DROPS

Document

Research

Semantically Reflected Programs

Authors: Eduard Kamburjan, Vidar Norstein Klungre, Yuanwei Qu, Rudolf Schlatte, Egor V. Kostylev, Martin Giese, and Einar Broch Johnsen

Published in: TGDK, Volume 4, Issue 1 (2026). Transactions on Graph Data and Knowledge, Volume 4, Issue 1

Abstract

This paper addresses the dichotomy between the formalization of structural and the formalization of executable behavioral knowledge by means of semantically lifted programs, which explore an intuitive connection between imperative programs and knowledge graphs. While knowledge graphs and ontologies are eminently useful to represent formal knowledge about a system’s individuals and universals, programming languages are designed to describe the system’s evolution. To address this dichotomy, we introduce a semantic lifting of the program states of an executing progam into a knowledge graph, for an object-oriented programming language. The resulting graph is exposed as a semantic reflection layer within the programming language, allowing programmers to leverage knowledge of the application domain in their programs during execution. In this paper, we formalize semantic lifting and semantic reflection for a small imperative programming language, SMOL, explain the operational aspects of the language, and consider type correctness and virtualization for runtime program queries through the semantic reflection layer. We illustrate semantic lifting and semantic reflection through a case study of geological modeling and discuss different applications of the technique. The language implementation is open source and available online.

Cite as

Eduard Kamburjan, Vidar Norstein Klungre, Yuanwei Qu, Rudolf Schlatte, Egor V. Kostylev, Martin Giese, and Einar Broch Johnsen. Semantically Reflected Programs. In Transactions on Graph Data and Knowledge (TGDK), Volume 4, Issue 1, pp. 3:1-3:52, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@Article{kamburjan_et_al:TGDK.4.1.3,
  author =	{Kamburjan, Eduard and Klungre, Vidar Norstein and Qu, Yuanwei and Schlatte, Rudolf and Kostylev, Egor V. and Giese, Martin and Johnsen, Einar Broch},
  title =	{{Semantically Reflected Programs}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{3:1--3:52},
  ISSN =	{2942-7517},
  year =	{2026},
  volume =	{4},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.4.1.3},
  URN =		{urn:nbn:de:0030-drops-256884},
  doi =		{10.4230/TGDK.4.1.3},
  annote =	{Keywords: Knowledge Graphs, Ontologies, Object-Oriented Modelling, Imperative Programming Languages, Reflection, Type Safety}
}

Document

Invited Paper

DOI: 10.4230/OASIcs.RW.2024/2025.3

Foundations of Graph Neural Networks (A Logician’s View) (Invited Paper)

Authors: Egor V. Kostylev

Published in: OASIcs, Volume 138, Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025)

Abstract

Graph Neural Networks (GNNs) are a family of neural architectures that are naturally suited to learning functions on graphs. They are now used in a wide range of applications. It has been observed that GNNs share many similarities with classical computer science (CS) formalisms, such as the Weisfeiler-Leman graph isomorphism test, bisimulation, and logic. Most notably, both GNNs and these formalisms deal with functions on graphs and graph-like structures. This observation opens up an opportunity to compare GNN architectures with these formalisms in terms of different kinds of expressibility, thus positioning these architectures within the well-established landscape of theoretical CS. This, in turn, helps us better understand the fundamental capabilities and limitations of various GNN architectures, enabling more informed choices about which architecture to use - if any at all. In these lecture notes, I give an introduction to the state-of-the-art foundations of GNNs - specifically, our current understanding of their expressibility in terms of the classical formalisms, considering several notions of expressive power.

Cite as

Egor V. Kostylev. Foundations of Graph Neural Networks (A Logician’s View) (Invited Paper). In Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025). Open Access Series in Informatics (OASIcs), Volume 138, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{kostylev:OASIcs.RW.2024/2025.3,
  author =	{Kostylev, Egor V.},
  title =	{{Foundations of Graph Neural Networks (A Logician’s View)}},
  booktitle =	{Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 \& RW 2025)},
  pages =	{3:1--3:19},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-405-5},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{138},
  editor =	{Artale, Alessandro and Bienvenu, Meghyn and Garc{\'\i}a, Yazm{\'\i}n Ib\'{a}\~{n}ez and Murlak, Filip},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.RW.2024/2025.3},
  URN =		{urn:nbn:de:0030-drops-250486},
  doi =		{10.4230/OASIcs.RW.2024/2025.3},
  annote =	{Keywords: Graph Neural Networks, Expressivity, Logic}
}

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

DOI: 10.4230/LIPIcs.ICALP.2020.112

Two Variable Logic with Ultimately Periodic Counting

Authors: Michael Benedikt, Egor V. Kostylev, and Tony Tan

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract

We consider the extension of FO² with quantifiers that state that the number of elements where a formula holds should belong to a given ultimately periodic set. We show that both satisfiability and finite satisfiability of the logic are decidable. We also show that the spectrum of any sentence is definable in Presburger arithmetic. In the process we present several refinements to the "biregular graph method". In this method, decidability issues concerning two-variable logics are reduced to questions about Presburger definability of integer vectors associated with partitioned graphs, where nodes in a partition satisfy certain constraints on their in- and out-degrees.

