 The definition of a formula of the language of pure quantificational logic proceeds recursively as follows. First, one defines an atomic formula to consist of an \(n\)-place predicate followed by \(n\) variables: \(P^{n}_{i} x_{1}\), …, \(x_{n}\). One then defines \(A\) to be a formula of the language of pure quantificational logic if, and only if, (i) \(A\) is an atomic formula, or (ii) \(A\) is of the form \(\lnot B\), where \(B\) is a formula, or (iii) \(A\) is of the form \((B \rightarrow C)\), where \(B\) and \(C\) are each a formula, or (iv) \(A\) is of the form \(\forall x B\), where \(x_i\) is a variable and \(B\) is a  formula.[2]