 On well-behaved sentences, we have the fixed point property that \(A\) and \(\Tr(\left\ulcorner A\right\urcorner)\) have the same truth value, and so the semantics of \(\mathcal{L}^{+}_0\) and the semantics it assigns to \(\Tr\) correspond exactly. On pathological sentences like \(L\), they do not, and indeed, cannot, on pain of triviality.