is recognized as one of the main mechanisms in combining logics, with great
significance in the theory and applications of mathematical logic.
an open challenge to fibring is posed by the collapsing problem: even
when no symbols are shared, certain combinations of logics simply collapse
to one of them, indicating that fibring imposes unwanted interconnections
between the given logics. Modulated fibring allows a finer 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 fibring is discussed, and some important
classes of examples are analyzed with respect to the collapsing problem.