arXiv subjects

Boris Motik

Publications and source records attributed to Boris Motik.

At least 19 recordsLinked to original sources

arXiv2024

Goal-Driven Query Answering over First- and Second-Order Dependencies with Equality

In this paper we present the first goal-driven query answering technique for first- and second-order dependencies with equality. 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 [59] that can handle function variables and that corrects an incompleteness of a related formulation by ten Cate et al. [73]. Second, we present a relevance analysis technique that can eliminate 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. 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.

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arXiv2023

On the Correspondence Between Monotonic Max-Sum GNNs and Datalog

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.

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arXiv2022

Rewriting the Infinite Chase

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.

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arXiv2019

Datalog Reasoning over Compressed RDF Knowledge Bases

Materialisation is often used in RDF systems as a preprocessing step to derive all facts implied by given RDF triples and rules. Although widely used, materialisation considers all possible rule applications and can use a lot of memory for storing the derived facts, which can hinder performance. We present a novel materialisation technique that compresses the RDF triples so that the rules can sometimes be applied to multiple facts at once, and the derived facts can be represented using structure sharing. Our technique can thus require less space, as well as skip certain rule applications. Our experiments show that our technique can be very effective: when the rules are relatively simple, our system is both faster and requires less memory than prominent state-of-the-art RDF systems.

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arXiv2019

Datalog Materialisation in Distributed RDF Stores with Dynamic Data Exchange

Several centralised RDF systems support datalog reasoning by precomputing and storing all logically implied triples using the wellknown seminaive algorithm. Large RDF datasets often exceed the capacity of centralised RDF systems, and a common solution is to distribute the datasets in a cluster of shared-nothing servers. While numerous distributed query answering techniques are known, distributed seminaive evaluation of arbitrary datalog rules is less understood. In fact, most distributed RDF stores either support no reasoning or can handle only limited datalog fragments. In this paper we extend the dynamic data exchange approach for distributed query answering by Potter et al. [12] to a reasoning algorithm that can handle arbitrary rules while preserving important properties such as nonrepetition of inferences. We also show empirically that our algorithm scales well to very large RDF datasets

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arXiv2018

Stream Reasoning in Temporal Datalog

In recent years, there has been an increasing interest in extending traditional stream processing engines with logical, rule-based, reasoning capabilities. This poses significant theoretical and practical challenges since rules can derive new information and propagate it both towards past and future time points; as a result, streamed query answers can depend on data that has not yet been received, as well as on data that arrived far in the past. Stream reasoning algorithms, however, must be able to stream out query answers as soon as possible, and can only keep a limited number of previous input facts in memory. In this paper, we propose novel reasoning problems to deal with these challenges, and study their computational properties on Datalog extended with a temporal sort and the successor function (a core rule-based language for stream reasoning applications).

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arXiv2018

Modular Materialisation of Datalog Programs

The seminaïve algorithm can materialise all consequences of arbitrary datalog rules, and it also forms the basis for incremental algorithms that update a materialisation as the input facts change. Certain (combinations of) rules, however, can be handled much more efficiently using custom algorithms. To integrate such algorithms into a general reasoning approach that can handle arbitrary rules, we propose a modular framework for materialisation computation and its maintenance. We split a datalog program into modules that can be handled using specialised algorithms, and handle the remaining rules using the seminaïve algorithm. We also present two algorithms for computing the transitive and the symmetric-transitive closure of a relation that can be used within our framework. Finally, we show empirically that our framework can handle arbitrary datalog programs while outperforming existing approaches, often by orders of magnitude.

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arXiv2018

Stratified Negation in Limit Datalog Programs

There has recently been an increasing interest in declarative data analysis, where analytic tasks are specified using a logical language, and their implementation and optimisation are delegated to a general-purpose query engine. Existing declarative languages for data analysis can be formalised as variants of logic programming equipped with arithmetic function symbols and/or aggregation, and are typically undecidable. In prior work, the language of $\mathit{limit\ programs}$ was proposed, which is sufficiently powerful to capture many analysis tasks and has decidable entailment problem. Rules in this language, however, do not allow for negation. In this paper, we study an extension of limit programs with stratified negation-as-failure. We show that the additional expressive power makes reasoning computationally more demanding, and provide tight data complexity bounds. We also identify a fragment with tractable data complexity and sufficient expressivity to capture many relevant tasks.

