Abstraction 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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答案集程序的基于省略的抽象

摘要是一种众所周知的方法，它通过故意丢失信息而过度近似来简化复杂问题。到目前为止，在答案集编程 (ASP) 中还没有考虑过它，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量同时确保过度近似（即，每个原始答案集映射到某个抽象答案集）来保留其结构。这允许生成可以帮助推理近似的部分答案集候选。由于较小的搜索空间，计算抽象答案集在直觉上更容易，但代价是遇到虚假答案集。忠实（非虚假）抽象可用于表示投影的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 调试方法来帮助抽象细化，它确定原子被严重遗漏，并将它们重新添加到抽象中。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，这是一组原子，使得对它们的抽象保持不可满足性。实验结果证明了它们的有用性。