Do Repeat Yourself: Understanding Sufficient Conditions for Restricted Chase Non-Termination

TL;DR

This paper investigates conditions that guarantee non-termination of the restricted chase procedure in knowledge bases, proposing new cyclicity notions and empirically evaluating their effectiveness to better understand when chase non-termination occurs.

Contribution

It introduces novel cyclicity notions for restricted chase non-termination and empirically assesses their generality compared to previous criteria.

Findings

New cyclicity notions effectively identify non-termination cases.

Proposed criteria are more general than previous notions.

Empirical results support the usefulness of the new criteria.

Abstract

The disjunctive restricted chase is a sound and complete procedure for solving boolean conjunctive query entailment over knowledge bases of disjunctive existential rules. Alas, this procedure does not always terminate and checking if it does is undecidable. However, we can use acyclicity notions (sufficient conditions that imply termination) to effectively apply the chase in many real-world cases. To know if these conditions are as general as possible, we can use cyclicity notions (sufficient conditions that imply non-termination). In this paper, we discuss some issues with previously existing cyclicity notions, propose some novel notions for non-termination by dismantling the original idea, and empirically verify the generality of the new criteria.