In this review, I assess a variety of constraint-based formal frameworks that can treat variable phenomena, such as well-formedness intuitions, outputs in free variation, and lexical frequency-matching. The idea behind this assessment is that data in gradient linguistics fall into natural mathematical patterns, which I call quantitative signatures. The key signatures treated here are the sigmoid curve, going from zero to one probability, and the wug-shaped curve, which combines two or more sigmoids. I argue that these signatures appear repeatedly in linguistics, and I adduce examples from phonology, syntax, semantics, sociolinguistics, phonetics, and language change. I suggest that the ability to generate these signatures is a trait that can help us choose between rival frameworks.

中文翻译：

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推导 Wug 形曲线：评估语言变异形式理论的标准

在这篇评论中，我评估了各种可以处理可变现象的基于约束的形式框架，例如良构直觉、自由变化的输出和词汇频率匹配。这种评估背后的想法是梯度语言学中的数据属于自然数学模式，我称之为定量特征。这里处理的关键签名是 sigmoid 曲线，从零到一个概率，以及 wug 形曲线，它结合了两个或多个 sigmoid。我认为这些特征在语言学中反复出现，并举出语音学、句法、语义学、社会语言学、语音学和语言变化的例子。我认为生成这些签名的能力是一种可以帮助我们在竞争框架之间进行选择的特性。