18 Search Results for "Ortiz, Magdalena"

Document
Invited Talk
DOI: 10.4230/LIPIcs.STACS.2026.1
Query Languages for Machine-Learning Models (Invited Talk)

Authors: Martin Grohe

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
In my invited talk and this accompanying paper, I discuss two logics for weighted finite structures: first-order logic with summation (FO(SUM)) and its recursive extension IFP(SUM). These logics originate from foundational work by Grädel, Gurevich, and Meer in the 1990s. In recent joint work with Standke, Steegmans, and Van den Bussche, we have investigated these logics as query languages for machine learning models, specifically neural networks, which are naturally represented as weighted graphs. I present illustrative examples of queries to neural networks that can be expressed in these logics and discuss fundamental results on their expressiveness and computational complexity.
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Martin Grohe. Query Languages for Machine-Learning Models (Invited Talk). In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{grohe:LIPIcs.STACS.2026.1,
  author =	{Grohe, Martin},
  title =	{{Query Languages for Machine-Learning Models}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{1:1--1:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.1},
  URN =		{urn:nbn:de:0030-drops-254904},
  doi =		{10.4230/LIPIcs.STACS.2026.1},
  annote =	{Keywords: Expressive power of query languages, fixed-point logics, weighted structures, neural networks, explainable AI}
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.36
A Game for Counting Logic Formula Size and an Application to Linear Orders

Authors: Grégoire Fournier and György Turán

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
Ehrenfeucht-Fraïssé (EF) games are a basic tool in finite model theory for proving definability lower bounds, with many applications in complexity theory and related areas. They have been applied to study various logics, giving insights on quantifier rank and other logical complexity measures. In this paper, we present an EF game to capture formula size in counting logic with a bounded number of variables. The game combines games introduced previously for counting logic quantifier rank due to Immerman and Lander, and for first-order formula size due to Adler and Immerman, and Hella and Väänänen. The game is used to prove an extension of a formula size lower bound of Grohe and Schweikardt for distinguishing linear orders, from 3-variable first-order logic to 3-variable counting logic.
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Grégoire Fournier and György Turán. A Game for Counting Logic Formula Size and an Application to Linear Orders. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 36:1-36:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fournier_et_al:LIPIcs.CSL.2026.36,
  author =	{Fournier, Gr\'{e}goire and Tur\'{a}n, Gy\"{o}rgy},
  title =	{{A Game for Counting Logic Formula Size and an Application to Linear Orders}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{36:1--36:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.36},
  URN =		{urn:nbn:de:0030-drops-254612},
  doi =		{10.4230/LIPIcs.CSL.2026.36},
  annote =	{Keywords: Finite Model Theory, Logical Aspects of Computational Complexity}
}
Document
Research
DOI: 10.4230/TGDK.3.3.1
A Logic Programming Approach to Repairing SHACL Constraint Violations

Authors: Shqiponja Ahmetaj, Robert David, Axel Polleres, and Mantas Šimkus

Published in: TGDK, Volume 3, Issue 3 (2025). Transactions on Graph Data and Knowledge, Volume 3, Issue 3

Abstract
The Shapes Constraint Language (SHACL) is a recent standard, a W3C recommendation, for validating RDF graphs against shape constraints to be checked on target nodes of a data graph. The standard also describes the notion of validation reports, which detail the results of the validation process. In case of violation of constraints, the validation report should explain the reasons for non-validation, offering guidance on how to identify or fix violations in the data graph. Since the specification left it open to SHACL processors to define such explanations, a recent work proposed the use of explanations in the style of database repairs, where a repair is a set of additions to or deletions from the data graph so that the resulting graph validates against the constraints. In this paper, we study such repairs for non-recursive SHACL, the largest fragment of SHACL that is fully defined in the specification. We propose an algorithm to compute repairs by encoding the explanation problem - using Answer Set Programming (ASP) - into a logic program, where the answer sets contain (minimal) repairs. We then study a scenario where it is not possible to simultaneously repair all the targets, which may be the case due to overall unsatisfiability or conflicting constraints. We introduce a relaxed notion of validation, which allows to validate a (maximal) subset of the targets and adapt the ASP translation to take into account this relaxation. Finally, we add support for repairing constraints which use property paths and equality of paths. Our implementation in clingo is - to the best of our knowledge - the first implementation of a repair program for SHACL.
Cite as

