 This observation leads to another point of view on abstract logics as models of a logic system. It transforms them into a collection of logical matrices (given by the closed sets) over the same algebra, or, to put it more simply, into a pair \(\langle \bA, \cB \rangle\) where \(\cB\) is a collection of subsets of \(A\). A structure of this type is called in the literature a generalized matrix (Wójcicki 1973) and more recently it has been called an atlas in Dunn &amp; Hardegree 2001. It is said to be a model of a logic system \(\bL\) if for every \(X \in \cB, \langle \bA, X \rangle\) is a matrix model of \(\bL\).