A Unifying Completeness Theorem in Quantified Modal logic
Giovanna Corsi

Abstract:
A general strategy for proving completeness theorems for quantified
modal logics is provided. Starting from free quantified modal logic
K, with or without identity, extensions obtained either by adding
the principle of universal instantiation or the converse of the
Barcan formula or the Barcan formula are considered and proved
complete in a uniform way. Completeness theorems are also shown
for systems with the extended Barcan rule as well as for some
quantified extensions of the propositional modal logic B. The
incompleteness of Q'.B+BF is proved too.