 The properties of a logic \(\bL\) depend in general, as we already said, on the global behavior of the family of its theories. In some logics, this behavior is reflected in the behavior of its set of theorems, as in classical and intuitionistic logic due to the deduction-detachment property, but this is by no means the most general situation, as it is witnessed by the example of the local and global modal logics of the normal modal logic \(K\). The two have the same theorems but do not share the same properties. Recall that the local logic has the deduction-detachment property but the global one does not. In a similar way, the properties of a logic are in general better encoded in an algebraic setting if we consider families of \(\bL\)-filters on the algebras than if we consider a single \(\bL\)-filter as it is done in logical matrices model theory.