Cite as

Michael Benedikt, Egor V. Kostylev, and Tony Tan. Two Variable Logic with Ultimately Periodic Counting. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 112:1-112:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{benedikt_et_al:LIPIcs.ICALP.2020.112,
  author =	{Benedikt, Michael and Kostylev, Egor V. and Tan, Tony},
  title =	{{Two Variable Logic with Ultimately Periodic Counting}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{112:1--112:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.112},
  URN =		{urn:nbn:de:0030-drops-125197},
  doi =		{10.4230/LIPIcs.ICALP.2020.112},
  annote =	{Keywords: Presburger Arithmetic, Two-variable logic}
}

Document

DOI: 10.4230/LIPIcs.ICDT.2016.5

Beyond Well-designed SPARQL

Authors: Mark Kaminski and Egor V. Kostylev

Published in: LIPIcs, Volume 48, 19th International Conference on Database Theory (ICDT 2016)

Abstract

SPARQL is the standard query language for RDF data. The distinctive feature of SPARQL is the OPTIONAL operator, which allows for partial answers when complete answers are not available due to lack of information. However, optional matching is computationally expensive - query answering is PSPACE-complete. The well-designed fragment of SPARQL achieves much better computational properties by restricting the use of optional matching - query answering becomes coNP-complete. However, well-designed SPARQL captures far from all real-life queries - in fact, only about half of the queries over DBpedia that use OPTIONAL are well-designed. In the present paper, we study queries outside of well-designed SPARQL. We introduce the class of weakly well-designed queries that subsumes well-designed queries and includes most common meaningful non-well-designed queries: our analysis shows that the new fragment captures about 99% of DBpedia queries with OPTIONAL. At the same time, query answering for weakly well-designed SPARQL remains coNP-complete, and our fragment is in a certain sense maximal for this complexity. We show that the fragment's expressive power is strictly in-between well-designed and full SPARQL. Finally, we provide an intuitive normal form for weakly well-designed queries and study the complexity of containment and equivalence.

Cite as

Mark Kaminski and Egor V. Kostylev. Beyond Well-designed SPARQL. In 19th International Conference on Database Theory (ICDT 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 48, pp. 5:1-5:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{kaminski_et_al:LIPIcs.ICDT.2016.5,
  author =	{Kaminski, Mark and Kostylev, Egor V.},
  title =	{{Beyond Well-designed SPARQL}},
  booktitle =	{19th International Conference on Database Theory (ICDT 2016)},
  pages =	{5:1--5:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-002-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{48},
  editor =	{Martens, Wim and Zeume, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2016.5},
  URN =		{urn:nbn:de:0030-drops-57744},
  doi =		{10.4230/LIPIcs.ICDT.2016.5},
  annote =	{Keywords: RDF, Query languages, SPARQL, Optional matching}
}

Document

DOI: 10.4230/LIPIcs.ICDT.2015.212

CONSTRUCT Queries in SPARQL

Authors: Egor V. Kostylev, Juan L. Reutter, and Martín Ugarte

Published in: LIPIcs, Volume 31, 18th International Conference on Database Theory (ICDT 2015)

Abstract

SPARQL has become the most popular language for querying RDF datasets, the standard data model for representing information in the Web. This query language has received a good deal of attention in the last few years: two versions of W3C standards have been issued, several SPARQL query engines have been deployed, and important theoretical foundations have been laid. However, many fundamental aspects of SPARQL queries are not yet fully understood. To this end, it is crucial to understand the correspondence between SPARQL and well-developed frameworks like relational algebra or first order logic. But one of the main obstacles on the way to such understanding is the fact that the well-studied fragments of SPARQL do not produce RDF as output. In this paper we embark on the study of SPARQL CONSTRUCT queries, that is, queries which output RDF graphs. This class of queries takes rightful place in the standards and implementations, but contrary to SELECT queries, it has not yet attracted a worth-while theoretical research. Under this framework we are able to establish a strong connection between SPARQL and well-known logical and database formalisms. In particular, the fragment which does not allow for blank nodes in output templates corresponds to first order queries, its well-designed sub-fragment corresponds to positive first order queries, and the general language can be re-stated as a data exchange setting. These correspondences allow us to conclude that the general language is not composable, but the aforementioned blank-free fragments are. Finally, we enrich SPARQL with a recursion operator and establish fundamental properties of this extension.

Cite as

Egor V. Kostylev, Juan L. Reutter, and Martín Ugarte. CONSTRUCT Queries in SPARQL. In 18th International Conference on Database Theory (ICDT 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 31, pp. 212-229, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

Copy BibTex To Clipboard

@InProceedings{kostylev_et_al:LIPIcs.ICDT.2015.212,
  author =	{Kostylev, Egor V. and Reutter, Juan L. and Ugarte, Mart{\'\i}n},
  title =	{{CONSTRUCT Queries in SPARQL}},
  booktitle =	{18th International Conference on Database Theory (ICDT 2015)},
  pages =	{212--229},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-79-8},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{31},
  editor =	{Arenas, Marcelo and Ugarte, Mart{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2015.212},
  URN =		{urn:nbn:de:0030-drops-49866},
  doi =		{10.4230/LIPIcs.ICDT.2015.212},
  annote =	{Keywords: RDF, SPARQL, Query Languages}
}

Search Results

Documents authored by Kostylev, Egor V.

Semantically Reflected Programs

Abstract

Cite as

Foundations of Graph Neural Networks (A Logician’s View) (Invited Paper)

Abstract

Cite as

Two Variable Logic with Ultimately Periodic Counting

Abstract

Cite as

Beyond Well-designed SPARQL

Abstract

Cite as

CONSTRUCT Queries in SPARQL

Abstract

Cite as

Thanks for your feedback!

Could not send message