Balder ten Cate

Ontology-Based Data Access: A Study through Disjunctive Datalog, CSP, and MMSNP

Ontology-based data access is concerned with querying incomplete data sources in the presence of domain-specific knowledge provided by an ontology. A central notion in this setting is that of an ontology-mediated query, which is a database query coupled with an ontology. In this article, we study several classes of ontology-mediated queries, where the database queries are given as some form of conjunctive query and the ontologies are formulated in description logics or other relevant fragments of first-order logic, such as the guarded fragment and the unary negation fragment. The contributions of the article are threefold. First, we show that popular ontology-mediated query languages have the same expressive power as natural fragments of disjunctive datalog, and we study the relative succinctness of ontology-mediated queries and disjunctive datalog queries. Second, we establish intimate connections between ontology-mediated queries and constraint satisfaction problems (CSPs) and their logical generalization, MMSNP formulas. Third, we exploit these connections to obtain new results regarding: (i) first-order rewritability and datalog rewritability of ontology-mediated queries; (ii) P/NP dichotomies for ontology-mediated queries; and (iii) the query containment problem for ontology-mediated queries.

Designing and refining schema mappings via data examples

A schema mapping is a specification of the relationship between a source schema and a target schema. Schema mappings are fundamental building blocks in data integration and data exchange and, as such, obtaining the right schema mapping constitutes a major step towards the integration or exchange of data. Up to now, schema mappings have typically been specified manually or have been derived using mapping-design systems that automatically generate a schema mapping from a visual specification of the relationship between two schemas. We present a novel paradigm and develop a system for the interactive design of schema mappings via data examples. Each data example represents a partial specification of the semantics of the desired schema mapping. At the core of our system lies a sound and complete algorithm that, given a finite set of data examples, decides whether or not there exists a GLAV schema mapping (i.e., a schema mapping specified by Global-and-Local-As-View constraints) that fits these data examples. If such a fitting GLAV schema mapping exists, then our system constructs the most general one. We give a rigorous computational complexity analysis of the underlying decision problem concerning the existence of a fitting GLAV schema mapping, given a set of data examples. Specifically, we prove that this problem is complete for the second level of the polynomial hierarchy, hence, in a precise sense, harder than NP-complete. This worst-case complexity analysis notwithstanding, we conduct an experimental evaluation of our prototype implementation that demonstrates the feasibility of interactively designing schema mappings using data examples. In particular, our experiments show that our system achieves very good performance in real-life scenarios.

Guarded Negation

We consider restrictions of first-order logic and of fixpoint logic in which all occurrences of negation are required to be guarded by an atomic predicate. In terms of expressive power, the logics in question, called GNFO and GNFP, extend the guarded fragment of first-order logic and the guarded least fixpoint logic, respectively. They also extend the recently introduced unary negation fragments of first-order logic and of least fixpoint logic. We show that the satisfiability problem for GNFO and for GNFP is 2ExpTime-complete, both on arbitrary structures and on finite structures. We also study the complexity of the associated model checking problems. Finally, we show that GNFO and GNFP are not only computationally well behaved, but also model theoretically: we show that GNFO and GNFP have the tree-like model property and that GNFO has the finite model property, and we characterize the expressive power of GNFO in terms of invariance for an appropriate notion of bisimulation. Our complexity upper bounds for GNFO and GNFP hold true even for their “clique-guarded” extensions CGNFO and CGNFP, in which clique guards are allowed in the place of guards.

Queries with guarded negation

A well-established and fundamental insight in database theory is that negation (also known as complementation) tends to make queries difficult to process and difficult to reason about. Many basic problems are decidable and admit practical algorithms in the case of unions of conjunctive queries, but become difficult or even undecidable when queries are allowed to contain negation. Inspired by recent results in finite model theory, we consider a restricted form of negation, guarded negation. We introduce a fragment of SQL, called GN-SQL, as well as a fragment of Datalog with stratified negation, called GN-Datalog, that allow only guarded negation, and we show that these query languages are computationally well behaved, in terms of testing query containment, query evaluation, open-world query answering, and boundedness. GN-SQL and GN-Datalog subsume a number of well known query languages and constraint languages, such as unions of conjunctive queries, monadic Datalog, and frontier-guarded tgds. In addition, an analysis of standard benchmark workloads shows that many uses of negation in SQL in practice are guarded.

