The Space-Efficient Core of Vadalog

Abstract

Vadalog is a system for performing complex reasoning tasks such as those required in advanced knowledge graphs. The logical core of the underlying Vadalog language is the warded fragment of tuple-generating dependencies (TGDs). This formalism ensures tractable reasoning in data complexity, while a recent analysis focusing on a practical implementation led to the reasoning algorithm around which the Vadalog system is built. A fundamental question that has emerged in the context of Vadalog is the following: can we limit the recursion allowed by wardedness in order to obtain a formalism that provides a convenient syntax for expressing useful recursive statements, and at the same time achieves space-efficiency? After analyzing several real-life examples of warded sets of TGDs provided by our industrial partners, as well as recent benchmarks, we observed that recursion is often used in a restricted way: the body of a TGD contains at most one atom whose predicate is mutually recursive with a predicate in the head. We show that this type of recursion, known as piece-wise linear in the Datalog literature, is the answer to our main question. We further show that piece-wise linear recursion alone, without the wardedness condition, is not enough as it leads to the undecidability of reasoning. We finally study the relative expressiveness of the query languages based on (piece-wise linear) warded sets of TGDs.(1) Recursion over KGs. It is able to express full recursion and joins, which are needed to express complex reasoning tasks over KGs. Moreover, navigational capabilities, empowered by recursion, are vital for graph-based structures.(2) Ontological Reasoning over KGs. After adding a very mild and easy to handle negation, the language is able to express SPARQL reasoning under the OWL 2 QL entailment regime. Recall that SPARQL is the standard language for querying

Datalog Unchained

“…Datalog for knowledge graphs An outgrowth of Datalog+/-, Vadalog is a Datalog-based language geared towards reasoning about knowledge graphs [33][34][35]. Vadalog has at its core Warded Datalog+/-, a variant of Datalog+/-that has good properties in terms of expressiveness and complexity [30,75].…”

Harmless but Useful: Beyond Separable Equality Constraints in Datalog+/-

“…Because EGD unification can be executed in constant time on polynomially many processors, depending on the specific subfragment of Datalog ± in which TGDs of Σ 𝑇 are specified, the algorithm may enjoy high parallelizability. For instance, while Warded Datalog ± is not highly paralellizable, it is the case for an interesting and quite expressive variant of it, namely Piecewise Linear Warded Datalog ± [8], for which CQ answering is in NL in data complexity.…”

On the Relationship between Shy and Warded Datalog+/-

“…Likewise, Warded was recently introduced as fragment of the Datalog ± family (Calì et al 2010) and is implemented as logic core of the reasoner Vadalog system (Bellomarini et al 2020). Both find many industrial applications in the financial, media intelligence, security, logistics, pricing domains, and more (Berger et al 2019;Adrian et al 2018).…”