 The class of the algebras of the matrices in \(\bRMatr(\bL)\) plays a prominent role in the theory of the algebraization of logics and it is denoted by \(\bAlg^*\bL\). It has been considered for a long time the natural class of algebras that has to be associated with a given logic \(\bL\) as its algebraic counterpart. For instance, in the examples considered above the classes of algebras that were given as algebraic semantics of the different logics (Boolean algebras, Heyting algebras, etc.) are exactly the class \(\bAlg^*\bL\) of the corresponding logic \(\bL\). And in fact, the class \(\bAlg^*\bL\) coincides with what was taken to be the natural class of algebras for all the logics \(\bL\) studied up to the 1990s. In the 1990s, due to the knowledge acquired of several logics not studied before, some authors proposed another way to define the class of algebras that has to be counted as the algebraic counterpart to be associated with a given logic \(\bL\). For many logics \(\bL\), it leads exactly to the class \(\bAlg^*\bL\) but for others it gives a class that extends it properly. We will discuss it in  Section 8.