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Egor V. Kostylev

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23 papers

2 author rows

AIJ Journal 2026 Journal Article

From monotonic graph neural networks to datalog and back: Expressive power and practical applications

David Tena Cucala
Bernardo Cuenca Grau
Boris Motik
Egor V. Kostylev

Many tasks over knowledge graphs, such as link prediction, can be conceptualised as a problem of learning a transformation of sets of relational facts. Machine learning models such as graph neural networks (GNNs) can be used to realise this transformation, allowing the transformation to be learned from examples. However, it is often difficult to verify formally the properties of such a transformation, or understand why it derives a specific fact. Alternatively, such a transformation can be realised using a set of rules expressed in a knowledge representation language such as Datalog. Formal properties of such a transformation can be verified using symbolic means, and each derived fact can be justified by a rule; however, writing and curating the rules is costly and requires expertise in both the application domain and the formal language. To bridge the gap between these two approaches, in this paper we study the relationship between transformations realised by monotonic max-sum GNNs , a subclass of GNNs with nonnegative weights and max and sum aggregation functions, and transformations realised by Datalog rules. First, we provide an algorithm that can verify whether a given Datalog rule is sound for a network, in the sense that the GNN always derives all consequences of the rule on any input dataset. Second, we provide an algorithm that allows us to justify any fact derived by a GNN by computing a rule that is sound for the GNN and that derives the fact. Third, we study the expressive power of monotonic max-sum GNNs and show that, for each such GNN, one can compute a Datalog program where applying the GNN to any dataset produces the same facts as a single round of application of the program’s rules to the dataset; we also 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. Finally, we carry out a practical evaluation and show that monotonic max-sum GNNs can be successfully trained in practice on common knowledge graph tasks, and that extracting rules from max-sum GNNs is practically feasible.

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ICLR Conference 2025 Conference Paper

GLoRa: A Benchmark to Evaluate the Ability to Learn Long-Range Dependencies in Graphs

Dongzhuoran Zhou
Evgeny Kharlamov
Egor V. Kostylev

Learning on graphs is one of the most active research topics in machine learning (ML). Among the key challenges in this field, effectively learning long-range dependencies in graphs has been particularly difficult. It has been observed that, in practice, the performance of many ML approaches, including various types of graph neural networks (GNNs), degrades significantly when the learning task involves long-range dependencies—that is, when the answer is determined by the presence of a certain path of significant length in the graph. This issue has been attributed to several phenomena, including over-smoothing, over-squashing, and vanishing gradient. A number of solutions have been proposed to mitigate these causes. However, evaluation of these solutions is currently challenging because existing benchmarks do not effectively test systems for their ability to learn tasks based on long-range dependencies in a transparent manner. In this paper, we introduce GLoRa, a synthetic benchmark that allows testing of systems for this ability in a systematic way. We then evaluate state-of-the-art systems using GLoRa and conclude that none of them can confidently claim to learn long-range dependencies well. We also observe that this weak performance cannot be attributed to any of the three causes, highlighting the need for further investigation.

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AAAI Conference 2024 Conference Paper

Recurrent Graph Neural Networks and Their Connections to Bisimulation and Logic

Maximilian Pflueger
David Tena Cucala
Egor V. Kostylev

The success of Graph Neural Networks (GNNs) in practice has motivated extensive research on their theoretical properties. This includes recent results that characterise node classifiers expressible by GNNs in terms of first order logic. Most of the analysis, however, has been focused on GNNs with fixed number of message-passing iterations (i.e., layers), which cannot realise many simple classifiers such as reachability of a node with a given label. In this paper, we start to fill this gap and study the foundations of GNNs that can perform more than a fixed number of message-passing iterations. We first formalise two generalisations of the basic GNNs: recurrent GNNs (RecGNNs), which repeatedly apply message-passing iterations until the node classifications become stable, and graph-size GNNs (GSGNNs), which exploit a built-in function of the input graph size to decide the number of message-passings. We then formally prove that GNN classifiers are strictly less expressive than RecGNN ones, and RecGNN classifiers are strictly less expressive than GSGNN ones. To get this result, we identify novel semantic characterisations of the three formalisms in terms of suitable variants of bisimulation, which we believe have their own value for our understanding of GNNs. Finally, we prove syntactic logical characterisations of RecGNNs and GSGNNs analogous to the logical characterisation of plain GNNs, where we connect the two formalisms to monadic monotone fixpoint logic---a generalisation of first-order logic that supports recursion.

