On Pretabular Extensions of Relevance Logic

IF 0.6 3区数学 Q2 LOGIC

Studia Logica Pub Date : 2023-11-16 DOI:10.1007/s11225-023-10081-2

Asadollah Fallahi, James Gordon Raftery

引用次数: 0

Abstract

We exhibit infinitely many semisimple varieties of semilinear De Morgan monoids (and likewise relevant algebras) that are not tabular, but which have only tabular proper subvarieties. Thus, the extension of relevance logic by the axiom \((p\rightarrow q)\vee (q\rightarrow p)\) has infinitely many pretabular axiomatic extensions, regardless of the presence or absence of Ackermann constants.

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论关联逻辑的表前扩展

我们展示了无限多的半线性De Morgan monoids(以及类似的相关代数)的半简单变种，它们不是表列的，而是只有表列的固有子变种。因此，无论阿克曼常数是否存在，公理\((p\rightarrow q)\vee (q\rightarrow p)\)对关联逻辑的扩展都具有无限多的表前公理扩展。

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.