, Volume 100, Issue 6, pp 1211-1221

A Pretabular Classical Relevance Logic

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Abstract

In this paper we construct an extension, ${\mathcal{L}}$ , of Anderson and Belnap’s relevance logic R that is classical in the sense that it contains ${p \& \neg p \rightarrow q}$ as a theorem, and we prove that ${\mathcal{L}}$ is pretabular in the sense that while it does not have a finite characteristic matrix, every proper normal extension of it does. We end the paper by commenting on the possibility of finding other classical relevance logics that are also pretabular.