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NeSy Conference 2023 Conference Paper

Inductive Future Time Prediction on Temporal Knowledge Graphs with Interval Time

Roxana Pop
Egor V. Kostylev

Temporal Knowledge Graphs (TKGs) are an extension of Knowledge Graphs where facts are temporally scoped. They have recently received increasing attention in knowledge management, mirroring an increased interest in temporal graph learning within the graph learning community. While there have been many systems proposed for TKG learning, there are many settings to be considered, and not all of them are yet fully explored. In this position paper we identify a problem not yet approached, inductive future time prediction on interval-based TKGs, and formalise it as a machine learning task. We then outline several promising approaches for solving it, focusing on a neurosymbolic framework connecting TKG learning with the temporal reasoning formalism DatalogMTL.

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KR Conference 2023 Conference Paper

On the Correspondence Between Monotonic Max-Sum GNNs and Datalog

David Tena Cucala
Bernardo Cuenca Grau
Boris Motik
Egor V. Kostylev

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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KR Conference 2023 Conference Paper

Revisiting Inferential Benchmarks for Knowledge Graph Completion

Shuwen Liu
Bernardo Cuenca Grau
Ian Horrocks
Egor V. Kostylev

Knowledge Graph (KG) completion is the problem of extending an incomplete KG with missing facts. A key feature of Machine Learning approaches for KG completion is their ability to learn inference patterns, so that the predicted facts are the results of applying these patterns to the KG. Standard completion benchmarks, however, are not well-suited for evaluating models' abilities to learn patterns, because the training and test sets of these benchmarks are a random split of a given KG and hence do not capture the causality of inference patterns. We propose a novel approach for designing KG completion benchmarks based on the following principles: there is a set of logical rules so that the missing facts are the results of the rules' application; the training set includes both premises matching rule antecedents and the corresponding conclusions; the test set consists of the results of applying the rules to the training set; the negative examples are designed to discourage the models from learning rules not entailed by the rule set. We use our methodology to generate several benchmarks and evaluate a wide range of existing KG completion systems. Our results provide novel insights on the ability of existing models to induce inference patterns from incomplete KGs.

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ICLR Conference 2022 Conference Paper

Explainable GNN-Based Models over Knowledge Graphs

David Jaime Tena Cucala
Bernardo Cuenca Grau
Egor V. Kostylev
Boris Motik

Graph Neural Networks (GNNs) are often used to learn transformations of graph data. While effective in practice, such approaches make predictions via numeric manipulations so their output cannot be easily explained symbolically. We propose a new family of GNN-based transformations of graph data that can be trained effectively, but where all predictions can be explained symbolically as logical inferences in Datalog—a well-known rule-based formalism. In particular, we show how to encode an input knowledge graph into a graph with numeric feature vectors, process this graph using a GNN, and decode the result into an output knowledge graph. We use a new class of monotonic GNNs (MGNNs) to ensure that this process is equivalent to a round of application of a set of Datalog rules. We also show that, given an arbitrary MGNN, we can automatically extract rules that completely characterise the transformation. We evaluate our approach by applying it to classification tasks in knowledge graph completion.

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KR Conference 2021 Conference Paper

DatalogMTL with Negation Under Stable Models Semantics

Przemysław A. Wałęga
David J. Tena Cucala
Egor V. Kostylev
Bernardo Cuenca Grau

We introduce negation under stable models semantics in DatalogMTL—a temporal extension of Datalog with metric operators. As a result, we obtain a rule language which combines the power of answer set programming with the temporal dimension provided by metric operators. We show that, in this setting, reasoning becomes undecidable over the rationals and decidable in EXPSPACE in data complexity over the integers. We also show that, if we restrict our attention to forward-propagating programs (where rules propagate information in a single temporal direction), reasoning over integers becomes PSPACE-complete in data complexity and hence no harder than over positive programs; however, reasoning over the rationals in this fragment remains undecidable.

