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.

摘要是一种众所周知的方法，可以通过故意使信息过分逼近来简化复杂问题。到目前为止，答案集编程（ASP）（一种解决问题的便捷工具）尚未考虑该问题。我们介绍了一种自动抽象ASP程序的方法，该方法可以通过减少词汇量同时确保其过​​度逼近来保留其结构（即，每个原始答案集都映射到某个抽象答案集）。这允许生成可帮助近似推理的部分答案集候选。由于搜索空间较小，因此计算抽象答案集在直观上更容易，但会遇到虚假的答案集。忠实的（非虚假的）抽象可以用来表示预期的答案集并在答案集构建中指导求解器。为了处理伪造的答案集，我们采用ASP调试方法来帮助优化抽象，该方法确定原子被严重忽略，并将其重新添加到抽象中。作为一个展示案例，我们用阻塞器集来解释ASP程序的不满足性，该阻塞器是原子集，因此对它们的抽象保留了不满足性。实验结果证明了其实用性。