Modulated fibring and the collapsing problem

Fibring is recognized as one of the main mechanisms in combining logics, with great signicance in the theory and applications of mathematical logic. However, an open challenge to bring is posed by the collapsing problem: even when no symbols are shared, certain combinations of logics simply collapse to one of them, indicating that bring imposes unwanted interconnections between the given logics. Modulated bring allows a ner control of the combination, solving the collapsing problem both at the semantic and deductive levels. Main properties like soundness and completeness are shown to be preserved, comparison with bring is discussed, and some important classes of examples are analyzed with respect to the collapsing problem.