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AAAI Conference 2020 Conference Paper

Complexity and Expressive Power of Disjunction and Negation in Limit Datalog

Mark Kaminski
Bernardo Cuenca Grau
Egor V. Kostylev
Ian Horrocks

Limit Datalog is a fragment of DatalogZ—the extension of Datalog with arithmetic functions over the integers—which has been proposed as a declarative language suitable for capturing data analysis tasks. In limit Datalog programs, all intensional predicates with a numeric argument are limit predicates that keep maximal (or minimal) bounds on numeric values. Furthermore, to ensure decidability of reasoning, limit Datalog imposes a linearity condition restricting the use of multiplication in rules. In this paper, we study the complexity and expressive power of limit Datalog programs extended with disjunction in the heads of rules and non-monotonic negation under the stable model semantics. We show that allowing for unrestricted use of negation leads to undecidability of reasoning. Decidability can be restored by stratifying the use of negation over predicates carrying numeric values. We show that the resulting language is ΠEXP 2 -complete in combined complexity and that it captures ΠP 2 over ordered structures in the sense of descriptive complexity. We also provide a study of several fragments of this language: we show that the complexity and expressive power of the full language are already reached for disjunction-free programs; furthermore, we show that semi-positive disjunctive programs are coNEXPcomplete and that they capture coNP.

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KR Conference 2020 Conference Paper

DatalogMTL over the Integer Timeline

Przemysław A. Wałęga
Bernardo Cuenca Grau
Mark Kaminski
Egor V. Kostylev

We study DatalogMTL—an extension of Datalog with metric temporal operators—under integer semantics, where the temporal domain of both interpretations and temporal operators consists of integer time points only. This is in contrast to the standard semantics, which is defined over the rational timeline. DatalogMTL under integer semantics is an interesting KR language: on the one hand, one can often assume the integer timeline in applications; on the other hand, it captures prominent temporal extensions of Datalog such as Datalog1S. We show that the choice of integer semantics leads to more favourable computational properties. We first show that reasoning over integers is at most as hard as reasoning over rationals for DatalogMTL and its natural fragments. Then, we investigate fragments of DatalogMTL where adopting the integer semantics makes reasoning easier. In particular, we show that complexity drops from P-hard to NC1-complete for the propositional fragment (where all object variables are grounded), and from TC0-hard to ACC0 for the linear fragment where the past diamond operator is the only metric operator allowed in rule bodies. Thus, reasoning in such fragments is both tractable and highly parallelisable, which suggests their appropriateness for data-intensive applications.

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ICLR Conference 2020 Conference Paper

The Logical Expressiveness of Graph Neural Networks

Pablo Barceló
Egor V. Kostylev
Mikaël Monet
Jorge Pérez 0001
Juan L. Reutter
Juan Pablo Silva

The ability of graph neural networks (GNNs) for distinguishing nodes in graphs has been recently characterized in terms of the Weisfeiler-Lehman (WL) test for checking graph isomorphism. This characterization, however, does not settle the issue of which Boolean node classifiers (i.e., functions classifying nodes in graphs as true or false) can be expressed by GNNs. We tackle this problem by focusing on Boolean classifiers expressible as formulas in the logic FOC2, a well-studied fragment of first order logic. FOC2 is tightly related to the WL test, and hence to GNNs. We start by studying a popular class of GNNs, which we call AC-GNNs, in which the features of each node in the graph are updated, in successive layers, only in terms of the features of its neighbors. We show that this class of GNNs is too weak to capture all FOC2 classifiers, and provide a syntactic characterization of the largest subclass of FOC2 classifiers that can be captured by AC-GNNs. This subclass coincides with a logic heavily used by the knowledge representation community. We then look at what needs to be added to AC-GNNs for capturing all FOC2 classifiers. We show that it suffices to add readout functions, which allow to update the features of a node not only in terms of its neighbors, but also in terms of a global attribute vector. We call GNNs of this kind ACR-GNNs. We experimentally validate our findings showing that, on synthetic data conforming to FOC2 formulas, AC-GNNs struggle to fit the training data while ACR-GNNs can generalize even to graphs of sizes not seen during training.

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IJCAI Conference 2020 Conference Paper

Tractable Fragments of Datalog with Metric Temporal Operators

Przemysław A. Wałęga
Bernardo Cuenca Grau
Mark Kaminski
Egor V. Kostylev

We study the data complexity of reasoning for several fragments of MTL - an extension of Datalog with metric temporal operators over the rational numbers. Reasoning in the full MTL language is PSPACE-complete, which handicaps its application in practice. To achieve tractability we first study the core fragment, which disallows conjunction in rule bodies, and show that reasoning remains PSPACE-hard. Intractability prompts us to also limit the kinds of temporal operators allowed in rules, and we propose a practical core fragment for which reasoning becomes TC0-complete. Finally, we show that this fragment can be extended by allowing linear conjunctions in rule bodies, where at most one atom can be intensional (IDB); we show that the resulting fragment is NL-complete, and hence no harder than plain linear Datalog.

