  Let X be a smooth variety over a field of positive characteristic, and let E
be an overconvergent isocrystal on X. We establish a criterion for the
existence of a "canonical logarithmic extension" of E to a good
compactification of X. In the process, we construct a category of
overconvergent log-isocrystals and discuss its basic properties. In subsequent
work, we will use these results to show that a canonical logarithmic extension
always exists after pulling back E along a suitable cover of X.
