  We give a criterion for the good reduction of semistable $K3$ surfaces over
$p$-adic fields using purely $p$-adic methods. We use neither $p$-adic Hodge
theory nor transcendental methods as in the analogous proofs of criteria for
good reduction of curves or $K3$ surfaces. We achieve our goal by realizing the
special fiber $X_s$ of a semistable model $X$ of a $K3$ surface over the
$p$-adic field $K$, $X_K$ as a special fiber of a log-family in characteristic
$p$ and use an arithmetic version of the Clemens-Schimd exact sequence in order
to obtain a Kulikov-Persson-Pinkham classification theorem in characteristic
$p$.
