Fibring: Completeness preservation

A completeness theorem is established for logics with congruence endowed wi th general semantics tin the style of general frames). As a corollary. comp leteness is shown to be preserved by fibring logics with congruence provide d that congruence is retained in the resulting logic. The class of logics w ith equivalence is shown to be closed under fibring and to be included in t he class of logics with congruence Thus. completeness is shown to be preser ved by fibring logics with equivalence and general semantics. An example is provided showing that completeness is not always preserved by fibring logi cs endowed with standard (non general) semantics. A categorial characteriza tion of fibring is provided using coproducts and cocartesian liftings.