KR is Anderson and Belnap’s relevance logic R with the addition of the axiom of EFQ: $$ (p \,\, \& \sim p) \rightarrow q$$ ( p & ∼ p ) → q . Since KR is relevantistic as to implication but classical as to negation, it has been dubbed, among many others, a ‘classical relevance logic.’ For KR, there have been known so far just two pretabular normal extensions. For these pretabular logics, no simple axiomatizations have yet been presented. In this paper, we offer some and show that they do the job. We also introduce some Routley–Meyer semantic conditions for these axioms. All these may facilitate realizing our desire to discover other classical pretabular extensions over KR, if such extensions exist.

中文翻译：

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Pretabular 经典相关逻辑的简单公理化

KR 是 Anderson 和 Belnap 的相关逻辑 R 加上 EFQ 的公理： $$ (p \,\, \& \sim p) \rightarrow q$$ ( p & ∼ p ) → q 。由于 KR 在蕴涵方面是相关的，而在否定方面是经典的，因此它被称为“经典相关逻辑”。对于 KR，迄今为止已知的只有两个 pretabular 正常扩展。对于这些表前逻辑，还没有提出简单的公理化。在本文中，我们提供了一些并表明它们可以完成这项工作。我们还为这些公理介绍了一些 Routley-Meyer 语义条件。如果这些扩展存在，所有这些可能有助于实现我们在 KR 上发现其他经典表前扩展的愿望。