A Pretabular Classical Relevance Logic

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.