 Here is the full definition. Assume a non-empty domain \(D\), a set of variables \(\textsf{VAR}\) and a model \(\mathcal{M}=\langle D, I\rangle\) of signature \(\Sigma\). Atomic conditions \(\pi\) are of the form \(P(x_0 , \ldots ,x_{n-1})\), where \(P\in \Sigma\) is of arity \(n\). Atomic resets \(\varepsilon\) are of the form \(\exists v\), where \(v\) is a variable. The language of predicate logic for \(\Sigma\) is given below (\(\cdot\) is conjunction and \({\sim}\) is negation): 