Converging to the Chase - a Tool for Finite Controllability

We solve a problem, stated in [CGP10], showing that Sticky Datalog, defined in the cited paper as an element of the Datalog\pm project, has the finite controllability property. In order to do that, we develop a technique, which we believe can have further applications, of approximating Chase(D, T), for a database instance D and some sets of tuple generating dependencies T, by an infinite sequence of finite structures, all of them being models of T

Decidability of Querying First-Order Theories via Countermodels of Finite Width

We propose a generic framework for establishing the decidability of a wide range of logical entailment problems (briefly called querying), based on the existence of countermodels that are structurally simple, gauged by certain types of width measures (with treewidth and cliquewidth as popular examples). As an important special case of our framework, we identify logics exhibiting width-finite finitely universal model sets, warranting decidable entailment for a wide range of homomorphism-closed queries, subsuming a diverse set of practically relevant query languages. As a particularly powerful width measure, we propose Blumensath's partitionwidth, which subsumes various other commonly considered width measures and exhibits highly favorable computational and structural properties. Focusing on the formalism of existential rules as a popular showcase, we explain how finite partitionwidth sets of rules subsume other known abstract decidable classes but -- leveraging existing notions of stratification -- also cover a wide range of new rulesets. We expose natural limitations for fitting the class of finite unification sets into our picture and provide several options for remedy

Dyadic existential rules

In the field of ontology-based query answering, existential rules (a.k.a. tuple-generating dependencies) form an expressive Datalog-based language to specify implicit knowledge. The presence of existential quantification in rule-heads, however, makes the main reasoning tasks undecidable. To overcome this limitation, in the last two decades, a number of classes of existential rules guaranteeing the decidability of query answering have been proposed. Unfortunately, such classes are typically based on different syntactic conditions imposing the development of different ad hoc reasoners. This paper introduces a novel general condition that allows to define, systematically, from any decidable class C of existential rules, a new class called Dyadic-C that enjoys the following properties: (i) it is decidable; (ii) it generalizes C; (iii) it keeps the same data complexity as C; and (iv) it can exploit any reasoner for query answering over C. Additionally, the paper proposes a simple and elegant syntactic condition that gives rise to the class Ward+ generalizing the well-known decidable classes Shy and Ward, and being included in Dyadic-Shy

Semantic Acyclicity Under Constraints

A conjunctive query (CQ) is semantically acyclic if it is equivalent to an acyclic one. Semantic acyclicity has been studied in the constraint-free case, and deciding whether a query enjoys this property is NP-complete. However, in case the database is subject to constraints such as tuple-generating dependencies (tgds) that can express, e.g., inclusion dependencies, or equality-generating dependencies (egds) that capture, e.g., functional dependencies, a CQ may turn out to be semantically acyclic under the constraints while not semantically acyclic in general. This opens avenues to new query optimization techniques. In this paper we initiate and develop the theory of semantic acyclicity under constraints. More precisely, we study the following natural problem: Given a CQ and a set of constraints, is the query semantically acyclic under the constraints, or, in other words, is the query equivalent to an acyclic one over all those databases that satisfy the set of constraints? We show that, contrary to what one might expect, decidability of CQ containment is a necessary but not sufficient condition for the decidability of semantic acyclicity. In particular, we show that semantic acyclicity is undecidable in presence of full tgds (i.e., Datalog rules). In view of this fact, we focus on the main classes of tgds for which CQ containment is decidable, and do not capture the class of full tgds, namely guarded, non-recursive and sticky tgds. For these classes we show that semantic acyclicity is decidable, and its complexity coincides with the complexity of CQ containment. In the case of egds, we show that semantic acyclicity is undecidable even over unary and binary predicates. When restricted to keys the problem becomes decidable (NP-complete) over such schemas. We finally consider the problem of evaluating a semantically acyclic query over a database that satisfies a set of constraints. For guarded tgds the evaluation problem is tractable. © Association Computing for Machiner