Aggregates provide a concise way to express complex knowledge. The problem of selecting an appropriate formalization of aggregates for answer set programming (ASP) remains unsettled. This paper revisits it from the viewpoint of Approximation Fixpoint Theory (AFT). We introduce an AFT formalization equivalent with the Gelfond–Lifschitz reduct for basic ASP programs and we extend it to handle aggregates. We analyze how existing approaches relate to our framework. We hope this work sheds some new light on the issue of a proper formalization of aggregates.

中文翻译：

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使用近似不动点理论分析聚合答案集编程的语义

聚合提供了一种简洁的方式来表达复杂的知识。为答案集编程 (ASP) 选择适当的聚合形式化的问题仍未解决。本文从近似不动点理论（AFT）的角度对其进行了重新审视。我们为基本的 ASP 程序引入了与 Gelfond-Lifschitz 约简等效的 AFT 形式化，并将其扩展为处理聚合。我们分析现有方法如何与我们的框架相关联。我们希望这项工作能为聚合的适当形式化问题提供一些新的思路。