 The other clauses are obvious, for instance: \(\Tr(\phi \amp \psi) = (\Tr(\phi)\) and \(\Tr(\psi))\). This translation allows us to interpret all sentences of \(L_{\textrm{PFO}}\) and \(L_{\textrm{PFO}+}\), relying on our intuitive understanding of English. It is useful to consider some examples. Applying \(\Tr\) to (\ref{ex2prime}), say, yields: