Conservativity of fibred logics without shared connectives *

Sérgio Marcelino, Carlos Caleiro
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
more » ... zation of the conserva-tivity 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 finite-valuedness is not preserved by fibring.