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arXiv2018

Estimating the Cardinality of Conjunctive Queries over RDF Data Using Graph Summarisation

Estimating the cardinality (i.e., the number of answers) of conjunctive queries is particularly difficult in RDF systems: queries over RDF data are navigational and thus tend to involve many joins. We present a new, principled cardinality estimation technique based on graph summarisation. We interpret a summary of an RDF graph using a possible world semantics and formalise the estimation problem as computing the expected cardinality over all RDF graphs represented by the summary, and we present a closed-form formula for computing the expectation of arbitrary queries. We also discuss approaches to RDF graph summarisation. Finally, we show empirically that our cardinality technique is more accurate and more consistent, often by orders of magnitude, than the state of the art.

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arXiv2017

Optimised Maintenance of Datalog Materialisations

To efficiently answer queries, datalog systems often materialise all consequences of a datalog program, so the materialisation must be updated whenever the input facts change. Several solutions to the materialisation update problem have been proposed. The Delete/Rederive (DRed) and the Backward/Forward (B/F) algorithms solve this problem for general datalog, but both contain steps that evaluate rules 'backwards' by matching their heads to a fact and evaluating the partially instantiated rule bodies as queries. We show that this can be a considerable source of overhead even on very small updates. In contrast, the Counting algorithm does not evaluate the rules 'backwards', but it can handle only nonrecursive rules. We present two hybrid approaches that combine DRed and B/F with Counting so as to reduce or even eliminate 'backward' rule evaluation while still handling arbitrary datalog programs. We show empirically that our hybrid algorithms are usually significantly faster than existing approaches, sometimes by orders of magnitude.

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arXiv2017

Goal-Driven Query Answering for Existential Rules with Equality

Inspired by the magic sets for Datalog, we present a novel goal-driven approach for answering queries over terminating existential rules with equality (aka TGDs and EGDs). Our technique improves the performance of query answering by pruning the consequences that are not relevant for the query. This is challenging in our setting because equalities can potentially affect all predicates in a dataset. We address this problem by combining the existing singularization technique with two new ingredients: an algorithm for identifying the rules relevant to a query and a new magic sets algorithm. We show empirically that our technique can significantly improve the performance of query answering, and that it can mean the difference between answering a query in a few seconds or not being able to process the query at all.

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arXiv2017

Foundations of Declarative Data Analysis Using Limit Datalog Programs

Motivated by applications in declarative data analysis, we study $\mathit{Datalog}_{\mathbb{Z}}$---an extension of positive Datalog with arithmetic functions over integers. This language is known to be undecidable, so we propose two fragments. In $\mathit{limit}~\mathit{Datalog}_{\mathbb{Z}}$ predicates are axiomatised to keep minimal/maximal numeric values, allowing us to show that fact entailment is coNExpTime-complete in combined, and coNP-complete in data complexity. Moreover, an additional $\mathit{stability}$ requirement causes the complexity to drop to ExpTime and PTime, respectively. Finally, we show that stable $\mathit{Datalog}_{\mathbb{Z}}$ can express many useful data analysis tasks, and so our results provide a sound foundation for the development of advanced information systems.

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arXiv2016

Extending Consequence-Based Reasoning to SRIQ

Consequence-based calculi are a family of reasoning algorithms for description logics (DLs), and they combine hypertableau and resolution in a way that often achieves excellent performance in practice. Up to now, however, they were proposed for either Horn DLs (which do not support disjunction), or for DLs without counting quantifiers. In this paper we present a novel consequence-based calculus for SRIQ---a rich DL that supports both features. This extension is non-trivial since the intermediate consequences that need to be derived during reasoning cannot be captured using DLs themselves. The results of our preliminary performance evaluation suggest the feasibility of our approach in practice.

