# A Uniform Treatment of Aggregates and Constraints in Hybrid ASP

arXiv: https://arxiv.org/abs/2003.04176 · HTML: https://mlsanity.com/paper/2003.04176/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2020.

## Built on by (most cited first, 8 of 8)

- [Treewidth-aware Reductions of Normal ASP to SAT -- Is Normal ASP Harder than SAT after All?](https://mlsanity.com/paper/2210.03553/) (2022)
- [Strong Equivalence in Answer Set Programming with Constraints](https://mlsanity.com/paper/2502.04302/) (2025)
- [Towards a Semantics for Hybrid ASP systems](https://mlsanity.com/paper/2108.03061/) (2021)
- [Quantitative and Stream Extensions of Answer Set Programming](https://mlsanity.com/paper/2109.08281/) (2021)
- [Finite Groundings for ASP with Functions: A Journey through Consistency](https://mlsanity.com/paper/2405.15794/) (2024)
- [A Unifying Framework for Semiring-Based Constraint Logic Programming With Negation (full version)](https://mlsanity.com/paper/2507.16067/) (2025)
- [Towards a Neurosymbolic Reasoning System Grounded in Schematic Representations](https://mlsanity.com/paper/2509.03644/) (2025)
- [FLINGO -- Instilling ASP Expressiveness into Linear Integer Constraints](https://mlsanity.com/paper/2602.09620/) (2026)

## Abstract (arXiv)

Characterizing hybrid ASP solving in a generic way is difficult since one needs to abstract from specific theories. Inspired by lazy SMT solving, this is usually addressed by treating theory atoms as opaque. Unlike this, we propose a slightly more transparent approach that includes an abstract notion of a term. Rather than imposing a syntax on terms, we keep them abstract by stipulating only some basic properties. With this, we further develop a semantic framework for hybrid ASP solving and provide aggregate functions for theory variables that adhere to different semantic principles, show that they generalize existing aggregate semantics in ASP and how we can rely on off-the-shelf hybrid solvers for implementation.