Queries with Guarded Negation (full version)

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 most usage of negation in SQL in practice is guarded negation

Evaluating Datalog via Tree Automata and Cycluits

We investigate parameterizations of both database instances and queries that make query evaluation fixed-parameter tractable in combined complexity. We show that clique-frontier-guarded Datalog with stratified negation (CFG-Datalog) enjoys bilinear-time evaluation on structures of bounded treewidth for programs of bounded rule size. Such programs capture in particular conjunctive queries with simplicial decompositions of bounded width, guarded negation fragment queries of bounded CQ-rank, or two-way regular path queries. Our result is shown by translating to alternating two-way automata, whose semantics is defined via cyclic provenance circuits (cycluits) that can be tractably evaluated.Comment: 56 pages, 63 references. Journal version of "Combined Tractability of Query Evaluation via Tree Automata and Cycluits (Extended Version)" at arXiv:1612.04203. Up to the stylesheet, page/environment numbering, and possible minor publisher-induced changes, this is the exact content of the journal paper that will appear in Theory of Computing Systems. Update wrt version 1: latest reviewer feedbac

Representing and Querying Incomplete Information: a Data Interoperability Perspective

This habilitation thesis presents some of my most recent work, which has been done in collaboration with several other people. In particular this thesis concentrates on our contributions to the study of incomplete information in the context of data interoperability. In this scenario data is heterogenous and decentralized, needs to be integrated from several sources and exchanged between different applications. Incompleteness, i.e. the presence of “missing” or “unknown” portions of data, is naturally generated in data exchange and integration, due to data heterogeneity. The management of incomplete information poses new challenges in this context.The focus of our study is the development of models of incomplete information suitable to data interoperability tasks, and the study of techniques for efficiently querying several forms of incompleteness

Coping with Incomplete Data: Recent Advances

International audienceHandling incomplete data in a correct manner is a notoriously hard problem in databases. Theoretical approaches rely on the computationally hard notion of certain answers, while practical solutions rely on ad hoc query evaluation techniques based on threevalued logic. Can we find a middle ground, and produce correct answers efficiently? The paper surveys results of the last few years motivated by this question. We reexamine the notion of certainty itself, and show that it is much more varied than previously thought. We identify cases when certain answers can be computed efficiently and, short of that, provide deterministic and probabilistic approximation schemes for them. We look at the role of three-valued logic as used in SQL query evaluation, and discuss the correctness of the choice, as well as the necessity of such a logic for producing query answers

Coping with Incomplete Data: Recent Advances

Handling incomplete data in a correct manner is a notoriously hard problem in databases. Theoretical approaches rely on the computationally hard notion of certain answers, while practical solutions rely on ad hoc query evaluation techniques based on three-valued logic. Can we find a middle ground, and produce correct answers efficiently? The paper surveys results of the last few years motivated by this question. We re-examine the notion of certainty itself, and show that it is much more varied than previously thought. We identify cases when certain answers can be computed efficiently and, short of that, provide deterministic and probabilistic approximation schemes for them. We look at the role of three-valued logic as used in SQL query evaluation, and discuss the correctness of the choice, as well as the necessity of such a logic for producing query answers

On First-Order Definable Colorings

We address the problem of characterizing $H$-coloring problems that are first-order definable on a fixed class of relational structures. In this context, we give several characterizations of a homomorphism dualities arising in a class of structure