Combinations and completeness transfer for quantified modal logics

This paper focuses on three research questions which are connected with combinations of modal logics: (i) Under which conditions can (frame-) completeness (and related properties) be transferred from a propositional modal logic (PML) to its quantificational counterpart (QML)? (ii) Does (frame-) completeness generally transfer from monomodal QMLs to their multimodal combination? (iii) Can completeness be transferred from QMLs with rigid designators to those with non-rigid designators? The paper reports some recent results on these questions and provides some new results.