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

On the k-Boundedness for Existential Rules

The chase is a fundamental tool for existential rules. Several chase variants are known, which differ on how they handle redundancies possibly caused by the introduction of nulls. Given a chase variant, the halting problem takes as input a set of existential rules and asks if this set of rules ensures the termination of the chase for any factbase. It is well-known that this problem is undecidable for all known chase variants. The related problem of boundedness asks if a given set of existential rules is bounded, i.e., whether there is a predefined upper bound on the number of (breadth-first) steps of the chase, independently from any factbase. This problem is already undecidable in the specific case of datalog rules. However, knowing that a set of rules is bounded for some chase variant does not help much in practice if the bound is unknown. Hence, in this paper, we investigate the decidability of the k-boundedness problem, which asks whether a given set of rules is bounded by an integer k. We prove that k-boundedness is decidable for three chase variants, namely the oblivious, semi-oblivious and restricted chase.Comment: 20 pages, revised version of the paper published at RuleML+RR 201

Recurrence with affine level mappings is P-time decidable for CLP(R)

In this paper we introduce a class of constraint logic programs such that their termination can be proved by using affine level mappings. We show that membership to this class is decidable in polynomial time.Comment: To appear in Theory and Practice of Logic Programming (TPLP

Tractable Query Answering and Optimization for Extensions of Weakly-Sticky Datalog+-

We consider a semantic class, weakly-chase-sticky (WChS), and a syntactic subclass, jointly-weakly-sticky (JWS), of Datalog+- programs. Both extend that of weakly-sticky (WS) programs, which appear in our applications to data quality. For WChS programs we propose a practical, polynomial-time query answering algorithm (QAA). We establish that the two classes are closed under magic-sets rewritings. As a consequence, QAA can be applied to the optimized programs. QAA takes as inputs the program (including the query) and semantic information about the "finiteness" of predicate positions. For the syntactic subclasses JWS and WS of WChS, this additional information is computable.Comment: To appear in Proc. Alberto Mendelzon WS on Foundations of Data Management (AMW15

Estimating the maximum rise in temperature according to climate models using abstract interpretation

Current climate models are complex computer programs that are typically iterated time-step by time-step to predict the next set of values of the climate-related variables. Since these iterative methods are necessarily computed only for a fixed number of iterations, they are unable to answer the natural question whether there is a limit to the rise of global temperature. In order to answer that question we propose to combine climate models with software verification techniques that can find invariant conditions for the set of program variables. In particular, we apply the constraint database approach to software verification to find that the rise in global temperature is bounded according to the common Java Climate Model that implements the Wigely/Raper Upwelling-Diffusion Energy Balance Model climate model