The goal of this paper is to present a new reconstruction of Aristotle's assertoric logic as he develops it in Prior Analytics, A1-7. This reconstruction will be much closer to Aristotle's original text than other such reconstructions brought forward up to now. To accomplish this, we will not use classical logic, but a novel system developed by Ben-Yami [2014. ‘The quantified argument calculus’, The Review of Symbolic Logic, 7, 120–46] called ‘QUARC’. This system is apt for a more adequate reconstruction since it does not need first-order variables (‘x’, ‘y’, …) on which the usual quantifiers act—a feature also not to be found in Aristotle. Further, in the classical reconstruction, there is also need for binary connectives (‘∧’, ‘→’) that don't have a counterpart in Aristotle. QUARC, again, does not need them either to represent the Aristotelian sentence types. However, the full QUARC is also not called for so that I develop a subsystem thereof (‘QUARC’) which closely resembles Aristotle's way of developing his logic. I show that we can prove all of Aristotle's claims within this systems and, lastly, how it relates to classical logic.

中文翻译：

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亚里士多德、逻辑和 QUARC

本文的目标是对亚里士多德在先验分析，A1-7 中发展的断言逻辑进行新的重构。与迄今为止提出的其他此类重建相比，这种重建将更接近亚里士多德的原文。为了实现这一点，我们不会使用经典逻辑，而是使用 Ben-Yami [2014. “量化论证演算”，符号逻辑评论，7, 120–46] 称为“QUARC”。该系统适用于更充分的重建，因为它不需要通常量词作用的一阶变量（“x”、“y”、……）——这一特征在亚里士多德中也找不到。此外，在经典重构中，还需要在亚里士多德中没有对应物的二元连接词（'∧'、'→'）。夸克，再次，也不需要它们来表示亚里士多德的句子类型。然而，也不需要完整的 QUARC，因此我开发了一个子系统（'QUARC'），它与亚里士多德的逻辑开发方式非常相似。我表明我们可以在这个系统中证明亚里士多德的所有主张，最后证明它与经典逻辑的关系。