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arXiv2015

Answering Conjunctive Queries over $\mathcal{EL}$ Knowledge Bases with Transitive and Reflexive Roles

Answering conjunctive queries (CQs) over $\mathcal{EL}$ knowledge bases (KBs) with complex role inclusions is PSPACE-hard and in PSPACE in certain cases; however, if complex role inclusions are restricted to role transitivity, the tight upper complexity bound has so far been unknown. Furthermore, the existing algorithms cannot handle reflexive roles, and they are not practicable. Finally, the problem is tractable for acyclic CQs and $\mathcal{ELH}$, and NP-complete for unrestricted CQs and $\mathcal{ELHO}$ KBs. In this paper we complete the complexity landscape of CQ answering for several important cases. In particular, we present a practicable NP algorithm for answering CQs over $\mathcal{ELHO}^s$ KBs---a logic containing all of OWL 2 EL, but with complex role inclusions restricted to role transitivity. Our preliminary evaluation suggests that the algorithm can be suitable for practical use. Moreover, we show that, even for a restricted class of so-called arborescent acyclic queries, CQ answering over $\mathcal{EL}$ KBs becomes NP-hard in the presence of either transitive or reflexive roles. Finally, we show that answering arborescent CQs over $\mathcal{ELHO}$ KBs is tractable, whereas answering acyclic CQs is NP-hard.

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arXiv2015

Combining Rewriting and Incremental Materialisation Maintenance for Datalog Programs with Equality

Materialisation precomputes all consequences of a set of facts and a datalog program so that queries can be evaluated directly (i.e., independently from the program). Rewriting optimises materialisation for datalog programs with equality by replacing all equal constants with a single representative; and incremental maintenance algorithms can efficiently update a materialisation for small changes in the input facts. Both techniques are critical to practical applicability of datalog systems; however, we are unaware of an approach that combines rewriting and incremental maintenance. In this paper we present the first such combination, and we show empirically that it can speed up updates by several orders of magnitude compared to using either rewriting or incremental maintenance in isolation.

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arXiv2014

Handling owl:sameAs via Rewriting

Rewriting is widely used to optimise owl:sameAs reasoning in materialisation based OWL 2 RL systems. We investigate issues related to both the correctness and efficiency of rewriting, and present an algorithm that guarantees correctness, improves efficiency, and can be effectively parallelised. Our evaluation shows that our approach can reduce reasoning times on practical data sets by orders of magnitude.

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arXiv2014

Acyclicity Notions for Existential Rules and Their Application to Query Answering in Ontologies

Answering conjunctive queries (CQs) over a set of facts extended with existential rules is a prominent problem in knowledge representation and databases. This problem can be solved using the chase algorithm, which extends the given set of facts with fresh facts in order to satisfy the rules. If the chase terminates, then CQs can be evaluated directly in the resulting set of facts. The chase, however, does not terminate necessarily, and checking whether the chase terminates on a given set of rules and facts is undecidable. Numerous acyclicity notions were proposed as sufficient conditions for chase termination. In this paper, we present two new acyclicity notions called model-faithful acyclicity (MFA) and model-summarising acyclicity (MSA). Furthermore, we investigate the landscape of the known acyclicity notions and establish a complete taxonomy of all notions known to us. Finally, we show that MFA and MSA generalise most of these notions. Existential rules are closely related to the Horn fragments of the OWL 2 ontology language; furthermore, several prominent OWL 2 reasoners implement CQ answering by using the chase to materialise all relevant facts. In order to avoid termination problems, many of these systems handle only the OWL 2 RL profile of OWL 2; furthermore, some systems go beyond OWL 2 RL, but without any termination guarantees. In this paper we also investigate whether various acyclicity notions can provide a principled and practical solution to these problems. On the theoretical side, we show that query answering for acyclic ontologies is of lower complexity than for general ontologies. On the practical side, we show that many of the commonly used OWL 2 ontologies are MSA, and that the number of facts obtained by materialisation is not too large. Our results thus suggest that principled development of materialisation-based OWL 2 reasoners is practically feasible.

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arXiv2014

Reasoning over Ontologies with Hidden Content: The Import-by-Query Approach

There is currently a growing interest in techniques for hiding parts of the signature of an ontology Kh that is being reused by another ontology Kv. Towards this goal, in this paper we propose the import-by-query framework, which makes the content of Kh accessible through a limited query interface. If Kv reuses the symbols from Kh in a certain restricted way, one can reason over Kv U Kh by accessing only Kv and the query interface. We map out the landscape of the import-by-query problem. In particular, we outline the limitations of our framework and prove that certain restrictions on the expressivity of Kh and the way in which Kv reuses symbols from Kh are strictly necessary to enable reasoning in our setting. We also identify cases in which reasoning is possible and we present suitable import-by-query reasoning algorithms.

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