 One possible relevance criterion that the \(h\)-\(r\)-\(w\) framework might suggest is atomicity. This amounts to identifying relevant consequences as basic ones, i.e., atomic sentences or their negations (Cevolani, Crupi and Festa 2011; Cevolani, Festa and Kuipers 2013). But even if we could avoid the problem of saying what it is for a sentence to be atomic, since many distinct propositions imply the same atomic sentences, this criterion would not satisfy the requirement that \(A\) be equivalent to \(A_R\). For example, \((h\vee r)\) and \(({\sim}h\vee{\sim}r)\), like tautologies, imply no atomic sentences at all. This latter problem can be solved by resorting to the notion of partial consequence; interestingly, the resulting account becomes virtually indentical to one version of the likeness approach (Cevolani and Festa 2020).