 To endow every logic with a semantics of an algebraic kind one has to consider, at least, algebras together with a set of designated elements, without any requirement about its definability using the corresponding algebraic language. These pairs are the logical matrices. Tarski defined the general concept of logical matrix in the 1920s but the concept was already implicit in previous work by Łukasiewicz, Bernays, Post and others, who used truth-tables, either in independence proofs or to define logics different from classical logic. A logical matrix is a pair \(\langle \bA, D \rangle\) where \(\bA\) is an algebra and \(D\) a subset of the universe \(A\) of \(\bA\); the elements of \(D\) are called the designated elements of the matrix and accordingly \(D\) is called the set of designated elements (and some authors call it the truth set of the matrix). Logical matrices were first used as models of the theorems of specific logic systems, for instance in the work of McKinsey and Tarski, and also to define sets of formulas with similar properties to those of the set of theorems of a logic system, namely closure under substitution instances. This was the case of the \(n\)-valued logics of Łukasiewicz and of his infinite-valued logic. And it was Tarski who first considered logical matrices as a general tool to define this kind of sets.