Existential Rule Languages with Finite Chase: Complexity and Expressiveness

TL;DR

This paper introduces a new classification for existential rule languages with finite chase, analyzing their complexity and expressiveness, and showing that some are more succinct despite similar expressiveness.

Contribution

It proposes a novel classification approach for rule languages with finite chase, extending existing languages and analyzing their complexity and expressiveness.

Findings

All languages with finite chase are tractable for data complexity.

Combined complexity can be arbitrarily high among these languages.

Languages extending weakly acyclic are equally expressive as weakly acyclic ones.

Abstract

Finite chase, or alternatively chase termination, is an important condition to ensure the decidability of existential rule languages. In the past few years, a number of rule languages with finite chase have been studied. In this work, we propose a novel approach for classifying the rule languages with finite chase. Using this approach, a family of decidable rule languages, which extend the existing languages with the finite chase property, are naturally defined. We then study the complexity of these languages. Although all of them are tractable for data complexity, we show that their combined complexity can be arbitrarily high. Furthermore, we prove that all the rule languages with finite chase that extend the weakly acyclic language are of the same expressiveness as the weakly acyclic one, while rule languages with higher combined complexity are in general more succinct than those with lower combined complexity.