Any set of truth-functional connectives has sequent calculus rules that can be generated systematically from the truth tables of the connectives. Such a sequent calculus gives rise to a multi-conclusion natural deduction system and to a version of Parigot’s free deduction. The elimination rules are “general,” but can be systematically simplified. Cut-elimination and normalization hold. Restriction to a single formula in the succedent yields intuitionistic versions of these systems. The rules also yield generalized lambda calculi providing proof terms for natural deduction proofs as in the Curry–Howard isomorphism. Addition of an indirect proof rule yields classical single-conclusion versions of these systems. Gentzen’s standard systems arise as special cases.

中文翻译：

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广义单多结论序列和自然演绎演算的割消元与归一化

任何一组真值函数连接词都有连续的微积分规则，可以从连接词的真值表中系统地生成。这样的连续演算产生了多结论自然演绎系统和帕里戈特自由演绎的一个版本。排除规则是“通用的”，但可以系统地简化。削减消除和归一化保持。对后续系统中单个公式的限制会产生这些系统的直觉版本。这些规则还产生广义 lambda 演算，为自然演绎证明提供证明项，如 Curry-Howard 同构。添加间接证明规则会产生这些系统的经典单结论版本。Gentzen 的标准系统是作为特殊情况出现的。