 With respect to axiomatics, the logics obtained by fibring by functions can, in some cases, be axiomatized by the union of the (schema) axioms of the given logics. But some logics may require the addition of some new bridge principles (mixing rules and axioms) in order to ensure the preservation of completeness. This may explain some discrepancy between the approaches of fusion and fibring; the completeness of fibring as exposed in Gabbay 1999 does not work exactly as a substitute for more technically intricate completeness proofs as in Kracht and Wolter 1991 and in Fine and Schurz 1996. For more on this discussion, see Kracht 2004.