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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Acknowledgements
The authors thank J.J. Wannenburg for correspondence on the subject of this manuscript. The first author’s research was funded by the Iran National Science Foundation (NSF) under Project No. 4005865. The second author was supported in part by the National Research Foundation of South Africa (UID 85407).
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Fallahi, A., Raftery, J.G. On Pretabular Extensions of Relevance Logic. Stud Logica (2023). https://doi.org/10.1007/s11225-023-10081-2
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DOI: https://doi.org/10.1007/s11225-023-10081-2