Shqiponja Ahmetaj, Robert David, Axel Polleres, and Mantas Šimkus. A Logic Programming Approach to Repairing SHACL Constraint Violations. In Transactions on Graph Data and Knowledge (TGDK), Volume 3, Issue 3, pp. 1:1-1:36, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{ahmetaj_et_al:TGDK.3.3.1,
  author =	{Ahmetaj, Shqiponja and David, Robert and Polleres, Axel and \v{S}imkus, Mantas},
  title =	{{A Logic Programming Approach to Repairing SHACL Constraint Violations}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{1:1--1:36},
  ISSN =	{2942-7517},
  year =	{2025},
  volume =	{3},
  number =	{3},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.3.3.1},
  URN =		{urn:nbn:de:0030-drops-252124},
  doi =		{10.4230/TGDK.3.3.1},
  annote =	{Keywords: SHACL, Shapes Constraint Language, Database Repairs, Knowledge Graphs, Semantic Web, Answer Set Programming}
}
Document
Invited Paper
DOI: 10.4230/OASIcs.RW.2024/2025.5
Inconsistency-Tolerant Semantics Based on (Preferred) Repairs (Invited Paper)

Authors: Camille Bourgaux

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

Abstract
Real-world datasets are plagued by data quality issues which may render the data inconsistent w.r.t. a set of constraints, be they given by database integrity constraints or ontologies. A prominent way to handle such inconsistent data is to use inconsistency-tolerant semantics to obtain meaningful answers to queries. Most of these semantics are based on some notion of repairs, which represent ways of restoring the data consistency. The most basic kind of repairs is that of subset repairs, which are maximal consistent subsets of the dataset. However, in many scenarios, one can define preferred repairs based on some preference information. These lecture notes present inconsistency-tolerant semantics, focusing on the repair-based ones, then review different kinds of preferred repairs that have been considered in the literature. We present in particular the relationships between different kinds of preferred repairs and other notions related to inconsistency handling, the computational complexity of reasoning with (preferred) repairs, and some implementations.
Cite as

Camille Bourgaux. Inconsistency-Tolerant Semantics Based on (Preferred) Repairs (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. 5:1-5:67, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bourgaux:OASIcs.RW.2024/2025.5,
  author =	{Bourgaux, Camille},
  title =	{{Inconsistency-Tolerant Semantics Based on (Preferred) Repairs}},
  booktitle =	{Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 \& RW 2025)},
  pages =	{5:1--5:67},
  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.2024/2025.5},
  URN =		{urn:nbn:de:0030-drops-250504},
  doi =		{10.4230/OASIcs.RW.2024/2025.5},
  annote =	{Keywords: Knowledge bases, databases, inconsistency handling, repairs, preferences}
}
Document
Invited Paper
DOI: 10.4230/OASIcs.RW.2024/2025.6
Explaining Reasoning Results for Description Logic Ontologies (Invited Paper)

Authors: Patrick Koopmann

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

Abstract
The Web Ontology Language (OWL), grounded in description logics, enables reasoning systems to infer implicit knowledge in a transparent manner. However, the expressivity of description logics and the complexity of large ontologies often results in reasoning outcomes that are hard to understand without additional tool support. Explanations of these outcomes are essential for users to understand ontology content, communicate its structure and behavior effectively, and debug undesired or missing inferences. This chapter provides an overview of the central explanation techniques that have been developed for explaining reasoning with description logic ontologies. Here, we consider both explanations for positive entailments (explaining why something can be deduced), as well as negative entailments (why something cannot be deduced). More specifically, we discuss justifications, proofs and interpolation as a means to explain positive entailments, and abduction for explaining negative entailments, where we also have a closer look at practical algorithms as well as practical and theoretical challenges.
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Patrick Koopmann. Explaining Reasoning Results for Description Logic Ontologies (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. 6:1-6:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{koopmann:OASIcs.RW.2024/2025.6,
  author =	{Koopmann, Patrick},
  title =	{{Explaining Reasoning Results for Description Logic Ontologies}},
  booktitle =	{Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 \& RW 2025)},
  pages =	{6:1--6:29},
  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.2024/2025.6},
  URN =		{urn:nbn:de:0030-drops-250514},
  doi =		{10.4230/OASIcs.RW.2024/2025.6},
  annote =	{Keywords: Explanations, Justifications, Proofs, Craig Interpolation, Contrastive Explanations}
}
Document
Invited Paper
DOI: 10.4230/OASIcs.RW.2024/2025.7
Modern Datalog: Concepts, Methods, Applications (Invited Paper)

