 We now define a relation of satisfaction between interpretations, variable-assignments, and formulas of \(\LKe\). If \(\phi\) is a formula of \(\LKe, M\) is an interpretation for \(\LKe\), and \(s\) is a variable-assignment on \(M\), then we write \(M,s\vDash \phi\) for \(M\) satisfies \(\phi\) under the assignment \(s\). The idea is that \(M,s\vDash \phi\) is an analogue of “\(\phi\) comes out true when interpreted as in \(M\) via \(s\)”.