This is a sequel article to [10] where a hypersequent calculus (HC) for some temporal logics of linear frames includingKt4.3and its extensions for dense and serial flow of time was investigated in detail. A distinctive feature of this approach is that hypersequents are noncommutative, i.e., they are finite lists of sequents in contrast to other hypersequent approaches using sets or multisets. Such a system in [10] was proved to be cut-free HC formalization of respective logics by means of semantical argument. In this article we present an equivalent variant of this calculus for which a constructive syntactical proof of cut elimination is provided.

中文翻译：

---

一些线性时间逻辑的超序微积分中的割消元

这是 [10] 的续篇文章，其中用于线性帧的一些时间逻辑的超序列演算 (HC)，包括Kt4.3并详细研究了它对密集和连续时间流的扩展。这种方法的一个显着特征是超序列是不可交换的，即，它们是序列的有限列表，与使用集合或多重集的其他超序列方法不同。[10] 中的这样一个系统被证明是通过语义论证的方式对各个逻辑进行无切 HC 形式化。在这篇文章中，我们提出了这个演算的一个等价变体，它提供了一个建设性的删减句法证明。