 One of the main traits of the consequence relations we study in logic is their formal character. This roughly means that if a sentence \(a\) follows from a set of sentences \(X\) and we have another sentence \(b\) and another set of sentences \(Y\) that share the same form with \(a\) and \(X\) respectively, then \(b\) also follows from \(Y\). In propositional logics this boils down to saying that if we uniformly replace basic sub-sentences of the sentences in \(X \cup \{a\}\) by other sentences obtaining \(Y\) and \(b\), then \(b\) follows from \(Y\). (The reader can find more information on the idea of formality in the entry  Logical Consequence.)