# Constraint Answer Set Programming: Integrational and Translational (or SMT-based) Approaches

arXiv: https://arxiv.org/abs/2107.08252 · HTML: https://mlsanity.com/paper/2107.08252/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 111 references that are in the map.
- First posted on arXiv 17 Jul 2021.

## Builds on (most cited first, 10 of 10)

- [ASP-Core-2 Input Language Format](https://mlsanity.com/paper/1911.04326/) (2019)
- [Clingo goes Linear Constraints over Reals and Integers](https://mlsanity.com/paper/1707.04053/) (2017)
- [Clingcon: The Next Generation](https://mlsanity.com/paper/1705.04569/) (2017)
- [Verifying Tight Logic Programs with anthem and Vampire](https://mlsanity.com/paper/2008.02025/) (2020)
- [Modular Answer Set Programming as a Formal Specification Language](https://mlsanity.com/paper/2008.02015/) (2020)
- [SMT-based Constraint Answer Set Solver EZSMT+](https://mlsanity.com/paper/1905.03334/) (2019)
- [On Relation between Constraint Answer Set Programming and Satisfiability Modulo Theories](https://mlsanity.com/paper/1702.07461/) (2017)
- [The informal semantics of Answer Set Programming: A Tarskian perspective](https://mlsanity.com/paper/1901.09125/) (2019)
- [Aspartame: Solving Constraint Satisfaction Problems with Answer Set Programming](https://mlsanity.com/paper/1312.6113/) (2013)
- [Linear Integer Arithmetic Revisited](https://mlsanity.com/paper/1503.02948/) (2015)

## Built on by (most cited first, 7 of 7)

- [Strong Equivalence in Answer Set Programming with Constraints](https://mlsanity.com/paper/2502.04302/) (2025)
- [Current and Future Challenges in Knowledge Representation and Reasoning](https://mlsanity.com/paper/2308.04161/) (2023)
- [Extending Answer Set Programming with Rational Numbers](https://mlsanity.com/paper/2312.04249/) (2023)
- [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)
- [EZSMT Version 3, Matured](https://mlsanity.com/paper/2607.13344/) (2026)
- [Logic, Optimization, and Artificial Intelligence](https://mlsanity.com/paper/2607.15532/) (2026)

## Abstract (arXiv)

Constraint answer set programming or CASP, for short, is a hybrid approach in automated reasoning putting together the advances of distinct research areas such as answer set programming, constraint processing, and satisfiability modulo theories. Constraint answer set programming demonstrates promising results, including the development of a multitude of solvers: acsolver, clingcon, ezcsp, idp, inca, dingo, mingo, aspmt, clingo[l,dl], and ezsmt. It opens new horizons for declarative programming applications such as solving complex train scheduling problems. Systems designed to find solutions to constraint answer set programs can be grouped according to their construction into, what we call, integrational or translational approaches. The focus of this paper is an overview of the key ingredients of the design of constraint answer set solvers drawing distinctions and parallels between integrational and translational approaches. The paper also provides a glimpse at the kind of programs its users develop by utilizing a CASP encoding of Travelling Salesman problem for illustration. In addition, we place the CASP technology on the map among its automated reasoning peers as well as discuss future possibilities for the development of CASP.