Labelled Calculi for Quantified Modal Logics with Non-rigid and Non-denoting Terms

We introduce labelled sequent calculi for quantified modal logics with non-rigid and non-denoting terms. We prove that these calculi have the good structural properties of G3-style calculi. In particular, all rules are height-preserving invertible, weakening and contraction are height-preserving admissible and cut is admissible. Finally, we show that each calculus gives a proof-theoretic characterization of validity in the corresponding class of models.