LC and Its Pretabular Relatives

Abstract

In 1970, J.M. Dunn published a paper on a logic called RM extending the logic R of relevance. He proved that the logic RM is pretabular, i.e., it has no finite characteristic matrix, but every proper extension of it has such a matrix. In 1971, J.M. Dunn and R.K. Meyer obtained a similar result for Dummett’s logic LC. This is a brief survey of pretabular logics. We consider pretabularity and tabularity problems over the intuitionistic and minimal logics, and also in families of positive, modal and relevant logics.