  We study a model in which particles interact through a hard-core repulsion
complemented by a short-ranged attractive potential, of the kind found in
colloidal suspensions. Combining theoretical and numerical work we locate the
line of higher-order glass transition singularities and its end-point -- named
$A_4$ -- on the fluid-glass line. Close to the $A_4$ point, we detect
logarithmic decay of density correlations and sub linear power-law increase of
the mean square displacement, for time intervals up to four order of
magnitudes. We establish the presence of the $A_4$ singularity by studying how
the range of the potential affects the time-window where anomalous dynamics is
observed.
