Analyzing Semantics of Aggregate Answer Set Programming Using Approximation Fixpoint Theory
This work addresses the unsettled issue of formalizing aggregates in ASP, which is a domain-specific problem for logic programming researchers, and appears incremental as it builds on existing AFT frameworks.
The paper tackles the problem of selecting an appropriate formalization of aggregates in answer set programming (ASP) by revisiting it from the viewpoint of Approximation Fixpoint Theory (AFT), introducing an AFT formalization equivalent to the Gelfond-Lifschitz reduct for basic ASP programs and extending it to handle aggregates.
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.