We study various extensions of Gentzen’s sequent calculus obtained by adding rules for equality. One of them is singled out as particularly natural and shown to satisfy full cut elimination, namely, also atomic cuts can be eliminated. Furthermore we tell apart the extensions that satisfy full cut elimination from those that do not and establish a strengthened form of the nonlenghtening property of Lifschitz and Orevkov.

中文翻译：

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Gentzen 等式微积分的原子削减的消除和半缩短性质

我们研究了通过添加等式规则获得的 Gentzen 后续演算的各种扩展。其中之一被挑选为特别自然并显示满足完全切割消除，即也可以消除原子切割。此外，我们将满足完全切割消除的扩展与不满足的扩展区分开来，并建立了 Lifschitz 和 Orevkov 的非延展性质的强化形式。