Extending Acyclicity Notions for Existential Rules (\emph{long version})

TL;DR

This paper introduces new acyclicity conditions that extend existing notions to ensure chase termination in existential rules, including nonmonotonic negation, improving the theoretical understanding of query answering.

Contribution

It proposes a novel tool for extending acyclicity conditions and extends these results to rules with nonmonotonic negation under stable model semantics.

Findings

Extended acyclicity conditions improve chase termination guarantees.

New tool maintains good complexity properties.

Results apply to rules with nonmonotonic negation.

Abstract

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.