This paper focuses on globally sound but possibly locally unsound analytic sequent calculi for quantifier macros defined by sequences of quantifiers. It is demonstrated that no locally sound analytic representation based on the usual eigenvariable condition exists. In consequence, representations by globally sound but possibly locally unsound analytic sequent calculi are used. Cut-elimination is shown by translating proofs into $\mathbf{\text{LK}}$ and retranslating cut-free proofs into the desired format. Finally, criteria are given for sequents to be proved without reference to the extended eigenvariable conditions.

中文翻译：

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迈向量词宏的证明理论

本文重点关注由量词序列定义的量词宏的全局合理但可能局部不合理的分析顺序演算。证明不存在基于通常特征变量条件的局部合理分析表示。因此，使用了全局健全但可能局部不健全的分析连续演算的表示。通过将证明翻译成$\mathbf{\text{力劲}}$并将无剪辑的校样重新翻译成所需的格式。最后，给出了在不参考扩展特征变量条件的情况下证明序列的标准。