Conservativity of Fibred Logics without Shared Connectives *

Fibring is a general mechanism for combining logics that provides valuable insight on designing and understanding complex logical systems. Mostly, the research on fibring has focused on its model and proof-theoretic aspects, and on transference results for relevant metalogical properties. Conservativity, however, a property that lies at the very heart of the original definition of fibring, has not deserved similar attention. In this paper, we provide the first full characterization of the conservativity of fibred logics, in the special case when the logics being combined do not share connectives. Namely, under this assumption, we provide necessary and sufficient conditions for a fibred logic to be a conservative extension of the logics being combined. Our characterization relies on a key technical result that provides a complete description of what follows from a set of non-mixed hypotheses in the fibred logic, in terms of the logics being combined. With such a powerful tool in hand, we also explore a semantic application. Namely, we use our key technical result to show that finitevaluedness is not preserved by fibring.