We investigate the modal logic of stepwise removal of objects, both for its intrinsic interest as a logic of quantification without replacement, and as a pilot study to better understand the complexity jumps between dynamic epistemic logics of model transformations and logics of freely chosen graph changes that get registered in a growing memory. After introducing this logic (MLSR) and its corresponding removal modality, we analyze its expressive power and prove a bisimulation characterization theorem. We then provide a complete Hilbert-style axiomatization for the logic of stepwise removal in a hybrid language enriched with nominals and public announcement operators. Next, we show that model-checking for MLSR is PSPACE-complete, while its satisfiability problem is undecidable. Lastly, we consider an issue of fine-structure: the expressive power gained by adding the stepwise removal modality to fragments of first-order logic.

我们研究了逐步移除对象的模态逻辑，既是因为它作为一种无需替换的量化逻辑的内在兴趣，也是为了更好地理解模型转换的动态认知逻辑和自由选择的图形变化逻辑之间的复杂性跳跃的试点研究。在不断增长的记忆中注册。引入这个逻辑后（MLSR) 及其相应的去除模态，我们分析了它的表达能力并证明了一个互模拟表征定理。然后，我们提供了一个完整的希尔伯特式公理化，用于在富含名词和公告运算符的混合语言中逐步删除的逻辑。接下来，我们展示模型检查MLSR是 PSPACE 完全的，而它的可满足性问题是不可判定的。最后，我们考虑一个精细结构的问题：通过将逐步删除模式添加到一阶逻辑片段中获得的表达能力。