This article studies the logical properties of a very general class of infinite ranked trees, namely, those generated by higher-order recursion schemes. We consider, for both monadic second-order logic and modal -calculus, three main problems: model-checking, logical reflection (a.k.a. global model-checking, that asks for a finite description of the set of elements for which a formula holds), and selection (that asks, if exists, for some finite description of a set of elements for which an MSO formula with a second-order free variable holds). For each of these problems, we provide an effective solution. This is obtained, thanks to a known connection between higher-order recursion schemes and collapsible pushdown automata and on previous work regarding parity games played on transition graphs of collapsible pushdown automata.

中文翻译：

---

高阶递归方案和可折叠下推自动机：逻辑属性

本文研究了一类非常一般的无限排序树的逻辑属性，即由高阶递归方案生成的那些。我们考虑，对于一元二阶逻辑和模态 -微积分，三个主要问题：模型检查，逻辑反射（也称为全局模型检查，要求对公式所适用的元素集进行有限描述）和选择（如果存在，则询问某些有限的具有二阶自由变量的 MSO 公式适用的一组元素的描述）。对于这些问题中的每一个，我们都提供了有效的解决方案。这要归功于高阶递归方案和可折叠下推自动机之间的已知联系以及先前关于在可折叠下推自动机的转换图上玩的奇偶游戏的工作。