Recursive Aggregates in Disjunctive Logic Programs: Semantics and Complexity

TL;DR: The addition of aggregates has been one of the most relevant enhancements to the language of answer set programming (ASP) and many of them do not satisfy desirable criteria, such as minimality or coincidence with answer sets in the aggregate-free case.

Abstract: The addition of aggregates has been one of the most relevant enhancements to the language of answer set programming (ASP). They strengthen the modeling power of ASP, in terms of concise problem representations. While many important problems can be encoded using nonrecursive aggregates, some relevant examples lend themselves for the use of recursive aggregates. Previous semantic definitions typically agree in the nonrecursive case, but the picture is less clear for recursion. Some proposals explicitly avoid recursive aggregates, most others differ, and many of them do not satisfy desirable criteria, such as minimality or coincidence with answer sets in the aggregate-free case.