If \(\textbf{C}\) is a complexity class, then a logic \(\mathcal{L}\) is said to capture \(\textbf{C}\) just in case for every problem \(X \in \textbf{C}\), there is a signature \(\tau\) and a formula \(\phi \in \text{Form}_{\mathcal{L}(\tau)}\) which defines \(X\).