Grounding Recursive Aggregates: Preliminary Report

Abstract. 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 pro-gram. 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.