Tags:Aggregates, Answer Set Programming, Approximation Fixpoint Theory, Logic Programming, Lower-regular and Ternary satisfaction relation
Abstract:
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 the problem 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.
Analyzing Semantics of Aggregate Answer Set Programming Using Approximation Fixpoint Theory