# Extending Acyclicity Notions for Existential Rules (long version)

arXiv: https://arxiv.org/abs/1407.6885 · HTML: https://mlsanity.com/paper/1407.6885/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jul 2014.

## Built on by (most cited first, 1 of 1)

- [Parallelisable Existential Rules: a Story of Pieces](https://mlsanity.com/paper/2107.06054/) (2021)

## Abstract (arXiv)

Existential rules have been proposed for representing ontological knowledge, specifically in the context of Ontology-Based Query Answering. Entailment with existential rules is undecidable. We focus in this paper on conditions that ensure the termination of a breadth-first forward chaining algorithm known as the chase. First, we propose a new tool that allows to extend existing acyclicity conditions ensuring chase termination, while keeping good complexity properties. Second, we consider the extension to existential rules with nonmonotonic negation under stable model semantics and further extend acyclicity results obtained in the positive case.