This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic paradigms: labelled and nested sequent calculi. The formalism of labelled sequents has been successful in that cut-free calculi in possession of desirable proof-theoretic properties can be automatically generated for large classes of logics. Despite these qualities, labelled systems make use of a complicated syntax that explicitly incorporates the semantics of the associated logic, and such systems typically violate the subformula property to a high degree. By contrast, nested sequent calculi employ a simpler syntax and adhere to a strict reading of the subformula property, making such systems useful in the design of automated reasoning algorithms. However, the downside of the nested sequent paradigm is that a general theory concerning the automated construction of such calculi (as in the labelled setting) is essentially absent, meaning that the construction of nested systems and the confirmation of their properties is usually done on a case-by-case basis. The refinement method connects both paradigms in a fruitful way, by transforming labelled systems into nested (or, refined labelled) systems with the properties of the former preserved throughout the transformation process. To demonstrate the method of refinement and some of its applications, we consider grammar logics, first-order intuitionistic logics, and deontic STIT logics. The introduced refined labelled calculi will be used to provide the first proof-search algorithms for deontic STIT logics. Furthermore, we employ our refined labelled calculi for grammar logics to show that every logic in the class possesses the effective Lyndon interpolation property.

中文翻译：

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使用应用程序改进模态逻辑和构造逻辑的标记系统

本论文介绍了“结构细化方法”，该方法通过连接两个证明理论范式：标记和嵌套顺序演算，将模态和/或构造逻辑的关系语义转换为“经济”证明系统。标记序列的形式主义已经成功，因为可以为大量逻辑自动生成具有理想证明理论特性的无割演算。尽管有这些特性，标记系统还是使用了一种复杂的语法，它明确地结合了相关逻辑的语义，并且此类系统通常在很大程度上违反了子公式的属性。相比之下，嵌套的连续演算使用更简单的语法并严格遵守子公式属性，使此类系统可用于设计自动推理算法。然而，嵌套顺序范式的缺点是关于自动构建这种演算（如在标记设置中）的一般理论基本上不存在，这意味着嵌套系统的构建及其属性的确认通常是在一个就事论事。细化方法通过将标记系统转换为嵌套（或细化标记）系统，并在整个转换过程中保留前者的属性，从而以卓有成效的方式将两种范式连接起来。为了演示细化方法及其一些应用，我们考虑语法逻辑、一阶直觉逻辑和道义 STIT 逻辑。引入的精制标记演算将用于为道义 STIT 逻辑提供第一个证明搜索算法。此外，我们将我们精炼的标记演算用于语法逻辑，以表明该类中的每个逻辑都具有有效的 Lyndon 插值属性。