl-style sentences while (i) maintaining conservativity, (ii) assuming a standard syntax/semantics mapping and (iii) reducing their context-dependence to mechanisms independently needed for degree constructions in general. In a nutshell, mirroring the decomposition of other degree expressions like tall, many is decomposed into the parametrized determiner many and the operator POS, where POS combines with a contextually salient comparison class C matching the alternatives triggered by some element X$$_{\text {ALT}}$$ in the sentence. Non-reverse readings obtain when X$$_{\text {ALT}}$$ is external to the original host NP and reverse readings when X$$_{\text {ALT}}$$ is internal to the host NP. Cohen’s (2001) (amended) truth conditions for Westerstahl-style sentences are derived as a (true) reverse proportional reading and Herburger’s (1997) interpretation as a sub-case of the non-reverse cardinal reading.

中文翻译：

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多读多：POS 反比例读

除了它们通常的基数和比例含义外，许多和很少有人认为允许“反比例”阅读（Westerstahl in Linguist and Philos 8:387–413, 1985）。这种解读后来被描述为两个相反的方向：Cohen (Nat Lang Semant 69:41–67, 2001) 的解读，其中比例 $$|P\cap Q|:|P|$$ 很重要，Herburger 的 (Nat Lang Semant 5 :53–78, 1997) 而不是。我们开发了一种组合分析，它为 Westerstahl 式句子的两种特征推导出正确的真值条件，同时 (i) 保持保守性，(ii) 假设标准句法/语义映射和 (iii) 将它们的上下文依赖减少到独立需要的机制一般的学位建设。简而言之，反映了其他程度表达式的分解，如高，many 被分解为参数化的限定词 many 和算子 POS，其中 POS 与上下文显着的比较类 C 相结合，匹配由句子中的某个元素 X$$_{\text {ALT}}$$ 触发的备选方案。当 X$$_{\text {ALT}}$$ 在原始宿主 NP 外部时获得非反向读数，当 X$$_{\text {ALT}}$$ 在宿主 NP 内部时获得反向读数。Cohen (2001)（修正）Westerstahl 式句子的真值条件被推导出为（真实的）反向比例阅读，而 Herburger (1997) 的解释是作为非反向基数阅读的一个子案例。当 X$$_{\text {ALT}}$$ 在原始宿主 NP 外部时获得非反向读数，当 X$$_{\text {ALT}}$$ 在宿主 NP 内部时获得反向读数。Cohen (2001)（修正）Westerstahl 式句子的真值条件被推导出为（真实的）反向比例阅读，而 Herburger (1997) 的解释是作为非反向基数阅读的一个子案例。当 X$$_{\text {ALT}}$$ 在原始宿主 NP 外部时获得非反向读数，当 X$$_{\text {ALT}}$$ 在宿主 NP 内部时获得反向读数。Cohen (2001)（修正）Westerstahl 式句子的真值条件被推导出为（真实的）反向比例阅读，而 Herburger (1997) 的解释是作为非反向基数阅读的一个子案例。