ion is a well-known approach to simplify a complex problem by over-approximating it with a deliberate loss of information. It was not considered so far in Answer Set Programming (ASP), a convenient tool for problem solving. We introduce a method to automatically abstract ASP programs that preserves their structure by reducing the vocabulary while ensuring an over-approximation (i.e., each original answer set maps to some abstract answer set). This allows for generating partial answer set candidates that can help with approximation of reasoning. Computing the abstract answer sets is intuitively easier due to a smaller search space, at the cost of encountering spurious answer sets. Faithful (non-spurious) abstractions may be used to represent projected answer sets and to guide solvers in answer set construction. For dealing with spurious answer sets, we employ an ASP debugging approach to help with abstraction refinement, which determines atoms as badly omitted and adds them back in the abstraction. As a show case, we apply abstraction to explain unsatisfiability of ASP programs in terms of blocker sets, which are the sets of atoms such that abstraction to them preserves unsatisfiability. Their usefulness is demonstrated by experimental results.

中文翻译：

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答案集程序的基于遗漏的抽象

ion 是一种众所周知的方法，可以通过故意丢失信息来过度近似复杂问题来简化复杂问题。到目前为止，答案集编程 (ASP) 没有考虑到它，这是一种解决问题的便捷工具。我们介绍了一种自动抽象 ASP 程序的方法，该方法通过减少词汇表来保持其结构，同时确保过度近似（即，每个原始答案集映射到一些抽象答案集）。这允许生成有助于推理近似的部分答案集候选者。由于搜索空间较小，以遇到虚假答案集为代价，计算抽象答案集直观上更容易。忠实（非虚假）抽象可用于表示投影答案集并指导求解器构建答案集。为了处理虚假的答案集，我们采用 ASP 调试方法来帮助进行抽象细化，确定原子被严重遗漏并将它们添加回抽象中。作为一个展示案例，我们应用抽象来解释 ASP 程序在阻塞集方面的不可满足性，阻塞集是原子的集合，因此对它们的抽象保留了不可满足性。实验结果证明了它们的有用性。