Abstract
KR is Anderson and Belnap’s relevance logic R with the addition of the axiom of EFQ: \( (p \,\, \& \sim p) \rightarrow q\). 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.
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Acknowledgements
I would like to thank Professor Mohammad Ardeshir and two anonymous referees for their corrections, suggestions and improvements. I also thank Dr. Amir Karbasi Zadeh for his help to improve the quality of English of the paper.
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Presented by Yde Venema
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Fallahi, A. Simple Axiomatizations for Pretabular Classical Relevance Logics. Stud Logica 108, 359–393 (2020). https://doi.org/10.1007/s11225-019-09844-7
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DOI: https://doi.org/10.1007/s11225-019-09844-7