 In order to make the exposition smooth we will now move from abstract logics to generalized matrices. Let \(\cA = \langle \bA, \cB \rangle\) be a generalized matrix. There exists the greatest congruence of \(\bA\) compatible with all the sets in \(\cB\); it is known as the Tarski congruence of \(\cA\). We denote it by \(\bOmega^{\sim}_{\bA }(\cB)\) and has the following characterization using the Leibniz operator