We introduce labelled sequent calculi for indexed modal logics. We prove that the structural rules of weakening and contraction are height-preserving admissible, that all rules are invertible, and that cut is admissible. Then we prove that each calculus introduced is sound and complete with respect to the appropriate class of transition frames.
Orlandelli, Eugenio (2014) Proof theory of quantified modal logics, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Science, cognition and technology , 26 Ciclo. DOI 10.6092/unibo/amsdottorato/6658.