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IJCAI Conference 2019 Conference Paper

DatalogMTL: Computational Complexity and Expressive Power

Przemysław A. Wałęga
Bernardo Cuenca Grau
Mark Kaminski
Egor V. Kostylev

We study the complexity and expressive power of DatalogMTL - a knowledge representation language that extends Datalog with operators from metric temporal logic (MTL) and which has found applications in ontology-based data access and stream reasoning. We establish tight PSpace data complexity bounds and also show that DatalogMTL extended with negation on input predicates can express all queries in PSpace; this implies that MTL operators add significant expressive power to Datalog. Furthermore, we provide tight combined complexity bounds for the forward-propagating fragment of DatalogMTL, which was proposed in the context of stream reasoning, and show that it is possible to express all PSpace queries in the fragment extended with the falsum predicate.

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AIJ Journal 2019 Journal Article

Foundations of ontology-based data access under bag semantics

Charalampos Nikolaou
Egor V. Kostylev
George Konstantinidis
Mark Kaminski
Bernardo Cuenca Grau
Ian Horrocks

Ontology-based data access (OBDA) is a popular approach for integrating and querying multiple data sources by means of a shared ontology. The ontology is linked to the sources using mappings, which assign to ontology predicates views over the data. The conventional semantics of OBDA is set-based—that is, the extension of the views defined by the mappings does not contain duplicate tuples. This treatment is, however, in disagreement with the standard semantics of database views and database management systems in general, which is based on bags and where duplicate tuples are retained by default. The distinction between set and bag semantics in databases is very significant in practice, and it influences the evaluation of aggregate queries. In this article, we propose and study a bag semantics for OBDA which provides a solid foundation for the future study of aggregate and analytic queries. Our semantics is compatible with both the bag semantics of database views and the set-based conventional semantics of OBDA. Furthermore, it is compatible with existing bag-based semantics for data exchange recently proposed in the literature. We show that adopting a bag semantics makes conjunctive query answering in OBDA coNP-hard in data complexity. To regain tractability of query answering, we consider suitable restrictions along three dimensions, namely, the query language, the ontology language, and the adoption of the unique name assumption. Our investigation shows a complete picture of the computational properties of query answering under bag semantics over ontologies in the DL-Lite family.

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JAIR Journal 2019 Journal Article

Logical Foundations of Linked Data Anonymisation

Bernardo Cuenca Grau
Egor V. Kostylev

The widespread adoption of the Linked Data paradigm has been driven by the increasing demand for information exchange between organisations, as well as by regulations in domains such as health care and governance that require certain data to be published. In this setting, sensitive information is at high risk of disclosure since published data can be often seamlessly linkedwith arbitrary external data sources.In this paper we lay the logical foundations of anonymisation in the context of Linked Data. We consider anonymisations of RDF graphs (and, more generally, relational datasets with labelled nulls) and define notions of policy-compliant and linkage-safe anonymisations. Policy compliance ensures that an anonymised dataset does not reveal any sensitive information as specified by a policy query. Linkage safety ensures that an anonymised dataset remains compliant even if it is linked to (possibly unknown) external datasets available on the Web, thus providing provable protection guarantees against data linkage attacks. We establish the computational complexity of the underpinning decision problems both under the open-world semantics inherent to RDF and under the assumption that an attacker has complete, closed-world knowledge over some parts of the original data.

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IJCAI Conference 2019 Conference Paper

Satisfaction and Implication of Integrity Constraints in Ontology-based Data Access

Charalampos Nikolaou
Bernardo Cuenca Grau
Egor V. Kostylev
Mark Kaminski
Ian Horrocks

We extend ontology-based data access with integrity constraints over both the source and target schemas. The relevant reasoning problems in this setting are constraint satisfaction—to check whether a database satisfies the target constraints given the mappings and the ontology—and source-to-target (resp. , target-to-source) constraint implication, which is to check whether a target constraint (resp. , a source constraint) is satisfied by each database satisfying the source constraints (resp. , the target constraints). We establish decidability and complexity bounds for all these problems in the case where ontologies are expressed in DL-LiteR and constraints range from functional dependencies to disjunctive tuple-generating dependencies.

