The concept of abstraction has been independently developed both in the context of AI Planning and discounted Markov Decision Processes (MDPs). However, the way abstractions are built and used in the context of Planning and MDPs is different even though lots of commonalities can be highlighted. To this day there is no work trying to relate and unify the two fields on the matter of abstractions unraveling all the different assumptions and their effect on the way they can be used. Therefore, in this paper we aim to do so by looking at projection abstractions in Planning through the lenses of discounted MDPs. Starting from a projection abstraction built according to Classical or Probabilistic Planning techniques, we will show how the same abstraction can be obtained under the abstraction frameworks available for discounted MDPs. Along the way, we will focus on computational as well as representational advantages and disadvantages of both worlds pointing out new research directions that are of interest for both fields.

翻译：抽象概念在人工智能规划与折扣马尔可夫决策过程（MDPs）领域各自独立发展。尽管两者存在诸多共性，但抽象在规划与MDPs中的构建与运用方式存在差异。迄今为止，尚未有研究尝试在抽象问题上关联并统一这两个领域，以揭示所有不同假设及其对应用方式的影响。因此，本文旨在通过折扣MDPs的视角审视规划中的投影抽象，以达成此目标。我们将从基于经典或概率规划技术构建的投影抽象出发，展示如何在折扣MDPs的现有抽象框架下获得相同的抽象。在此过程中，我们将聚焦于两个领域在计算与表示层面的优势与局限，并指出对双方均有价值的新研究方向。