Abstract Selectively forgetting information while preserving what matters the most is becoming an increasingly important issue in many areas, including in knowledge representation and reasoning. Depending on the application at hand, forgetting operators are defined to obey different sets of desirable properties. It turns out that, of the myriad of desirable properties discussed in the context of forgetting in Answer Set Programming, strong persistence, which imposes certain conditions on the correspondence between the answer sets of the program pre- and post-forgetting, and a certain independence from non-forgotten atoms, seems to best capture its essence, and be desirable in general. However, it has remained an open problem whether it is always possible to forget a set of atoms from a program while obeying strong persistence. In this paper, we investigate the limits of forgetting in Answer Set Programming. After showing that it is not always possible to forget a set of atoms from a program while obeying this property, we move forward and precisely characterize what can and cannot be forgotten from a program, by presenting a necessary and sufficient criterion. This characterization allows us to draw some important conclusions regarding the existence of forgetting operators for specific classes of logic programs, to characterize the class of forgetting operators that achieve the correct result whenever forgetting is possible, and investigate the related question of determining what we can forget from some specific logic program. Subsequently, we address the issue of what to do when we must forget a set of atoms, but cannot without violating this property. To this end, we investigate three natural alternatives to forget when forgetting without violating strong persistence is not possible, which turn out to correspond to the different natural possible relaxations of the characterization of strong persistence. Additionally, before concluding, we address computational complexity issues – namely of checking whether the novel criterion holds and whether a certain program is a result according to the different classes of forgetting operators we introduce – and discuss the related literature.

中文翻译：

---

论答案集编程中遗忘的极限

摘要 在保留最重要的信息的同时选择性地遗忘信息正成为许多领域中越来越重要的问题，包括知识表示和推理。根据手头的应用程序，遗忘运算符被定义为遵循不同的所需属性集。事实证明，在 Answer Set Programming 中在遗忘的上下文中讨论的无数理想属性中，强持久性，这对程序的遗忘前后的答案集之间的对应关系施加了一定的条件，并且具有一定的独立性来自未被遗忘的原子，似乎最好地捕捉了它的本质，并且通常是可取的。然而，在遵守强持久性的同时，是否总是可以忘记程序中的一组原子仍然是一个悬而未决的问题。在本文中，我们研究了答案集编程中遗忘的局限性。在证明了在遵守这个特性的同时，并不总是可以忘记程序中的一组原子之后，我们继续前进，并通过提出一个必要和充分的标准来精确描述程序中可以忘记和不能忘记的内容。这种表征使我们能够得出关于特定类别的逻辑程序是否存在遗忘算子的一些重要结论，表征在可能遗忘时获得正确结果的遗忘算子类别，并研究确定我们可以忘记什么的相关问题从一些特定的逻辑程序。随后，我们解决了当我们必须忘记一组原子时该怎么办的问题，但不能不违反这个属性。为此，我们研究了在不违反强持久性的情况下遗忘不可能的三种自然替代方法，结果证明它们对应于强持久性表征的不同自然可能松弛。此外，在结束之前，我们解决了计算复杂性问题——即根据我们引入的不同类别的遗忘算子检查新标准是否成立以及某个程序是否是结果——并讨论相关文献。