论文标题
代数逻辑，用于否定古典逻辑的片段
Algebraic logic for the negation fragment of classical logic
论文作者
论文摘要
本文的一般目的是研究当代（摘要）代数逻辑框架内的经典逻辑的否定片段。更确切地说，我们将找到与代数逻辑中逻辑相关联的三类代数，也就是说，我们找到了$ \ mathrm {alg}^*$，$ \ mathrm {alg} $的类$ \ mathrm {alg}^*$，以及本质上的固有逻辑片段。为了实现这一目标，首先，我们为此片段提出了希尔伯特式的公理化。然后，我们表征还原的矩阵模型和该逻辑的完整广义矩阵模型。另外，我们将莱布尼兹和弗莱格层次结构中的否定片段分类。
The general aim of this article is to study the negation fragment of classical logic within the framework of contemporary (Abstract) Algebraic Logic. More precisely, we shall find the three classes of algebras that are canonically associated with a logic in Algebraic Logic, that is, we find the classes $\mathrm{Alg}^*$, $\mathrm{Alg}$ 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.
