Labelled quantified modal logics

We present an approach to providing natural deduction style proof systems for a large class of quantified modal logics with varying, increasing, decreasing or constant domains of quantification. The systems we develop are modular both in the behavior of the accessibility relation and quantification relative to the semantics, and in the proofs of soundness and completeness relative to that semantics. Our systems also provide the basis of simple implementations of quantified modal logics in a standard logical framework theorem prover.