 A valuation on an \(L\)-algebra \(\bA\) is a map \(v\) from the set of variables into its carrier \(A\). Algebras together with valuations are used to interpret in a compositional way the formulas of \(L\), assuming that a connective \(*\) of \(L\) is interpreted in an \(L\)-algebra \(\bA\) by the function \(* ^{\bA}\). Let \(\bA\) be an algebra of type \(L\) and \(v\) a valuation on \(\bA\). The value of a compound formula \(* \phi_1 \ldots \phi_n\) is computed by applying the function \(* ^{\bA}\) that interprets \(*\) in \(\bA\) to the previously computed values \(\bv(\phi_1), \ldots,\bv(\phi_n)\) of the formulas \(\phi_1,\ldots,\phi_n\). Precisely speaking, the value \(\bv(\phi)\) of a formula \(\phi\) is defined inductively as follows: