 An assignment of values in the frame \(\{\cD_{\alpha}\}_{\alpha}\) to variables is a function \(\phi\) such that \(\phi \bx_{\alpha} \in \cD_{\alpha}\) for each variable \(\bx_{\alpha}\). (Notation: The assignment \(\phi[a/x]\) maps variable x to value a and it is identical with \(\phi\) for all other variable symbols different from x.)