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AIJ Journal 2018 Journal Article

Logical foundations of information disclosure in ontology-based data integration

Michael Benedikt
Bernardo Cuenca Grau
Egor V. Kostylev

Ontology-based data integration systems allow users to effectively access data sitting in multiple sources by means of queries over a global schema described by an ontology. In practice, data sources often contain sensitive information that the data owners want to keep inaccessible to users. Our aim in this paper is to lay the logical foundations of information disclosure in ontology-based data integration. Our focus is on the semantic requirements that a data integration system should satisfy before it is made available to users for querying, as well as on the computational complexity of checking whether such requirements are fulfilled. In particular, we formalise and study the problem of determining whether a given data integration system discloses a source query to an attacker. We consider disclosure on a particular dataset, and also whether a schema admits a dataset on which disclosure occurs. We provide matching lower and upper complexity bounds on disclosure analysis, in the process introducing a number of techniques for analysing logical privacy issues in ontology-based data integration.

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IJCAI Conference 2018 Conference Paper

Stratified Negation in Limit Datalog Programs

Mark Kaminski
Bernardo Cuenca Grau
Egor V. Kostylev
Boris Motik
Ian Horrocks

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 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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IJCAI Conference 2017 Conference Paper

Foundations of Declarative Data Analysis Using Limit Datalog Programs

Mark Kaminski
Bernardo Cuenca Grau
Egor V. Kostylev
Boris Motik
Ian Horrocks

Motivated by applications in declarative data analysis, we study DatalogZ---an extension of positive Datalog with arithmetic functions over integers. This language is known to be undecidable, so we propose two fragments. In limit DatalogZ 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 stability requirement causes the complexity to drop to ExpTime and PTime, respectively. Finally, we show that stable DatalogZ 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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IJCAI Conference 2017 Conference Paper

Reformulating Queries: Theory and Practice

Michael Benedikt
Egor V. Kostylev
Fabio Mogavero
Efthymia Tsamoura

We consider a setting where a user wants to pose a query against a dataset where background knowledge, expressed as logical sentences, is available, but only a subset of the information can be used to answer the query. We thus want to reformulate the user query against the subvocabulary, arriving at a query equivalent to the user’s query assuming the background theory, but using only the restricted vocabulary. We consider two variations of the problem, one where we want any such reformulation and another where we restrict the size. We present a classification of the complexity of the problem, then provide algorithms for solving the problems in practice and evaluate their performance.

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IJCAI Conference 2017 Conference Paper

The Bag Semantics of Ontology-Based Data Access

Charalampos Nikolaou
Egor V. Kostylev
George Konstantinidis
Mark Kaminski
Bernardo Cuenca Grau
Ian Horrocks

Ontology-based data access (OBDA) is a popular approach for integrating and querying multiple data sources by means of a shared ontology. The ontology is linked to the sources using mappings, which assign views over the data to ontology predicates. Motivated by the need for OBDA systems supporting database-style aggregate queries, we propose a bag semantics for OBDA, where duplicate tuples in the views defined by the mappings are retained, as is the case in standard databases. We show that bag semantics makes conjunctive query answering in OBDA coNP-hard in data complexity. To regain tractability, we consider a rather general class of queries and show its rewritability to a generalisation of the relational calculus to bags.

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KR Conference 2016 Conference Paper

On Expressibility of Non-Monotone Operators in SPARQL

Roman Kontchakov
Egor V. Kostylev

SPARQL, a query language for RDF graphs, is one of the key technologies for the Semantic Web. The expressivity and complexity of various fragments of SPARQL have been studied extensively. It is usually assumed that the optional matching operator OPTIONAL has only two graph patterns as arguments. The speciﬁcation of SPARQL, however, deﬁnes it as a ternary operator, with an additional ﬁlter condition. We address the problem of expressibility of the full ternary OPTIONAL via the simpliﬁed binary version and show that it is possible, but only with an exponential blowup in the size of the query (under common complexity-theoretic assumptions). We also study expressibility of other non-monotone SPARQL operators via optional matching and each other.

IJCAI Conference 2015 Conference Paper

Controlled Query Evaluation for Datalog and OWL 2 Profile Ontologies

Bernardo Cuenca Grau
Evgeny Kharlamov
Egor V. Kostylev
Dmitriy Zheleznyakov

We study confidentiality enforcement in ontologies under the Controlled Query Evaluation framework, where a policy specifies the sensitive information and a censor ensures that query answers that may compromise the policy are not returned. We focus on censors that ensure confidentiality while maximising information access, and consider both Datalog and the OWL 2 profiles as ontology languages.

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