Finite Hilbert Systems for Weak Kleene Logics

IF 0.6 3区数学 Q2 LOGIC

Studia Logica Pub Date : 2024-03-16 DOI:10.1007/s11225-023-10079-w

引用次数: 0

Abstract

Multiple-conclusion Hilbert-style systems allow us to finitely axiomatize every logic defined by a finite matrix. Having obtained such axiomatizations for Paraconsistent Weak Kleene and Bochvar–Kleene logics, we modify them by replacing the multiple-conclusion rules with carefully selected single-conclusion ones. In this way we manage to introduce the first finite Hilbert-style single-conclusion axiomatizations for these logics.

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弱克莱因逻辑的有限希尔伯特系统

摘要多重结论希尔伯特式系统使我们能够对有限矩阵定义的每种逻辑进行有限公理化。在获得了 Paraconsistent Weak Kleene 和 Bochvar-Kleene 逻辑的公理化之后，我们用精心挑选的单结论规则取代多结论规则，对它们进行了修改。这样，我们就为这些逻辑引入了第一个有限希尔伯特式的单结论公理化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Studia Logica MATHEMATICS-LOGIC

CiteScore

1.70

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The leading idea of Lvov-Warsaw School of Logic, Philosophy and Mathematics was to investigate philosophical problems by means of rigorous methods of mathematics. Evidence of the great success the School experienced is the fact that it has become generally recognized as Polish Style Logic. Today Polish Style Logic is no longer exclusively a Polish speciality. It is represented by numerous logicians, mathematicians and philosophers from research centers all over the world.