 Concentrating now on 1-ary relations between—i.e., classes of—formulas, we transfer the above terminology to connectives by saying that a connective is universally representative or special according to a consequence relation if the class of formulas with the given connective as main connective is itself a universally representative class or a special class of formulas, respectively, according to the consequence relation in question. While every non-constant  connective[37]  is universally representative according to ⊢CL our discussion of inverses for intuitionistic ¬ shows that ¬ is special according to ⊢, since we can take σ(p) as ¬¬p ≻ p and every substitution instance of this IL-unprovable sequent in which p is replaced by a negated formula is IL-provable. Negation is therefore not universally representative in intuitionistic logic. (This means that we could usefully speak, from the perspective of ⊢I L, of negative propositions, thinking of the equivalence class, with respect to the relation of synonymy, of a formula as the proposition thereby expressed, and meaning by this the equivalence classes of negated formulas. Classically, the corresponding notion is not useful since all propositions would count as negative, just as for both ⊢CL and ⊢I L, there are no specifically conjunctive or disjunctive propositions.)