  We develop a kinetic approach to the production of light nuclei up to mass
number $A$ $\leqslant$ $4$ in intermediate-energy heavy-ion collisions by
including them as dynamic degrees of freedom. The conversions between nucleons
and light nuclei during the collisions are incorporated dynamically via the
breakup of light nuclei by a nucleon and their inverse reactions. We also
include the Mott effect on light nuclei, i.e., a light nucleus would no longer
be bound if the phase-space density of its surrounding nucleons is too large.
With this kinetic approach, we obtain a reasonable description of the measured
yields of light nuclei in central Au+Au collisions at energies of $0.25$ -
$1.0A~\rm GeV$ by the FOPI collaboration. Our study also indicates that the
observed enhancement of the $\alpha$-particle yield at low incident energies
can be attributed to a weaker Mott effect on the $\alpha$-particle, which makes
it more difficult to dissolve in nuclear medium, as a result of its much larger
binding energy.
