Given a block of second-order relation variables $R_1, \dots, R_m$ and $k$ first-order variables $x_1, \dots, x_k$, an atom is an expression $R_i(x_{j_1}, \dots, x_{j_r})$, with $r$ the arity of $R_i$. It holds under an assignment of relations to the block and a valuation $v$ of the variables when the tuple $(v(x_{j_1}), \dots, v(x_{j_r}))$ belongs to the relation assigned to $R_i$. The clausal fragments of existential second-order logic, Krom and Horn, are built from these atoms.