 With a normal modal logic \(\Lambda\) it is associated the consequence relation defined by the calculus that takes as axioms all the formulas in \(\Lambda\) and as the only rule of inference Modus Ponens. The logic system given by this consequence relation is called the local consequence of \(\Lambda\). We denote it by \(\blLambda\). Its theorems are the elements of \(\Lambda\) and it holds that