We say that an argument \(\langle \Gamma,\theta \rangle\) is semantically valid, or just valid, written \(\Gamma \vDash \theta\), if for every interpretation \(M\) of the language, if \(M\vDash\psi\), for every member \(\psi\) of \(\Gamma\), then \(M\vDash\theta\). If \(\Gamma \vDash \theta\), we also say that \(\theta\) is a logical consequence, or semantic consequence, or model-theoretic consequence of \(\Gamma\). The definition corresponds to the informal idea that an argument is valid if it