Query Rewriting with Disjunctive Existential Rules and Mappings

TL;DR

This paper introduces a sound and complete query rewriting method for unions of conjunctive queries with disjunctive existential rules, revealing limitations and undecidability issues in query rewriting and mappings.

Contribution

It proposes a novel query rewriting operator linked to chase steps, and demonstrates the non-existence of UCQ-rewritings for certain disjunctive rules, highlighting fundamental limitations.

Findings

A tight relationship between chase and rewriting steps is established.

Not all conjunctive queries with disjunctive rules have UCQ-rewritings.

Determining UCQ-rewritability via disjunctive mappings is undecidable.

Abstract

We consider the issue of answering unions of conjunctive queries (UCQs) with disjunctive existential rules and mappings. While this issue has already been well studied from a chase perspective, query rewriting within UCQs has hardly been addressed yet. We first propose a sound and complete query rewriting operator, which has the advantage of establishing a tight relationship between a chase step and a rewriting step. The associated breadth-first query rewriting algorithm outputs a minimal UCQ-rewriting when one exists. Second, we show that for any ``truly disjunctive'' nonrecursive rule, there exists a conjunctive query that has no UCQ-rewriting. It follows that the notion of finite unification sets (fus), which denotes sets of existential rules such that any UCQ admits a UCQ-rewriting, seems to have little relevance in this setting. Finally, turning our attention to mappings, we show that the problem of determining whether a UCQ admits a UCQ-rewriting through a disjunctive mapping is undecidable. We conclude with a number of open problems.