Aggregates provide a concise way to express complex knowledge. While they are easily understood by humans, formalizing aggregates for answer set programming (ASP) has proven to be challenging . The literature offers many approaches that are not always compatible. One of these approaches, based on Approximation Fixpoint Theory (AFT), has been developed in a logic programming context and has not found much resonance in the ASP-community. In this paper we revisit this work. We introduce the abstract notion of a ternary satisfaction relation and define stable semantics in terms of it. We show that ternary satisfaction relations bridge the gap between the standard Gelfond-Lifschitz reduct, and stable semantics as defined in the framework of AFT. We analyse the properties of ternary satisfaction relations for handling aggregates in ASP programs. Finally, we show how different methods for handling aggregates taken from the literature can be described in the framework and we study the corresponding ternary satisfaction relations.

该研究在近似不动点理论的观点下重新考虑了选择用于回答集编程（ASP）中聚合的适当形式化问题，介绍了一种等同于基本ASP程序的Gelfond-Lifschitz规约的AFT形式化，并将其扩展到聚合处理。

使用近似不动点理论分析聚合答案集编程的语义