The paper presents a uniform proof-theoretic treatment of several kinds of free logic, including the logics of existence and definedness applied in constructive mathematics and computer science, and called here quasi-free logics. All free and quasi-free logics considered are formalised in the framework of sequent calculus, the latter for the first time. It is shown that in all cases remarkable simplifications of the starting systems are possible due to the special rule dealing with identity and existence predicate. Cut elimination is proved in a constructive way for sequent calculi adequate for all logics under consideration.

中文翻译：

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自由逻辑是免剪切的

本文提出了几种自由逻辑的统一证明理论处理，包括应用于构造数学和计算机科学的存在性和定义性逻辑，这里称为准自由逻辑。所有考虑的自由和准自由逻辑都在顺序演算的框架内形式化，后者是第一次。结果表明，在所有情况下，由于处理身份和存在谓词的特殊规则，起始系统的显着简化是可能的。对于适合所有考虑的逻辑的连续演算，以一种建设性的方式证明了消减。