  We derive the generating functional of $|\Delta S| =1, 2$ hadronic weak
interactions at one loop for a generic number of flavours and its counterpart
in the quenched approximation. A systematic analysis of the ultraviolet
divergences in the full theory (with and without a singlet dynamical field) and
in the quenched case is performed. We show that the quenched chiral logarithms
in the presence of weak interactions amount to a redefinition of the weak mass
term in the $\Delta S=\pm 1$ weak effective Lagrangian at leading order.
Finally, we apply the results to $B_K$ and $K\to\pi\pi$ matrix elements with
$\Delta I=1/2,3/2$ to analyze the modifications induced by quenching on the
coefficients of chiral logarithms in the one-loop corrections.
