Aggregates provide a concise way to express complex knowledge. The problem of selecting an appropriate formalisation 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 formalisation equivalent with the Gelfond-Lifschitz reduct for basic ASP programs and we extend it to handle aggregates. We analyse how existing approaches relate to our framework. We hope this work sheds some new light on the issue of a proper formalisation of aggregates. This paper is under consideration for acceptance in TPLP.
翻译:综合数据为表达复杂的知识提供了简洁的方法。 选择对答题集成编程(ASP)进行适当正规化的问题仍未解决。 本文件从近似定点理论(AFT)的角度重新审视了这个问题。 我们为基本 ASP 程序引入了相当于 Gelfond-Lifschitz 转录的 AFT 正规化,我们将其扩展至处理总量。 我们分析了现有方法与我们框架的关系。 我们希望这项工作能为综合集成的适当正规化问题提供一些新线索。 本文正在审议供TPLP 接受。