 Those who wish to retain (2) may be consoled by the following observation: though substitutivity salve veritate of co-extensive open formulas fails for nearly all free logics, a related but weaker principle, the substitutivity salve veritate of co-comprehensive open formulas, is valid for positive free logics. Open formulas \(A\) and \(B\) in \(n\) free variables \(x_1 ,\ldots ,x_n\) are co-comprehensive if every assignment of denotations in the outer domain \(\bD_o\) to \(x_1 ,\ldots ,x_n\) satisfies \(A\) if and only if it satisfies \(B\). Among the open formulas mentioned in the previous paragraph, for example, \(x=x\) and \((\rE!x \rightarrow x=x)\) are co-comprehensive in a dual-domain positive free logic, being satisfied by all members of \(\bD_o\), but \((x=x \amp \rE!x)\) is not co-comprehensive with them, since it is satisfied only by the members of \(\bD\). Unlike co-extensiveness, however, co-comprehensiveness is not expressible in the language of PFL. But it becomes expressible with the introduction of quantifiers over the outer domain—a strategy considered in  Section 5.5.