Taming the Infinite Chase: Query Answering under Expressive Relational Constraints

Abstract

The chase algorithm is a fundamental tool for query evaluation and for testing query containment under tuple-generating dependencies (TGDs) and equality-generating dependencies (EGDs). So far, most of the research on this topic has focused on cases where the chase procedure terminates. This paper introduces expressive classes of TGDs defined via syntactic restrictions: guarded TGDs (GTGDs) and weakly guarded sets of TGDs (WGTGDs). For these classes, the chase procedure is not guaranteed to terminate and thus may have an infinite outcome. Nevertheless, we prove that the problems of conjunctive-query answering and query containment under such TGDs are decidable. We provide decision procedures and tight complexity bounds for these problems. Then we show how EGDs can be incorporated into our results by providing conditions under which EGDs do not harmfully interact with TGDs and do not affect the decidability and complexity of query answering. We show applications of the aforesaid classes of constraints to the problem of answering conjunctive queries in F-Logic Lite, an object-oriented ontology language, and in some tractable Description Logics.

On the Chase for All Provenance Paths with Existential Rules

“…In this section we will describe how to build the Graph of Atom Dependency using a breadth-first forward chaining algorithm (chase) [5]. We describe the effects of different variants of the chase on the resulting GAD.…”

“…Oblivious Chase The oblivious chase σ obl − chase (also called naive chase) [5] relies on the oblivious derivation reducer denoted by σ obl and is defined as follows: for any derivation D, σ obl (D 1 ) = F 1 and…”

“…In this paper we focus on classes of existential rules where forward chaining is finite while backward chaining might be infinite. Different types of chases have been defined in the literature (Oblivious [5], Skolem [14], Restricted [8], etc. ), each chase provides a more powerful restriction test for detecting when to stop.…”

An Introduction to Description Logics and Query Rewriting

“…Note that rules (c ) and (r ) are similar to the rules from Section 3.1 except that they are applied without checking whether d and (d, d ) are already present in the interpretation of the concept and role, respectively. This modification of the chase procedure is usually called the oblivious chase (Johnson and Klug, 1984); see also (Calì et al, 2013). Example 17.…”

Complexity of Inconsistency-Tolerant Query Answering in Datalog+/–

“…The answer for a BCQ Q to D and Σ is Yes, denoted D ∪ Σ |= Q, iff ans(Q, D, Σ) = ∅. Note that query answering under general TGDs is undecidable [5], even when the schema and TGDs are fixed [9]. Both problems of CQ and BCQ evaluation under TGDs are LOGSPACE-equivalent [17,16].…”