  In this paper, we establish a criterion for an overconvergent isocrystal on a
smooth variety over a field of characteristic $p>0$ to extend logarithmically
to its smooth compactification whose complement is a strict normal crossing
divisor. This is a generalization of a result of Kedlaya, who treated the case
of unipotent monodromy. Our result is regarded as a $p$-adic analogue of the
theory of canonical extension of regular singular integrable connections on
smooth varieties of characteristic 0.
