# An ASP semantics for Constraints involving Conditional Aggregates

arXiv: https://arxiv.org/abs/2002.06911 · HTML: https://mlsanity.com/paper/2002.06911/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Feb 2020.

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

- [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)
- [A Unifying Framework for Semiring-Based Constraint Logic Programming With Negation (full version)](https://mlsanity.com/paper/2507.16067/) (2025)
- [ASP-FZN: A Translation-based Constraint Answer Set Solver](https://mlsanity.com/paper/2507.22774/) (2025)
- [FLINGO -- Instilling ASP Expressiveness into Linear Integer Constraints](https://mlsanity.com/paper/2602.09620/) (2026)

## Abstract (arXiv)

We elaborate upon the formal foundations of hybrid Answer Set Programming (ASP) and extend its underlying logical framework with aggregate functions over constraint values and variables. This is achieved by introducing the construct of conditional expressions, which allow for considering two alternatives while evaluating constraints. Which alternative is considered is interpretation-dependent and chosen according to an associated condition. We put some emphasis on logic programs with linear constraints and show how common ASP aggregates can be regarded as particular cases of so-called conditional linear constraints. Finally, we introduce a polynomial-size, modular and faithful translation from our framework into regular (condition-free) Constraint ASP, outlining an implementation of conditional aggregates on top of existing hybrid ASP solvers.