 Note that in this way we have obtained a map \(\bv\) from the set of \(L\)-formulas to the carrier of \(\bA\). It is important to notice that the value of a formula under a valuation depends only on the propositional variables that actually appear in the formula. Accordingly, if \(\phi\) is a formula, then we use the notation \(\phi(p_1 , \ldots ,p_n)\) to indicate that the variables that appear in \(\phi\) are in the list \(p_1 , \ldots ,p_n\), and given elements \(a_1 , \ldots ,a_n\) of an algebra \(\bA\) we refer by \(\phi^{\bA }[a_1 , \ldots ,a_n]\) to the value of \(\phi(p_1 , \ldots ,p_n)\) under any valuation \(v\) on \(\bA\) such that \(v(p_1) = a_1 , \ldots ,v(p_n) = a_n\).