Conuclear images of substructural logics

Our work proposes to study the conuclear image of a substructural logic and in particular to investigate the relationship between a substructural logic and its conuclear image. We analyze some axioms familiar to substructural logics and we check if they: (a) are preserved under conuclear images, (b) never hold in a conuclear image, or (c) are compatible with conuclear images but are not necessarily preserved under conuclear images. Moreover, we prove that the conuclear image of any substructural logic has the disjunction property. We finally give a sufficient condition in order that an inequality is preserved under conuclear images and observe that if we slightly relax this condition, we meet counterexamples of inequalities that are not preserved under conuclear images.