The chase procedure and its applications

The goal of this thesis is not only to introduce and present new chase-based algorithms, but also to investigate the differences between the main existing chase procedures. In order to achieve this, first we will investigate and do a clear delimitation between the existing chase algorithms based on their termination criteria. This will give a better picture of which chase algorithm can be used for different dependency classes. Next, we will investigate the data exchange, data repair and data correspondence problems and show how the chase algorithm can be used to characterize different types of solutions. For the later two problems, we will also investigate the data complexity of solution-existence and solution-check problems. Further, we will introduce a new chase based algorithm which computes representative solutions under constructible models, a new closed world semantics. This new semantics is, in our view, appropriate to be used as a closed world semantics in data exchange. We will also show that the conditional table computed by this chase algorithm can help to get both possible and certain answers for general queries. And finally, we will investigate strong representation systems and strong data exchange representation system. We will prove, by introducing a new chase based algorithm, that mappings specified by source-to-target second order dependencies and target richly acyclic TGD’s are strong data exchange representation systems for the class of first order queries

The data-exchange chase under the microscope

In this paper we take closer look at recent developments for the chase procedure, and provide additional results. Our analysis allows us create a taxonomy of the chase variations and the properties they satisfy. Two of the most central problems regarding the chase is termination, and discovery of restricted classes of sets of dependencies that guarantee termination of the chase. The search for the restricted classes has been motivated by a fairly recent result that shows that it is undecidable to determine whether the chase with a given dependency set will terminate on a given instance. There is a small dissonance here, since the quest has been for classes of sets of dependencies guaranteeing termination of the chase on all instances, even though the latter problem was not known to be undecidable. We resolve the dissonance in this paper by showing that determining whether the chase with a given set of dependencies terminates on all instances is coRE-complete. For the hardness proof we use a reduction from word rewriting systems, thereby also showing the close connection between the chase and word rewriting. The same reduction also gives us the aforementioned instance-dependent RE-completeness result as a byproduct. For one of the restricted classes guaranteeing termination on all instances, the stratified sets dependencies, we provide new complexity results for the problem of testing whether a given set of dependencies belongs to it. These results rectify some previous claims that have occurred in the literature.Comment: arXiv admin note: substantial text overlap with arXiv:1303.668

Query Rewriting and Optimization for Ontological Databases

Ontological queries are evaluated against a knowledge base consisting of an extensional database and an ontology (i.e., a set of logical assertions and constraints which derive new intensional knowledge from the extensional database), rather than directly on the extensional database. The evaluation and optimization of such queries is an intriguing new problem for database research. In this paper, we discuss two important aspects of this problem: query rewriting and query optimization. Query rewriting consists of the compilation of an ontological query into an equivalent first-order query against the underlying extensional database. We present a novel query rewriting algorithm for rather general types of ontological constraints which is well-suited for practical implementations. In particular, we show how a conjunctive query against a knowledge base, expressed using linear and sticky existential rules, that is, members of the recently introduced Datalog+/- family of ontology languages, can be compiled into a union of conjunctive queries (UCQ) against the underlying database. Ontological query optimization, in this context, attempts to improve this rewriting process so to produce possibly small and cost-effective UCQ rewritings for an input query.Comment: arXiv admin note: text overlap with arXiv:1312.5914 by other author

Reasoning about embedded dependencies using inclusion dependencies

The implication problem for the class of embedded dependencies is undecidable. However, this does not imply lackness of a proof procedure as exemplified by the chase algorithm. In this paper we present a complete axiomatization of embedded dependencies that is based on the chase and uses inclusion dependencies and implicit existential quantification in the intermediate steps of deductions