(2.2.1) A $dlt$-model of $X$ is a normal proper $\mathscr{C}$-model $\mathscr{X}$ of $X$ such that $(\mathscr{X},(\mathscr{X}_{s})_{\mathrm{red}})$ is a $dlt$-pair. This means that $(\mathscr{X},(\mathscr{X}_{s})_{\mathrm{red}})$ is log canonical and that each log canonical center of $(\mathscr{X},(\mathscr{X}_{s})_{\mathrm{red}})$ has non-empty intersection with $\mathscr{X}^{\mathrm{snc}}$. In particular, every proper $snc$-model of $X$ is a $dlt$-model. An equivalent formulation of the definition is the following: $K_{\mathscr{X}}+(\mathscr{X}_{s})_{\mathrm{red}}$ is $\mathbb{Q}$-Cartier, and for every log resolution $h:\mathscr{Y}\to\mathscr{X}$ of $(\mathscr{X},\mathscr{X}_{s})$ and every irreducible component $E$ of $\mathscr{Y}_{s}$, the multiplicity of $E$ in the log pullback $\Delta$ of $(\mathscr{X}_{s})_{\mathrm{red}}$ to $\mathscr{Y}$ is at most $1$. Moreover, if it is equal to $1$, then $h(E)$ must have non-empty intersection with $\mathscr{X}^{\mathrm{snc}}$. In practice, we will apply the $dlt$ property via Lemma 3.2.3 below.