Authors: Markus Krötzsch

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

Abstract
Pure Datalog is arguably the most fundamental rule language, elegant and simple, but also often too limited to be useful in practice. This has motivated the introduction of many new expressive features, ranging from datatypes and related functions, over aggregates and semi-ring generalisations, to existential quantifiers and complex terms. In spite of their variety, all these approaches remain true to the nature of Datalog as a direct, pattern-based way of computing on structured data. We therefore find that a modern notion of Datalog is emerging, distinctly different from other approaches of logic programming and with its own set of related methods and applications. In this course, we introduce Datalog and its most common extensions, and explain when and how these features can be used together (which is often, but not always, safe to do). We further look at modern Datalog systems and some of their primary use cases. Hands-on work with Datalog and its extensions is done with the free Datalog engine https://knowsys.github.io/nemo-doc/. The course is accessible to all audiences and does not assume specific prior knowledge.
Cite as

Markus Krötzsch. Modern Datalog: Concepts, Methods, Applications (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. 7:1-7:41, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{krotzsch:OASIcs.RW.2024/2025.7,
  author =	{Kr\"{o}tzsch, Markus},
  title =	{{Modern Datalog: Concepts, Methods, Applications}},
  booktitle =	{Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 \& RW 2025)},
  pages =	{7:1--7:41},
  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.2024/2025.7},
  URN =		{urn:nbn:de:0030-drops-250524},
  doi =		{10.4230/OASIcs.RW.2024/2025.7},
  annote =	{Keywords: Datalog, query language, knowlegde representation and reasoning, logic programming, Horn logic, SPARQL, datatypes and aggregation, lecture notes, tutorial}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.MFCS.2025.4
On Graph Queries and Modal Constraints (Invited Talk)

Authors: Filip Murlak

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Some fundamental problems in database theory and knowledge representation can be viewed as instances of the query entailment problem. While query evaluation asks whether a given query holds in a specific structure, query entailment consists in determining whether the query holds in every model of a given theory that extends that structure. The input structure represents the raw data stored in a database; the theory captures contextual information such as a set of database constraints or an ontology; and the query is used to extract specific information of interest. The recent proliferation of graph databases has brought the database and knowledge representation communities closer together, as many key problems in both fields involve the same structures - labelled graphs - and similar combinations of formalisms for theories and queries. A notable example is the combination of description logics and conjunctive regular path queries. Description logics are a family of formalisms based on fragments of first order logic, akin to modal logics. They are among the most prominent ontology languages and they are capable of expressing most kinds of constraints relevant in graph databases. Conjunctive regular path queries extend conjunctive queries (primitive positive first-order formulas) by allowing regular expressions over binary predicates to be used as atoms. They form the core of practical query languages employed in graph database systems and the Semantic Web. What distinguishes the two fields is the approach to infinity: knowledge representation embraces infinite models, whereas database theory focuses on finite models. Although many cases of the entailment problem have long been solved over unrestricted (finite or infinite) models, their finite-model counterparts have only recently seen progress, and many questions remain open.
Cite as

Filip Murlak. On Graph Queries and Modal Constraints (Invited Talk). In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, p. 4:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{murlak:LIPIcs.MFCS.2025.4,
  author =	{Murlak, Filip},
  title =	{{On Graph Queries and Modal Constraints}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{4:1--4:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.4},
  URN =		{urn:nbn:de:0030-drops-241117},
  doi =		{10.4230/LIPIcs.MFCS.2025.4},
  annote =	{Keywords: conjunctive regular path queries, query entailment, query containment, graph databases, database schemas, integrity constraints, description logics, finite-model reasoning, ontology-mediated query answering, static analysis}
}
Document
Survey
DOI: 10.4230/TGDK.3.1.3
Uncertainty Management in the Construction of Knowledge Graphs: A Survey

Authors: Lucas Jarnac, Yoan Chabot, and Miguel Couceiro

Published in: TGDK, Volume 3, Issue 1 (2025). Transactions on Graph Data and Knowledge, Volume 3, Issue 1

Abstract
Knowledge Graphs (KGs) are a major asset for companies thanks to their great flexibility in data representation and their numerous applications, e.g., vocabulary sharing, Q&A or recommendation systems. To build a KG, it is a common practice to rely on automatic methods for extracting knowledge from various heterogeneous sources. However, in a noisy and uncertain world, knowledge may not be reliable and conflicts between data sources may occur. Integrating unreliable data would directly impact the use of the KG, therefore such conflicts must be resolved. This could be done manually by selecting the best data to integrate. This first approach is highly accurate, but costly and time-consuming. That is why recent efforts focus on automatic approaches, which represent a challenging task since it requires handling the uncertainty of extracted knowledge throughout its integration into the KG. We survey state-of-the-art approaches in this direction and present constructions of both open and enterprise KGs. We then describe different knowledge extraction methods and discuss downstream tasks after knowledge acquisition, including KG completion using embedding models, knowledge alignment, and knowledge fusion in order to address the problem of knowledge uncertainty in KG construction. We conclude with a discussion on the remaining challenges and perspectives when constructing a KG taking into account uncertainty.
Cite as

