 An important question connected to combination of logics (and, in particular, to algebraic fibring) is the preservation of metaproperties such as completeness, interpolation etc. For instance, when \({{\cal L}}_1\) and \({{\cal L}}_2\) are complete logic systems presented both semantically and syntactically, under which condition is their fibring also complete? In this regard, Zanardo et al. 2001 and Sernadas et al. 2002a give a partial solution to this question. The preservation of soundness and completeness with respect to the technique of importing logics (see  subsection 4.6)  was proved in Rasga et al. 2013. Besides, in a series of papers (Marcelino et al. 2015, Marcelino and Caleiro 2016, and Marcelino and Caleiro 2017a), S. Marcelino et al. study the preservation of decidability by unconstrained fibring (that is, by algebraic fibring without sharing connectives). The key result is a general characterization of the derivations in the system obtained by fibring in terms of the derivations in each component. The complexity of the decision procedures was also analyzed in these papers. Thus, it was shown that the decision problem for the fibred logic can be reduced polynomially to the worst decision problem of the given logics. This means that, in particular, if the decision problems for two given logics \({{\cal L}}_1\) and \({{\cal L}}_2\) are both in a complexity class \(\mathcal{C}\) then the decision problem for the unconstrained fibring \({{\cal L}}_1 \oplus {{\cal L}}_2\) is also in \(\mathcal{C}\), provided that \(\mathcal{C}\) contains the basic complexity class P (also known as PTIME) and is closed for composition with polynomials. Other examples of preservation of metaproperties are provided by the mechanism for combining logics known as meet combination of logics, introduced by Sernadas et al. 2012 (see subsection 4.6).  Specifically, the preservation of soundness and completeness (see Sernadas et al. 2012), Craig interpolation (see C. Sernadas et al.  2013 ) and admissibility of rules (see Rasga et al. 2016) have been obtained for this method. On the other hand, transfer results have been extensively studied in the case of fusion of modal logics, as already mentioned in subsection 4.1.