The general aim of this article is to study the negation fragment of classical logic within the framework of contemporary () Algebraic Logic. More precisely, we shall find the three classes of algebras that are canonically associated with a logic in Algebraic Logic, i.e. we find the classes $\textrm{Alg}^*$, $\textrm{Alg}$ and the intrinsic variety of the negation fragment of classical logic. In order to achieve this, firstly, we propose a Hilbert-style axiomatization for this fragment. Then, we characterize the reduced matrix models and the full generalized matrix models of this logic. Also, we classify the negation fragment in the Leibniz and Frege hierarchies.

中文翻译：

---

经典逻辑否定片段的代数逻辑

本文的总体目的是在当代（）代数逻辑的框架内研究经典逻辑的否定片段。更准确地说，我们将找到与代数逻辑中的逻辑规范相关的三类代数，即我们找到类 $\textrm{Alg}^*$, $\textrm{Alg}$ 和内在多样性经典逻辑的否定片段。为了实现这一点，首先，我们为这个片段提出了希尔伯特式公理化。然后，我们描述了该逻辑的简化矩阵模型和完全广义矩阵模型。此外，我们在 Leibniz 和 Frege 层次结构中对否定片段进行分类。