 The generalized matrix models that have naturally attracted most of the attention in the research on the algebraization of logics are the generalized matrices of the form \(\langle \bA, \tFi_{\bL }\bA \rangle\) where \(\tFi_{\bL }\bA\) is the set of all the \(\bL\)-filters of \(\bA\). An example of a property of logics encoded in the structure of the lattices of \(\bL\)-filters of the \(L\)-algebras is that for every finitary protoalgebraic logic \(\bL, \bL\) has the deduction-detachment property if and only if for every algebra \(\bA\) the join-subsemilattice of the lattice of all \(\bL\)-filters of \(\bA\) that consists of the finitely generated \(\bL\)-filters is dually residuated; see Czelakowski 2001.