 The logics with a set of equations \(\iEq(p)\) with this property, namely such that for every \(\bA \in \bAlg^*\bL\) the class of reduced matrix models of \(\bL\) is \(\{\langle \bA, \iEq(\bA) \rangle : \bA \in \bAlg^*\bL\}\), are called truth-equational, a name introduced in Raftery 2006b. Some truth-equational logics are protoalgebraic but others are not. We will see later an example of the last ones.