Lucas Jarnac, Yoan Chabot, and Miguel Couceiro. Uncertainty Management in the Construction of Knowledge Graphs: A Survey. In Transactions on Graph Data and Knowledge (TGDK), Volume 3, Issue 1, pp. 3:1-3:48, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{jarnac_et_al:TGDK.3.1.3,
  author =	{Jarnac, Lucas and Chabot, Yoan and Couceiro, Miguel},
  title =	{{Uncertainty Management in the Construction of Knowledge Graphs: A Survey}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{3:1--3:48},
  ISSN =	{2942-7517},
  year =	{2025},
  volume =	{3},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.3.1.3},
  URN =		{urn:nbn:de:0030-drops-233733},
  doi =		{10.4230/TGDK.3.1.3},
  annote =	{Keywords: Knowledge reconciliation, Uncertainty, Heterogeneous sources, Knowledge graph construction}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2025.9
Query Languages for Neural Networks

Authors: Martin Grohe, Christoph Standke, Juno Steegmans, and Jan Van den Bussche

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

Abstract
We lay the foundations for a database-inspired approach to interpreting and understanding neural network models by querying them using declarative languages. Towards this end we study different query languages, based on first-order logic, that mainly differ in their access to the neural network model. First-order logic over the reals naturally yields a language which views the network as a black box; only the input-output function defined by the network can be queried. This is essentially the approach of constraint query languages. On the other hand, a white-box language can be obtained by viewing the network as a weighted graph, and extending first-order logic with summation over weight terms. The latter approach is essentially an abstraction of SQL . In general, the two approaches are incomparable in expressive power, as we will show. Under natural circumstances, however, the white-box approach can subsume the black-box approach; this is our main result. We prove the result concretely for linear constraint queries over real functions definable by feedforward neural networks with a fixed number of hidden layers and piecewise linear activation functions.
Cite as

Martin Grohe, Christoph Standke, Juno Steegmans, and Jan Van den Bussche. Query Languages for Neural Networks. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{grohe_et_al:LIPIcs.ICDT.2025.9,
  author =	{Grohe, Martin and Standke, Christoph and Steegmans, Juno and Van den Bussche, Jan},
  title =	{{Query Languages for Neural Networks}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{9:1--9:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.9},
  URN =		{urn:nbn:de:0030-drops-229508},
  doi =		{10.4230/LIPIcs.ICDT.2025.9},
  annote =	{Keywords: Expressive power of query languages, Machine learning models, languages for interpretability, explainable AI}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.20
On Cascades of Reset Automata

Authors: Roberto Borelli, Luca Geatti, Marco Montali, and Angelo Montanari

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
The Krohn-Rhodes decomposition theorem is a pivotal result in automata theory. It introduces the concept of cascade product, where two semiautomata, that is, automata devoid of initial and final states, are combined in a feed-forward fashion. The theorem states that any semiautomaton can be decomposed into a sequence of permutation-reset semiautomata. For the counter-free case, this decomposition consists entirely of reset components with two states each. This decomposition has significantly impacted recent research in various areas of computer science, including the identification of a class of transformer encoders equivalent to star-free languages and the conversion of Linear Temporal Logic formulas into past-only expressions (pastification). The paper revisits the cascade product in the context of reset automata, thus considering each component of the cascade as a language acceptor. First, we give regular expression counterparts of cascades of reset automata. We then establish several expressiveness results, identifying hierarchies of languages based on the restriction of the height (number of components) of the cascade or of the number of states in each level. We also show that any cascade of reset automata can be transformed, with a quadratic increase in height, into a cascade that only includes two-state components. Finally, we show that some fundamental operations on cascades, like intersection, union, negation, and concatenation with a symbol to the left, can be directly and efficiently computed by adding a two-state component.
Cite as

Roberto Borelli, Luca Geatti, Marco Montali, and Angelo Montanari. On Cascades of Reset Automata. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 20:1-20:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{borelli_et_al:LIPIcs.STACS.2025.20,
  author =	{Borelli, