Abstraction is an important technique utilized by humans in model building and problem solving, in order to figure out key elements and relevant details of a world of interest. This naturally has led to investigations of using abstraction in AI and Computer Science to simplify problems, especially in the design of intelligent agents and automated problem solving. By omitting details, scenarios are reduced to ones that are easier to deal with and to understand, where further details are added back only when they matter. Despite the fact that abstraction is a powerful technique, it has not been considered much in the context of nonmonotonic knowledge representation and reasoning, and specifically not in Answer Set Programming (ASP), apart from some related simplification methods. In this work, we introduce a notion for abstracting from the domain of an ASP program such that the domain size shrinks while the set of answer sets (i.e., models) of the program is over-approximated. To achieve the latter, the program is transformed into an abstract program over the abstract domain while preserving the structure of the rules. We show in elaboration how this can be also achieved for single or multiple sub-domains (sorts) of a domain, and in case of structured domains like grid environments in which structure should be preserved. Furthermore, we introduce an abstraction-&-refinement methodology that makes it possible to start with an initial abstraction and to achieve automatically an abstraction with an associated abstract answer set that matches an answer set of the original program, provided that the program is satisfiable. Experiments based on prototypical implementations reveal the potential of the approach for problem analysis, by its ability to focus on the parts of the program that cause unsatisfiability and by achieving concrete abstract answer sets that merely reflect relevant details. This makes domain abstraction an interesting topic of research whose further use in important areas like Explainable AI remains to be explored.

摘要是人类在模型构建和问题解决中使用的一项重要技术，目的是找出感兴趣世界的关键元素和相关细节。这自然导致了在人工智能和计算机科学中使用抽象来简化问题的研究，特别是在智能代理的设计和自动化问题解决方面。通过省略细节，场景被简化为更容易处理和理解的场景，只有在它们重要时才会添加更多细节。尽管抽象是一种强大的技术，但除了一些相关的简化方法外，在非单调知识表示和推理的上下文中，特别是在答案集编程 (ASP) 中，它并没有被考虑太多。在这项工作中，我们引入了一种从 ASP 程序域中抽象的概念，使得域大小缩小而程序的答案集（即模型）集过度近似。为了实现后者，在保留规则结构的同时，将程序转换为抽象域上的抽象程序。我们详细说明了如何也可以为域的单个或多个子域（排序）实现这一点，以及在结构化域（如应保留结构的网格环境）的情况下。此外，我们引入了一种抽象和细化方法，它可以从初始抽象开始，并自动实现具有与原始程序的答案集匹配的关联抽象答案集的抽象，前提是该程序是可满足的。基于原型实现的实验揭示了问题分析方法的潜力，因为它能够专注于程序中导致不满意的部分，并通过实现仅反映相关细节的具体抽象答案集。这使得领域抽象成为一个有趣的研究课题，其在可解释人工智能等重要领域的进一步应用仍有待探索。