Oblivious and Semi-Oblivious Boundedness for Existential Rules

TL;DR

This paper investigates the boundedness of positive existential rules, providing characterizations, decidability results, and complexity analysis for oblivious and semi-oblivious chase variants, with implications for query rewriting and chase termination.

Contribution

It offers a new characterization of boundedness in terms of FO-rewritability and chase termination, and analyzes the decidability and complexity for various rule classes.

Findings

Boundedness is characterized via FO-rewritability and chase termination.

Decidability results are established for several classes of rules.

Complexity bounds for recognizing boundedness are provided.

Abstract

We study the notion of boundedness in the context of positive existential rules, that is, whether there exists an upper bound to the depth of the chase procedure, that is independent from the initial instance. By focussing our attention on the oblivious and the semi-oblivious chase variants, we give a characterization of boundedness in terms of FO-rewritability and chase termination. We show that it is decidable to recognize if a set of rules is bounded for several classes and outline the complexity of the problem. This report contains the paper published at IJCAI 2019 and an appendix with full proofs.