 Another consequence relation is associated naturally with each normal modal logic \(\Lambda\), defined by the calculus that has as axioms the formulas of \(\Lambda\) and as rules of inference Modus Ponens and Modal Generalization. The logic system given by this consequence relation is called the global consequence of \(\Lambda\) and will be denoted by \(\bgLambda\). It has the same theorems as the local \(\blLambda\), namely the elements of \(\Lambda\). The difference between \(\blLambda\) and \(\bgLambda\) lies in the consequences they allow to draw from nonempty sets of premises. For example we have  \(p \vdash_{\bgK} \Box p\)  but \(p \not\vdash_{\blK} \Box p\).  This difference has an enormous effect on their algebraic behavior.