Following Smiley’s (The Journal of Symbolic Logic, 28, 113–134 1963) influential proposal, it has become standard practice to characterise notions of relative necessity in terms of simple strict conditionals. However, Humberstone (Reports on Mathematical Logic, 13, 33–42 1981) and others have highlighted various flaws with Smiley’s now standard account of relative necessity. In their recent article, Hale and Leech (Journal of Philosophical Logic, 46, 1–26 2017) propose a novel account of relative necessity designed to overcome the problems facing the standard account. Nevertheless, the current article argues that Hale & Leech’s account suffers from its own defects, some of which Hale & Leech are aware of but underplay. To supplement this criticism, the article offers an alternative account of relative necessity which overcomes these defects. This alternative account is developed in a quantified modal propositional logic and is shown model-theoretically to meet several desiderata of an account of relative necessity.

中文翻译：

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相对必要性和命题量化

根据 Smiley 的（符号逻辑杂志，28, 113–134 1963）有影响力的提议，根据简单的严格条件来表征相对必要性的概念已成为标准做法。然而，Humberstone（Reports on Mathematical Logic, 13, 33–42 1981）和其他人已经强调了 Smiley 现在关于相对必要性的标准解释的各种缺陷。在他们最近的文章中，Hale 和 Leech（Journal of Philosophical Logic, 46, 1–26 2017）提出了一种相对必要性的新解释，旨在克服标准解释面临的问题。尽管如此，目前的文章认为，Hale & Leech 的帐户存在其自身的缺陷，Hale & Leech 意识到其中的一些缺陷，但未充分说明。为了补充这一批评，该文章提供了克服这些缺陷的相对必要性的替代说明。这种替代说明是在量化的模态命题逻辑中开发的，并以模型理论的方式显示，以满足相对必要性说明的几个需求。