Two distinct vertices are adjacent in $G ⊕ (p̄, R)$ exactly when either they are adjacent and the pair of their atomic types over $p̄$ is not in $R$, or they are non-adjacent and the pair is in $R$. Membership of the pair of atomic types in $R$ is a finite disjunction, over the pairs in $R$, of conjunctions of the atomic formulas $x = pᵢ$, $x ≠ pᵢ ∧ E(x, pᵢ)$ and $x ≠ pᵢ ∧ ¬E(x, pᵢ)$.