Abstraction has been used in combinatorial search and action planning from the very beginning of AI. Many different methods and formalisms for state abstraction have been proposed in the literature, but they have been designed from various points of view and with varying purposes. Hence, these methods have been notoriously difficult to analyse and compare in a structured way. In order to improve upon this situation, we present a coherent and flexible framework for modelling abstraction (and abstraction-like) methods based on graph transformations. The usefulness of the framework is demonstrated by applying it to problems in both search and planning. We model six different abstraction methods from the planning literature and analyse their intrinsic properties. We show how to capture many search abstraction concepts (such as avoiding backtracking between levels) and how to put them into a broader context. We also use the framework to identify and investigate connections between refinement and heuristics—two concepts that have usually been considered as unrelated in the literature. This provides new insights into various topics, e.g. Valtorta's theorem and spurious states. We finally extend the framework with composition of transformations to accommodate for abstraction hierarchies, and other multi-level concepts. We demonstrate the latter by modelling and analysing the merge-and-shrink abstraction method.

从人工智能一开始，抽象就被用于组合搜索和行动计划。文献中已经提出了许多不同的状态抽象方法和形式，但它们是从不同的观点和不同的目的设计的。因此，众所周知，这些方法很难以结构化的方式进行分析和比较。为了改善这种情况，我们提出了一个连贯且灵活的框架，用于对基于图转换的抽象（和类抽象）方法进行建模。该框架的实用性通过将其应用于搜索和规划中的问题来证明。我们从规划文献中对六种不同的抽象方法进行建模并分析它们的内在属性。我们展示了如何捕获许多搜索抽象概念（例如避免级别之间的回溯）以及如何将它们放入更广泛的上下文中。我们还使用该框架来识别和研究细化和启发式之间的联系——这两个概念在文献中通常被认为是不相关的。这提供了对各种主题的新见解，例如 Valtorta 定理和伪态。我们最终通过组合转换来扩展框架，以适应抽象层次结构和其他多级概念。我们通过对合并收缩抽象方法进行建模和分析来演示后者。我们还使用该框架来识别和研究细化和启发式之间的联系——这两个概念在文献中通常被认为是不相关的。这提供了对各种主题的新见解，例如 Valtorta 定理和伪态。我们最终通过组合转换来扩展框架，以适应抽象层次结构和其他多级概念。我们通过对合并收缩抽象方法进行建模和分析来演示后者。我们还使用该框架来识别和研究细化和启发式之间的联系——这两个概念在文献中通常被认为是不相关的。这提供了对各种主题的新见解，例如 Valtorta 定理和伪态。我们最终通过组合转换来扩展框架，以适应抽象层次结构和其他多级概念。我们通过对合并收缩抽象方法进行建模和分析来演示后者。