Monotone Rewritability and the Analysis of Queries, Views, and Rules

TL;DR

This paper investigates the conditions under which queries can be deterministically reconstructed from views using monotone functions within existential rules, revealing complex boundaries between decidability and intractability.

Contribution

It provides new decidability results for monotonic determinacy in the context of existential rules and compares recoverability within different query languages.

Findings

Decidability of monotonic determinacy varies with rule complexity.

The boundary between well-behaved and badly-behaved answerability is more complex with existential rules.

New results on entailment problems involving views and rules were established.

Abstract

We study the interaction of views, queries, and background knowledge in the form of existential rules. The motivating questions concern monotonic determinacy of a query using views w.r.t. rules, which refers to the ability to recover the query answer from the views via a monotone function. We study the decidability of monotonic determinacy, and compare with variations that require the ``recovery function'' to be in a well-known monotone query language, such as conjunctive queries or Datalog. Surprisingly, we find that even in the presence of basic existential rules, the borderline between well-behaved and badly-behaved answerability differs radically from the unconstrained case. In order to understand this boundary, we require new results concerning entailment problems involving views and rules.