Boris Motik’s research while affiliated with University of Oxford and other places

Query answering over data with dependencies plays a central role in most applications of dependencies. The problem is commonly solved by using a suitable variant of the chase algorithm to compute a universal model of the dependencies and the data and thus explicate all knowledge implicit in the dependencies. After this preprocessing step, an arbitrary conjunctive query over the dependencies and the data can be answered by evaluating it the computed universal model. If, however, the query to be answered is fixed and known in advance, computing the universal model is often inefficient as many inferences made during this process can be irrelevant to a given query. In such cases, a goal-driven approach, which avoids drawing unnecessary inferences, promises to be more efficient and thus preferable in practice. In this paper we present what we believe to be the first technique for goal-driven query answering over first- and second-order dependencies with equality reasoning. Our technique transforms the input dependencies so that applying the chase to the output avoids many inferences that are irrelevant to the query. The transformation proceeds in several steps, which comprise the following three novel techniques. First, we present a variant of the singularisation technique by Marnette [60] that is applicable to second-order dependencies and that corrects an incompleteness of a related formulation by ten Cate et al. [74]. Second, we present a relevance analysis technique that can eliminate from the input dependencies that provably do not contribute to query answers. Third, we present a variant of the magic sets algorithm [19] that can handle second-order dependencies with equality reasoning. We also present the results of an extensive empirical evaluation, which show that goal-driven query answering can be orders of magnitude faster than computing the full universal model.

Guarded tuple-generating dependencies (GTGDs) are a natural extension of description logics and referential constraints. It has long been known that queries over GTGDs can be answered by a variant of the chase —a quintessential technique for reasoning with dependencies. However, there has been little work on concrete algorithms and even less on implementation. To address this gap, we revisit Datalog rewriting approaches to query answering, where a set of GTGDs is transformed to a Datalog program that entails the same base facts on each base instance. We show that a rewriting consists of “shortcut” rules that circumvent certain chase steps, we present several algorithms that compute a rewriting by deriving such “shortcuts” efficiently, and we discuss important implementation issues. Finally, we show empirically that our techniques can process complex GTGDs derived from synthetic and real benchmarks and are thus suitable for practical use.

Accurately estimating the cardinality (i.e., the number of answers) of complex queries plays a central role in database systems. This problem is particularly difficult in graph databases, where queries often involve a large number of joins and self-joins. Recently, Park et al. [55] surveyed seven state-of-the-art cardinality estimation approaches for graph queries. The results of their extensive empirical evaluation show that a sampling method based on the WanderJoin online aggregation algorithm [47] consistently offers superior accuracy. We extended the framework by Park et al. [55] with three additional datasets and repeated their experiments. Our results showed that WanderJoin is indeed very accurate, but it can often take a large number of samples and thus be very slow. Moreover, when queries are complex and data distributions are skewed, it often fails to find valid samples and estimates the cardinality as zero. Finally, complex graph queries often go beyond simple graph matching and involve arbitrary nesting of relational operators such as disjunction, difference, and duplicate elimination. Neither of the methods considered by Park et al. [55] is applicable to such queries. In this paper we present a novel approach for estimating the cardinality of complex graph queries. Our approach is inspired by WanderJoin, but, unlike all approaches known to us, it can process complex queries with arbitrary operator nesting. Our estimator is strongly consistent, meaning that the average of repeated estimates converges with probability one to the actual cardinality. We present optimisations of the basic algorithm that aim to reduce the chance of producing zero estimates and improve accuracy. We show empirically that our approach is both accurate and quick on complex queries and large datasets. Finally, we discuss how to integrate our approach into a simple dynamic programming query planner, and we confirm empirically that our planner produces high-quality plans that can significantly reduce end-to-end query evaluation times.

Although there has been significant interest in applying machine learning techniques to structured data, the expressivity (i.e., a description of what can be learned) of such techniques is still poorly understood. In this paper, we study data transformations based on graph neural networks (GNNs). First, we note that the choice of how a dataset is encoded into a numeric form processable by a GNN can obscure the characterisation of a model's expressivity, and we argue that a canonical encoding provides an appropriate basis. Second, we study the expressivity of monotonic max-sum GNNs, which cover a subclass of GNNs with max and sum aggregation functions. We show that, for each such GNN, one can compute a Datalog program such that applying the GNN to any dataset produces the same facts as a single round of application of the program's rules to the dataset. Monotonic max-sum GNNs can sum an unbounded number of feature vectors which can result in arbitrarily large feature values, whereas rule application requires only a bounded number of constants. Hence, our result shows that the unbounded summation of monotonic max-sum GNNs does not increase their expressive power. Third, we sharpen our result to the subclass of monotonic max GNNs, which use only the max aggregation function, and identify a corresponding class of Datalog programs.

