From depth relevance to connexivity

Abstract

Brady [4] used the matrix for Meyer’s crystal lattice CL to build a
hierachical model structure for his deep relevant logic DRd. In this paper
we modify the matrix for CL so as to define a connexive conditional. In
doing so, we arrive at a family of connexive logics satisfying the depth
relevance property. As a result, we show a way to satisfactorily combine
connexivity and relevance without trivializing the logic and without vali-
dating unappealing theorems