The Complexity of Datalog on Linear Orders

We study the program complexity of datalog on both finite and infinite linear orders. Our main result states that on all linear orders with at least two elements, the nonemptiness problem for datalog is EXPTIME-complete. While containment of the nonemptiness problem in EXPTIME is known for finite linear orders and actually for arbitrary finite structures, it is not obvious for infinite linear orders. It sharply contrasts the situation on other infinite structures; for example, the datalog nonemptiness problem on an infinite successor structure is undecidable. We extend our upper bound results to infinite linear orders with constants. As an application, we show that the datalog nonemptiness problem on Allen's interval algebra is EXPTIME-complete.Comment: 21 page

Structurally Tractable Uncertain Data

Many data management applications must deal with data which is uncertain, incomplete, or noisy. However, on existing uncertain data representations, we cannot tractably perform the important query evaluation tasks of determining query possibility, certainty, or probability: these problems are hard on arbitrary uncertain input instances. We thus ask whether we could restrict the structure of uncertain data so as to guarantee the tractability of exact query evaluation. We present our tractability results for tree and tree-like uncertain data, and a vision for probabilistic rule reasoning. We also study uncertainty about order, proposing a suitable representation, and study uncertain data conditioned by additional observations.Comment: 11 pages, 1 figure, 1 table. To appear in SIGMOD/PODS PhD Symposium 201

The Vadalog System: Datalog-based Reasoning for Knowledge Graphs

Over the past years, there has been a resurgence of Datalog-based systems in the database community as well as in industry. In this context, it has been recognized that to handle the complex knowl\-edge-based scenarios encountered today, such as reasoning over large knowledge graphs, Datalog has to be extended with features such as existential quantification. Yet, Datalog-based reasoning in the presence of existential quantification is in general undecidable. Many efforts have been made to define decidable fragments. Warded Datalog+/- is a very promising one, as it captures PTIME complexity while allowing ontological reasoning. Yet so far, no implementation of Warded Datalog+/- was available. In this paper we present the Vadalog system, a Datalog-based system for performing complex logic reasoning tasks, such as those required in advanced knowledge graphs. The Vadalog system is Oxford's contribution to the VADA research programme, a joint effort of the universities of Oxford, Manchester and Edinburgh and around 20 industrial partners. As the main contribution of this paper, we illustrate the first implementation of Warded Datalog+/-, a high-performance Datalog+/- system utilizing an aggressive termination control strategy. We also provide a comprehensive experimental evaluation.Comment: Extended version of VLDB paper <https://doi.org/10.14778/3213880.3213888

Distribution Constraints: The Chase for Distributed Data

This paper introduces a declarative framework to specify and reason about distributions of data over computing nodes in a distributed setting. More specifically, it proposes distribution constraints which are tuple and equality generating dependencies (tgds and egds) extended with node variables ranging over computing nodes. In particular, they can express co-partitioning constraints and constraints about range-based data distributions by using comparison atoms. The main technical contribution is the study of the implication problem of distribution constraints. While implication is undecidable in general, relevant fragments of so-called data-full constraints are exhibited for which the corresponding implication problems are complete for EXPTIME, PSPACE and NP. These results yield bounds on deciding parallel-correctness for conjunctive queries in the presence of distribution constraints

Inductive Logic Programming in Databases: from Datalog to DL+log

In this paper we address an issue that has been brought to the attention of the database community with the advent of the Semantic Web, i.e. the issue of how ontologies (and semantics conveyed by them) can help solving typical database problems, through a better understanding of KR aspects related to databases. In particular, we investigate this issue from the ILP perspective by considering two database problems, (i) the definition of views and (ii) the definition of constraints, for a database whose schema is represented also by means of an ontology. Both can be reformulated as ILP problems and can benefit from the expressive and deductive power of the KR framework DL+log. We illustrate the application scenarios by means of examples. Keywords: Inductive Logic Programming, Relational Databases, Ontologies, Description Logics, Hybrid Knowledge Representation and Reasoning Systems. Note: To appear in Theory and Practice of Logic Programming (TPLP).Comment: 30 pages, 3 figures, 2 tables