# Finite Groundings for ASP with Functions: A Journey through Consistency

arXiv: https://arxiv.org/abs/2405.15794 · HTML: https://mlsanity.com/paper/2405.15794/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 31 references that are in the map.
- First posted on arXiv 8 May 2024.

## Builds on (most cited first, 7 of 7)

- [Multi-shot ASP solving with clingo](https://mlsanity.com/paper/1705.09811/) (2017)
- [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)
- [Advancing Lazy-Grounding ASP Solving Techniques -- Restarts, Phase Saving, Heuristics, and More](https://mlsanity.com/paper/2008.03526/) (2020)
- [A Uniform Treatment of Aggregates and Constraints in Hybrid ASP](https://mlsanity.com/paper/2003.04176/) (2020)
- [On the Foundations of Grounding in Answer Set Programming](https://mlsanity.com/paper/2108.04769/) (2021)
- [lpopt: A Rule Optimization Tool for Answer Set Programming](https://mlsanity.com/paper/1608.05675/) (2016)

## Abstract (arXiv)

Answer set programming (ASP) is a logic programming formalism used in various areas of artificial intelligence like combinatorial problem solving and knowledge representation and reasoning. It is known that enhancing ASP with function symbols makes basic reasoning problems highly undecidable. However, even in simple cases, state of the art reasoners, specifically those relying on a ground-and-solve approach, fail to produce a result. Therefore, we reconsider consistency as a basic reasoning problem for ASP. We show reductions that give an intuition for the high level of undecidability. These insights allow for a more fine-grained analysis where we characterize ASP programs as "frugal" and "non-proliferous". For such programs, we are not only able to semi-decide consistency but we also propose a grounding procedure that yields finite groundings on more ASP programs with the concept of "forbidden" facts.