# Grounding Recursive Aggregates: Preliminary Report

arXiv: https://arxiv.org/abs/1603.03884 · HTML: https://mlsanity.com/paper/1603.03884/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Mar 2016.

## Built on by (most cited first, 4 of 4)

- [On the Foundations of Grounding in Answer Set Programming](https://mlsanity.com/paper/2108.04769/) (2021)
- [Aggregate Semantics for Propositional Answer Set Programs](https://mlsanity.com/paper/2109.08662/) (2021)
- [Generalizing Level Ranking Constraints for Monotone and Convex Aggregates](https://mlsanity.com/paper/2308.15888/) (2023)
- [Automated Hybrid Grounding Using Structural and Data-Driven Heuristics](https://mlsanity.com/paper/2507.17493/) (2025)

## Abstract (arXiv)

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.