Taming the Infinite Chase: Query Answering under Expressive Integrity Constraints (1212.3357v2)

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.

• The paper presents a framework ensuring decidability of conjunctive query answering under expressive relational constraints despite potential infinite chase sequences.
• It introduces Guarded and Weakly Guarded TGDs to manage infinite chase outcomes and establishes precise complexity bounds from exptime-hard to 2exptime-hard.
• The authors propose innocuous integration conditions for EGDs that preserve decidability, facilitating advanced ontology-based reasoning.

Overview of "Taming the Infinite Chase: Query Answering under Expressive Relational Constraints"

This paper addresses the critical challenge of determining query answers in the presence of potentially infinite chase sequences under complex relational constraints. Specifically, it focuses on Tuple-Generating Dependencies (TGDs) and Equality-Generating Dependencies (EGDs), which are foundational in database theory and ontological reasoning.

The authors introduce expressive classes of TGDs, namely Guarded TGDs (GTGDs) and Weakly Guarded TGDs (WGTGDs), which acknowledge that the chase procedure might not terminate, thus leading to infinite outcomes. Nevertheless, the paper establishes decidability of conjunctive-query answering and query containment under these TGDs, offering decision procedures and precise complexity bounds.

An imperative contribution is the proposal of conditions that integrate EGDs into the framework without negatively impacting decidability. These conditions ensure that EGDs do not interact harmfully with TGDs, allowing the integration of EGDs in a manner that preserves the complexity and decidability of query answering.

The paper posits that for WGTGDs, the results of the chase exhibit finite treewidth, facilitating the application of known decidability results from logic theory. The complexity analysis reveals that conjunctive query answering under WGTGDs is exptime-hard with fixed TGDs and 2exptime-hard when TGDs vary, illustrating the computational demands when handling such expressive constraints.

Significant in this research is the extension to ontology languages, particularly showing the application of TGDs and EGDs in ontologies like F-Logic Lite and specific Description Logics. This paves the way for tractable and expressive query answering in complex ontology-based systems.

The exploration also acknowledges the limitations posed by EGDs in conjunction with TGDs, where the combination can often lead to undecidability. However, the proposed framework contains conditions under which EGDs are deemed innocuous and thus can be seamlessly incorporated without compromising the decision processes.

Emphasizing practical applications, the paper suggests that this research underpins significant advancements in the field of AI, particularly regarding the intersection of database systems and knowledge representation. Future studies are likely to explore optimizing these procedures for broader classes of dependencies and real-world data scenarios.

In conclusion, this paper makes substantial strides in providing a robust theoretical foundation for dealing with infinite chase scenarios in query answering. Its impact on both theoretical advancements and practical applications in AI and database management is evident, setting the stage for further exploration in this complex yet crucial domain.