# ASP(AC): Answer Set Programming with Algebraic Constraints

arXiv: https://arxiv.org/abs/2008.04008 · HTML: https://mlsanity.com/paper/2008.04008/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Aug 2020.

## Built on by (most cited first, 3 of 3)

- [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)
- [Complexity of Arithmetic in Warded Datalog+-](https://mlsanity.com/paper/2202.05086/) (2022)

## Abstract (arXiv)

Weighted Logic is a powerful tool for the specification of calculations over semirings that depend on qualitative information. Using a novel combination of Weighted Logic and Here-and-There (HT) Logic, in which this dependence is based on intuitionistic grounds, we introduce Answer Set Programming with Algebraic Constraints (ASP(AC)), where rules may contain constraints that compare semiring values to weighted formula evaluations. Such constraints provide streamlined access to a manifold of constructs available in ASP, like aggregates, choice constraints, and arithmetic operators. They extend some of them and provide a generic framework for defining programs with algebraic computation, which can be fruitfully used e.g. for provenance semantics of datalog programs. While undecidable in general, expressive fragments of ASP(AC) can be exploited for effective problem-solving in a rich framework. This work is under consideration for acceptance in Theory and Practice of Logic Programming.