We provide a non-Gentzen, though fully syntactical, cut-elimination algorithm for classical propositional logic. The designed procedure is implemented on \(\textsf{GS4}\), the one-sided version of Kleene’s sequent system \(\textsf{G4}\). The algorithm here proposed proves to be more ‘dexterous’ than other, more traditional, Gentzen-style techniques as the size of proofs decreases at each step of reduction. As a corollary result, we show that analyticity always guarantees minimality of the size of \(\textsf{GS4}\)-proofs.

中文翻译：

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通过退线消除切割

我们为经典命题逻辑提供了一种非 Gentzen，但完全语法化的剪切消除算法。设计的过程在 Kleene 序列系统\(\textsf{G4}\)的单侧版本\(\textsf{GS4}\)上实现。事实证明，这里提出的算法比其他更传统的 Gentzen 风格的技术更“灵巧”，因为证明的大小在每个缩减步骤中都会减小。作为推论结果，我们表明分析性总是保证\(\textsf{GS4}\)证明的大小最小。