Although there has been significant interest in applying machine learning techniques to structured data, the expressivity (i.e., a description of what can be learned) of such techniques is still poorly understood. In this paper, we study data transformations based on graph neural networks (GNNs). First, we note that the choice of how a dataset is encoded into a numeric form processable by a GNN can obscure the characterisation of a model's expressivity, and we argue that a canonical encoding provides an appropriate basis. Second, we study the expressivity of monotonic max-sum GNNs, which cover a subclass of GNNs with max and sum aggregation functions. We show that, for each such GNN, one can compute a Datalog program such that applying the GNN to any dataset produces the same facts as a single round of application of the program's rules to the dataset. Monotonic max-sum GNNs can sum an unbounded number of feature vectors which can result in arbitrarily large feature values, whereas rule application requires only a bounded number of constants. Hence, our result shows that the unbounded summation of monotonic max-sum GNNs does not increase their expressive power. Third, we sharpen our result to the subclass of monotonic max GNNs, which use only the max aggregation function, and identify a corresponding class of Datalog programs.

Guarded tuple-generating dependencies (GTGDs) are a natural extension of description logics and referential constraints. It has long been known that queries over GTGDs can be answered by a variant of the chase - a quintessential technique for reasoning with dependencies. However, there has been little work on concrete algorithms and even less on implementation. To address this gap, we revisit Datalog rewriting approaches to query answering, where GTGDs are transformed to a Datalog program that entails the same base facts on each base instance. We show that the rewriting can be seen as containing "shortcut" rules that circumvent certain chase steps, we present several algorithms that compute the rewriting by simulating specific types of chase steps, and we discuss important implementation issues. Finally, we show empirically that our techniques can process complex GTGDs derived from synthetic and real benchmarks and are thus suitable for practical use.

Guarded tuple-generating dependencies (GTGDs) are a natural extension of description logics and referential constraints. It has long been known that queries over GTGDs can be answered by a variant of the chase ---a quintessential technique for reasoning with dependencies. However, there has been little work on concrete algorithms and even less on implementation. To address this gap, we revisit Datalog rewriting approaches to query answering, where GTGDs are transformed to a Datalog program that entails the same base facts on each base instance. We show that the rewriting can be seen as containing "shortcut" rules that circumvent certain chase steps, we present several algorithms that compute the rewriting by simulating specific types of chase steps, and we discuss important implementation issues. Finally, we show empirically that our techniques can process complex GTGDs derived from synthetic and real benchmarks and are thus suitable for practical use.

Rule learning involves developing machine learning models that can be applied to a set of logical facts to predict additional facts, as well as providing methods for extracting from the learned model a set of logical rules that explain symbolically the model's predictions. Existing such approaches, however, do not describe formally the relationship between the model's predictions and the derivations of the extracted rules; rather, it is often claimed without justification that the extracted rules `approximate' or `explain' the model, and rule quality is evaluated by manual inspection. In this paper, we study the formal properties of Neural-LP--a prominent rule learning approach. We show that the rules extracted from Neural-LP models can be both unsound and incomplete: on the same input dataset, the extracted rules can derive facts not predicted by the model, and the model can make predictions not derived by the extracted rules. We also propose a modification to the Neural-LP model that ensures that the extracted rules are always sound and complete. Finally, we show that, on several prominent benchmarks, the classification performance of our modified model is comparable to that of the standard Neural-LP model. Thus, faithful learning of rules is feasible from both a theoretical and practical point of view.

Dow Jones is a leading provider of market, industry and portfolio intelligence serving a wide range of financial applications including asset management, trading, analysis and bankruptcy/restructuring. The information needed to provide such intelligence comes from a variety of heterogeneous data sources. Integrating this information and answering complex queries over it presents both conceptual and computational challenges. In order to address these challenges Dow Jones have used the RDFox system to integrate the various sources in a large RDF knowledge graph. The knowledge graph is being used to power an expanding range of internal processes and market intelligence products.

Answering queries over large datasets extended with Datalog rules plays a key role in numerous data management applications, and it has been implemented in several highly optimised Datalog systems in both academic and commercial contexts. Many systems implement reasoning via materialisation, which involves precomputing all consequences of the rules and the dataset in a preprocessing step. Some systems also use incremental reasoning algorithms, which can update the materialisation efficiently when the input dataset changes. Such techniques allow queries to be processed without any reference to the rules, so they are often used in applications where the performance of query answering is critical. Existing materialisation and incremental reasoning techniques enumerate all possible ways to apply rules to the data in order to derive all relevant consequences. This, however, can be inefficient because derivations of rules commonly used in practice are redundant; for example, rules axiomatising a binary predicate as symmetric and transitive can have a cubic number of applications, yet they can derive at most a quadratic number of facts. Such redundancy can be a significant source of overhead in practice and can prevent Datalog systems from successfully processing large datasets. To address this issue, in this paper we present a novel framework for modular materialisation and incremental reasoning. Our key idea is that, for certain combinations of rules commonly used in practice, all consequences can be derived using specialised procedures that do not necessarily enumerate all possible rule applications. Thus, our framework supports materialisation and incremental reasoning via a collection of modules. Each module is responsible for deriving consequences of a subset of the program, by using either standard rule application or proprietary algorithms. We prove that such an approach is complete as long as each module satisfies certain properties. Our formalisation of a module is very general, and in fact it allows modules to keep arbitrary auxiliary information. We also show how to realise custom procedures for four types of modules: transitivity, symmetry–transitivity, chain rules, and sequencing elements of a total order. Finally, we demonstrate empirically that using our custom procedures can speed up materialisation and incremental reasoning by several orders of magnitude on several well-known benchmarks. Thus, our technique has the potential to significantly improve the scalability of Datalog reasoners.