We follow [Ko13] for the definitions of various notions of a singular pair from the Minimal Model Program, including klt, dlt and log canonical pairs. In particular, we refer to [Ko13, 4.15] for the definition of log canonical centers. The non-archimedean analytic spaces that appear in this paper are $K$-analytic spaces in the sense of [Be90]. We refer to [Te13] for a gentle introduction. We will also make use of some basic logarithmic geometry; all log structures in this paper are defined with respect to the Zariski topology, and they are fine and saturated ($fs$). The standard introduction to logarithmic geometry is [Ka89].