Degree semantics has been developed to study how the meanings of measurement and comparison are encoded in natural language. Within degree semantics, this paper proposes a difference-based (or subtraction-based) approach to analyze the semantics of comparatives. The motivation is the measurability and comparability of differences involved in comparatives. The main claim is that comparatives encode a subtraction equation among three scalar values: two measurements along an interval scale and the difference between them. We contribute two innovations: (i) using interval arithmetic to implement subtraction, and (ii) analyzing comparative morpheme -er/more as an additive particle, denoting the default, most general, positive difference. Our analysis inherits existing insights in the literature. Moreover, the innovations bring new conceptual and empirical advantages. In particular, we address the interpretation of comparatives containing than-clause-internal quantifiers and various kinds of numerical differentials. We also account for three puzzles with regard to the scope island issue, the monotonicity of than-clauses, and the discourse status of the standard in comparison.

中文翻译：

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比较语义学：基于差异的方法

已经开发了度语义来研究测量和比较的含义如何以自然语言编码。在度语义中，本文提出了一种基于差异（或基于减法）的方法来分析比较语义。动机是比较中涉及的差异的可衡量性和可比性。主要主张是比较编码三个标量值之间的减法方程：沿间隔尺度的两次测量以及它们之间的差异。我们贡献了两项创新：（i）使用区间算术来实现减法，以及（ii）将比较语素 -er/more 分析为加法粒子，表示默认的、最普遍的、正的差异。我们的分析继承了文献中现有的见解。而且，这些创新带来了新的概念和经验优势。特别是，我们解决了包含比从句内部量词和各种数值微分的比较词的解释。我们还解释了关于范围岛问题、than 子句的单调性以及比较标准的话语地位的三个难题。