 The definition of satisfaction in a model \(\langle D, I\rangle\) by an assignment \(s\) proceeds much like before, except for the obvious clauses for atomic formulas of the form \(P^n_i t_1, \ldots, t_n\) and \(t_i = t_j\): \(P^n_i t_1, \ldots, t_n\) is satisfied by \(s\) in \(\langle D, I\rangle\) if and only if \(\langle Den_{s}(t_1), \ldots, Den_{s}(t_n) \rangle \in I(P^n_i)\). And \(t_i = t_j\) is satisfied by \(s\) in \(\langle D, I\rangle\) if and only if the denotation of \(t_i\) under \(s\) is identical to the denotation of \(t_j\) under \(s\).