Grounding Recursive Aggregates: Preliminary Report
This work addresses a technical bottleneck in ASP grounding for developers and researchers, but it is incremental as it builds upon existing methods in the Gringo series.
The paper tackles the treatment of recursive aggregates during the grounding phase in Answer Set Programming, providing algorithms based on semi-naive database evaluation techniques for the Gringo series 4 system.
Problem solving in Answer Set Programming consists of two steps, a first grounding phase, systematically replacing all variables by terms, and a second solving phase computing the stable models of the obtained ground program. An intricate part of both phases is the treatment of aggregates, which are popular language constructs that allow for expressing properties over sets. In this paper, we elaborate upon the treatment of aggregates during grounding in Gringo series 4. Consequently, our approach is applicable to grounding based on semi-naive database evaluation techniques. In particular, we provide a series of algorithms detailing the treatment of recursive aggregates and illustrate this by a running example.