On the data complexity of consistent query answering

The framework of database repairs is a principled approach to managing inconsistency in databases. In particular, the consistent answers of a query on an inconsistent database provide sound semantics and the guarantee that the values obtained are those returned by the query on every repair of the given inconsistent database. In this paper, we carry out a systematic investigation of the data complexity of the consistent answers of conjunctive queries for set-based repairs and with respect to classes of constraints that, in recent years, have been extensively studied in the context of data exchange and data integration. Our results, which range from polynomial-time computability to undecidability, complement or improve on earlier work, and provide a fairly comprehensive picture of the data complexity of consistent query answering. We also address the problem of finding a representative or useful repair of an inconsistent database. To this effect, we introduce the notion of a universal repair, as well as relaxations of it, and then apply it to the investigation of the data complexity of consistent query answering.

Rewriting Guarded Negation Queries

The Guarded Negation Fragment (GNFO) is a fragment of first-order logic that contains all unions of conjunctive queries, a restricted form of negation that suffices for expressing some common uses of negation in SQL queries, and a large class of integrity constraints. At the same time, as was recently shown, the syntax of GNFO is restrictive enough so that static analysis problems such as query containment are still decidable. This suggests that, in spite of its expressive power, GNFO queries are amenable to novel optimizations. In this paper we provide further evidence for this, establishing that GNFO queries have distinctive features with respect to rewriting. Our results include effective preservation theorems for GNFO, Craig Interpolation and Beth Definability results, and the ability to express the certain answers of queries with respect to GNFO constraints within very restricted logics.

Database constraints and homomorphism dualities

Global-as-view (GAV) constraints form a class of database constraints that has been widely used in the study of data exchange and data integration. Specifically, relationships between different database schemas are commonly described by a schema mapping consisting of a finite set of GAV constraints. Such schema mappings can be viewed as representations of an infinite set of data examples. We study the following problem: when is finite set of GAV constraints uniquely characterizable via a finite set of data examples? By establishing a tight connection between this problem and homomorphism dualities, we obtain a simple criterion for unique characterizability. We also pinpoint the computational complexity of the corresponding decision problem.

An easy completeness proof for the modal µ-calculus on finite trees

We give a complete axiomatization for the modal μ-calculus on finite trees. While the completeness of our axiomatization already follows from a more powerful result by Igor Walukiewicz in [11], our proof is easier and uses very different tools, inspired from model theory. We show that our approach generalizes to certain axiomatic extensions, and to the extension of the μ-calculus with graded modalities. We hope that the method might be helpful for other completeness proofs as well.

On the equivalence of distributed systems with queries and communication

Distributed data management systems consist of peers that store, exchange and process data in order to collaboratively achieve a common goal, such as evaluate some query. We study the equivalence of such systems. We model a distributed system by a collection of Active XML documents, i.e., trees augmented with function calls for performing tasks such as sending, receiving and querying data. As our model is quite general, the equivalence problem turns out to be undecidable. However, we exhibit several restrictions of the model, for which equivalence can be effectively decided. We also study the computational complexity of the equivalence problem, and present an axiomatization of equivalence, in the form of a set of equivalence-preserving rewrite rules allowing us to optimize a system by rewriting it into an equivalent, but possibly more efficient system.

Some modal aspects of XPath

This paper provides several examples of how modal logic can be used in studying the XML document navigation language XPath. More specifically, we derive complete axiomatizations, computational complexity and expressive power results for XPath fragments from known results for corresponding logics. A secondary aim of the paper is to introduce XPath in a way that makes it accessible to an audience of modal logicians.