Normalisations of Existential Rules: Not so Innocuous!

TL;DR

This paper investigates how normalising existential rules affects reasoning properties like chase termination and FO-rewritability, revealing that such procedures can impact decidability and raising open problems.

Contribution

It provides a systematic analysis of the effects of rule normalisation on chase properties and decidability in existential rules, highlighting potential issues and open questions.

Findings

Normalisation can affect chase termination properties.

Certain normal forms may preserve or break FO-rewritability.

Open problems remain regarding chase termination in normalised rules.

Abstract

Existential rules are an expressive knowledge representation language mainly developed to query data. In the literature, they are often supposed to be in some normal form that simplifies technical developments. For instance, a common assumption is that rule heads are atomic, i.e., restricted to a single atom. Such assumptions are considered to be made without loss of generality as long as all sets of rules can be normalised while preserving entailment. However, an important question is whether the properties that ensure the decidability of reasoning are preserved as well. We provide a systematic study of the impact of these procedures on the different chase variants with respect to chase (non-)termination and FO-rewritability. This also leads us to study open problems related to chase termination of independent interest.