# On the Foundations of Grounding in Answer Set Programming

arXiv: https://arxiv.org/abs/2108.04769 · HTML: https://mlsanity.com/paper/2108.04769/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 69 references that are in the map.
- First posted on arXiv 10 Aug 2021.

## Builds on (most cited first, 6 of 6)

- [Advancing Lazy-Grounding ASP Solving Techniques -- Restarts, Phase Saving, Heuristics, and More](https://mlsanity.com/paper/2008.03526/) (2020)
- [Modularity Aspects of Disjunctive Stable Models](https://mlsanity.com/paper/1401.3484/) (2014)
- [Predicate Logic as a Modelling Language: The IDP System](https://mlsanity.com/paper/1401.6312/) (2014)
- [Analyzing Semantics of Aggregate Answer Set Programming Using Approximation Fixpoint Theory](https://mlsanity.com/paper/2104.14789/) (2021)
- [Grounding Recursive Aggregates: Preliminary Report](https://mlsanity.com/paper/1603.03884/) (2016)
- [Grounding FO and FO(ID) with Bounds](https://mlsanity.com/paper/1401.3840/) (2014)

## Built on by (most cited first, 6 of 6)

- [Decomposition Strategies and Multi-shot ASP Solving for Job-shop Scheduling](https://mlsanity.com/paper/2205.07537/) (2022)
- [Current and Future Challenges in Knowledge Representation and Reasoning](https://mlsanity.com/paper/2308.04161/) (2023)
- [System Predictor: Grounding Size Estimator for Logic Programs under Answer Set Semantics](https://mlsanity.com/paper/2303.17018/) (2023)
- [Finite Groundings for ASP with Functions: A Journey through Consistency](https://mlsanity.com/paper/2405.15794/) (2024)
- [Operator-based semantics for choice programs: is choosing losing? (full version)](https://mlsanity.com/paper/2407.21556/) (2024)
- [Intermediate Languages Matter: Formal Languages and LLMs affect Neurosymbolic Reasoning](https://mlsanity.com/paper/2509.04083/) (2025)

## Abstract (arXiv)

We provide a comprehensive elaboration of the theoretical foundations of variable instantiation, or grounding, in Answer Set Programming (ASP). Building on the semantics of ASP's modeling language, we introduce a formal characterization of grounding algorithms in terms of (fixed point) operators. A major role is played by dedicated well-founded operators whose associated models provide semantic guidance for delineating the result of grounding along with on-the-fly simplifications. We address an expressive class of logic programs that incorporates recursive aggregates and thus amounts to the scope of existing ASP modeling languages. This is accompanied with a plain algorithmic framework detailing the grounding of recursive aggregates. The given algorithms correspond essentially to the ones used in the ASP grounder gringo.