 What happens to the Liar sentence on this approach? As in the three-valued case, the Liar is interpreted as falling within the gap. \(L\) is neither in \(\mathcal{E}\) nor \(\mathcal{A}. L\) thus falls outside of the domain where \(\Tr\) is interpreted as well-behaved. Because the situation is classical, and \(\left\ulcorner L\right\urcorner\not\in \mathcal{E}\), we know that \(\neg \Tr(\left\ulcorner L\right\urcorner)\) is true in the closed-off model; likewise, so is \(\neg \Tr(\left\ulcorner \neg L\right\urcorner)\).