 Concepts of satisfiability, validity and consequence are defined as in classical first-order logic. Given language \(L\) of signature \(\Sigma\) and a formula \(\varphi\) of \(L\): \(\varphi\) is satisfiable if and only if there exists a Σ-structure \(\mathcal{A}\) and assignment \(s\) on it such that \(\mathcal{A},s\models \varphi\) holds; \(\varphi\) is valid (\(\models \varphi\)) if and only if \(\mathcal{A},s\models \varphi\) holds for all \(\mathcal{A}\) of signature \(\Sigma\) and any assignment \(s\) on \(\mathcal{A}\).