The notion of a critical successor [5] in relational semantics has been central to most classic modal completeness proofs in interpretability logics. In this paper we shall work with a more general notion, that of an assuring successor. This will enable more concisely formulated completeness proofs, both with respect to ordinary and generalised Veltman semantics. Due to their interesting theoretical properties, we will devote some space to the study of a particular kind of assuring labels, the so-called full labels and maximal labels. After a general treatment of assuringness, we shall apply it to obtain a completeness result for the modal logic ILP$\mathsf{ILP}$$\mathsf{ILP}$ w.r.t. generalised semantics for a restricted class of frames.

中文翻译：

---

可解释性逻辑标记技术的理论与应用

关系语义中的关键后继者[5]的概念一直是可解释性逻辑中大多数经典模态完整性证明的核心。在本文中，我们将使用一个更一般的概念，即保证继任者的概念。这将实现更简洁的完整性证明，无论是关于普通的还是广义的 Veltman 语义。由于它们有趣的理论特性，我们将花一些篇幅来研究一种特定类型的保证标签，即所谓的完整标签和最大标签。在对保证性进行一般处理之后，我们将应用它来获得模态逻辑的完整性结果ILP$\mathsf{ILP}$$\mathsf{ILP}$为受限制的帧类写通用语义。