 The semantics for the extended language is also straightforward. Suppose, for instance, \(\mathcal{D}\) is a definition of a name \(a\) and suppose that, when put in normal form, it is equivalent to (7). Then, each classical interpretation \(M\) of \(L\) expands to a unique classical interpretation \(M^{+}\) of the extended language \(L^{+}\). The denotation of \(a\) in \(M^{+}\) is the unique object that satisfies \(\psi(x)\) in \(M\); the conditions on \(\psi(x)\) ensure that such an object exists. The semantics of defined predicates and function-symbols is similar. The logic and semantics of definitions in non-classical logics receive, under the traditional account, a parallel treatment.