### Abstract

The recent series 5 of the Answer Set Programming (ASP) system clingo provides generic means to enhance basic ASP with theory reasoning capabilities. We instantiate this framework with different forms of linear constraints and elaborate upon its formal properties. Given this, we discuss the respective implementations, and present techniques for using 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 language fragments and contrast them to related ASP systems.

Original language | English |
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Pages (from-to) | 872-888 |

Journal | Theory and Practice of Logic Programming |

Volume | 17 |

Issue number | 5-6 |

DOIs | |

Publication status | Published - 2017 |

MoE publication type | A1 Journal article-refereed |

Event | International Conference on Logic Programming - Melbourne, Australia Duration: 28 Aug 2017 → 1 Sep 2017 Conference number: 33 |

### Keywords

- answer set programming
- constraints
- constraint processing
- theory solving

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## Cite this

Janhunen, T., Kaminski, R., Ostrowski, M., Schellhorn, S., Wanko, P., & Schaub, T. (2017). Clingo goes linear constraints over reals and integers.

*Theory and Practice of Logic Programming*,*17*(5-6), 872-888. https://doi.org/10.1017/S1471068417000242