Taming the Infinite Chase: Query Answering under Expressive Integrity Constraints

TL;DR

This paper explores classes of tuple-generating dependencies (TGDs) that allow for decidable query answering despite non-termination of the chase, by imposing syntactic restrictions inspired by guarded logic, and extends results to EGDs and practical ontology languages.

Contribution

It introduces new syntactic classes of TGDs ensuring decidability of query answering even when the chase does not terminate, and analyzes their complexity and applications.

Findings

Decidability of query answering under non-terminating chase for new TGD classes.

Tight complexity bounds for conjunctive query evaluation.

Applicability to ontology languages like F-Logic Lite and Description Logics.

Abstract

The chase algorithm is a fundamental tool for query evaluation and query containment under constraints, where the constraints are (sub-classes of) tuple-generating dependencies (TGDs) and equality generating depencies (EGDs). So far, most of the research on this topic has focused on cases where the chase procedure terminates, with some notable exceptions. In this paper we take a general approach, and we propose large classes of TGDs under which the chase does not always terminate. Our languages, in particular, are inspired by guarded logic: we show that by enforcing syntactic properties on the form of the TGDs, we are able to ensure decidability of the problem of answering conjunctive queries despite the non-terminating chase. We provide tight complexity bounds for the problem of conjunctive query evaluation for several classes of TGDs. We then introduce EGDs, and provide a condition under which EGDs do not interact with TGDs, and therefore do not take part in query answering. We show applications of our classes of constraints to the problem of answering conjunctive queries under F-Logic Lite, a recently introduced ontology language, and under prominent tractable Description Logics languages. All the results in this paper immediately extend to the problem of conjunctive query containment.