Analyzing Semantics of Aggregate Answer Set Programming Using Approximation Fixpoint Theory
Linde Vanbesien, Maurice Bruynooghe, Marc Denecker · Theory and Practice of Logic Programming · 2022
Abstract 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.