 We define a formula to be satisfied in a model \(\langle D, I \rangle\) by an assignment \(s\) recursively as follows. An atomic formula \(P^{n}_{i} x_{1}, \ldots , x_{n}\) is satisfied in \(\langle D, I\rangle\) by \(s\) if, and only if, \(\langle s(x_{1}), \ldots, s(x_{n})\rangle \in I(P^{n}_{i})\), which means that the \(n\)-tuple of objects \(s\) assigns to the variables that occur in the formula is in the interpretation of the predicate \(P^{n}_{i}\) under \(I\). A negation \(\lnot B\) is satisfied in \(\langle D, I\rangle\) by \(s\) if, and only if, \(B\) is not satisfied in \(\langle D, I\rangle\) by \(s\). A conditional \((B \rightarrow C)\) is satisfied in \(\langle D, I\rangle\) by \(s\) if, and only if, \(B\) is not satisfied or \(C\) is satisfied in \(\langle D, I\rangle\) by \(s\). Finally, \(\forall xB\) is satisfied in \(\langle D, I\rangle\) by \(s\) if, and only if, \(B\) is satisfied in \(\langle D, I\rangle\) by all assignments of the form \(s[x/d]\), where \(d\) is a member of the domain \(D\).