 More explicitly, a supervaluation begins with a neutral model \(\bM\) with a single, possibly empty domain. We then construct the set of completions of \(\bM\). These may be regarded as bivalent dual-domain positive models whose inner domain is the domain of \(\bM\), but which also have an outer domain \(\bD_o\) to provide referents for the empty terms. In each completion, singular terms that are nonempty in \(\bM\) retain their referents, and those that are empty in \(\bM\) denote a member of \(\bD_o - \bD\). For each \(n\)-place predicate \(P\), the extension of \(P\) is a subset of \(\bD_o^n\) and a superset of \(P\text{'s}\) extension in \(\bM\).