We introduce labelled sequent calculi for quantified modal logics with definite descriptions. 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 syntactically admissible. Finally, we show that each calculus gives a proof-theoretic characterization of validity in the corresponding class of models.

中文翻译：

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带有明确描述的量化模态逻辑的标记演算

我们为具有明确描述的量化模态逻辑引入了标记的连续演算。我们证明这些结石具有G3型结石的良好结构特性。特别是，所有规则都是保高可逆的，弱化和收缩是保高可接受的，cut 是语法上可接受的。最后，我们表明，每个微积分都给出了相应模型类中有效性的证明理论表征。