# Clingo goes Linear Constraints over Reals and Integers

arXiv: https://arxiv.org/abs/1707.04053 · HTML: https://mlsanity.com/paper/1707.04053/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2017.

## Built on by (most cited first, 18 of 18)

- [Constraint Answer Set Programming: Integrational and Translational (or SMT-based) Approaches](https://mlsanity.com/paper/2107.08252/) (2021)
- [Aggregate Semantics for Propositional Answer Set Programs](https://mlsanity.com/paper/2109.08662/) (2021)
- [Decomposition Strategies and Multi-shot ASP Solving for Job-shop Scheduling](https://mlsanity.com/paper/2205.07537/) (2022)
- [Answer-Set Programming for Lexicographical Makespan Optimisation in Parallel Machine Scheduling](https://mlsanity.com/paper/2212.09077/) (2022)
- [Solving a Multi-resource Partial-ordering Flexible Variant of the Job-shop Scheduling Problem with Hybrid ASP](https://mlsanity.com/paper/2101.10162/) (2021)
- [Strong Equivalence in Answer Set Programming with Constraints](https://mlsanity.com/paper/2502.04302/) (2025)
- [ASP-driven User-interaction with Clinguin](https://mlsanity.com/paper/2502.09222/) (2025)
- [Towards a Semantics for Hybrid ASP systems](https://mlsanity.com/paper/2108.03061/) (2021)
- [Hybrid ASP-based multi-objective scheduling of semiconductor manufacturing processes (Extended version)](https://mlsanity.com/paper/2307.14799/) (2023)
- [Finite Groundings for ASP with Functions: A Journey through Consistency](https://mlsanity.com/paper/2405.15794/) (2024)
- [Probabilistic Answer Set Programming with Discrete and Continuous Random Variables](https://mlsanity.com/paper/2409.20274/) (2024)
- [Compiling Metric Temporal Answer Set Programming](https://mlsanity.com/paper/2506.08150/) (2025)
- [Fine-grained Timing Analysis of Digital Integrated Circuits in Answer Set Programming](https://mlsanity.com/paper/2507.11150/) (2025)
- [ASP-FZN: A Translation-based Constraint Answer Set Solver](https://mlsanity.com/paper/2507.22774/) (2025)
- [EZSMT Version 3, Matured](https://mlsanity.com/paper/2607.13344/) (2026)
- [Logic, Optimization, and Artificial Intelligence](https://mlsanity.com/paper/2607.15532/) (2026)
- [Declarative Problem Solving in UAM Strategic Deconfliction](https://mlsanity.com/paper/2607.21197/) (2026)
- [Bound-Founded Semantics for Answer Set Programming with Difference Constraints: Preliminary Report](https://mlsanity.com/paper/2607.21201/) (2026)

## Abstract (arXiv)

The recent series 5 of the ASP system clingo provides generic means to enhance basic Answer Set Programming (ASP) with theory reasoning capabilities. We instantiate this framework with different forms of linear constraints, discuss the respective implementations, and present techniques of how to use these constraints in a reactive context. More precisely, we introduce extensions to clingo with difference and linear constraints over integers and reals, respectively, and realize them in complementary ways. Finally, we empirically evaluate the resulting clingo derivatives clingo[dl] and clingo[lp] on common fragments and contrast them to related ASP systems. This paper is under consideration for acceptance in TPLP.