Nested Sequents for Quantified Modal Logics

Abstract This paper studies nested sequents for quantified modal logics. In particular, it considers extensions of the propositional logics definable by axioms D , T B 4 and 5 with varying, increasing, decreasing, constant domains. Each calculus is proved to have good structural properties: weakening contraction are height-preserving admissible cut (syntactically) admissible. shown be equivalent corresponding axiomatic system and, thus, sound complete. Finally, argued that calculi internal—i.e., each sequent has a formula interpretation—whenever existence predicate expressible in language.