There exists an uncountable set of pretabular extensions of the relevant logic R and each logic of this set is generated by a variety of finite height

Abstract

In Handbook of Philosophical Logic M. Dunn formulated a problem of describing pretabular extensions of relevant logics (cf. M. Dunn [1984], p. 211; M. Dunn, G. Restall [2002], p. 79). The main result of this paper is described in the title.

Nilpotent Minimum Logic NM and Pretabularity

“…This paper is a contribution to the study of pretabularity of fuzzy logics. In general, a logic L is said to be pretabular if it does not itself have a finite characteristic matrix (algebra, or frame), but every normal extension of it does (see [4,7,8,11,13]). Note that Dunn (and Meyer) [3,5] investigated the pretabularity of the semi-relevance logic RM (R with mingle) and the Dummett-Gödel logic G. One interesting fact is that these systems can be also regarded as fuzzy logics.…”