<p>Often, two logical systems differ in what seems a merely superficial way; for example, in the symbols they choose for a given operation. When this happens, we say that the systems are <i>notational variants</i> of each other and that, as a consequence, they are presentations of the same logical theory. In recent years, increasing attention has been paid to certain logical systems that are radically substructural, in the sense that they abandon the reflexivity and/or transitivity of consequence. The contribution of this paper is twofold. First, I argue that such systems pose serious challenges to our extant criteria for deciding <i>when</i> two systems are notational variants. Second, I give some steps towards a new, improved criterion. Intuitively, I suggest that two logical systems are notational variants just in case, once we translate them properly, they give rise to the same non-logical theories—where, crucially, a non-logical theory can contain not only statements, but also inferences.</p>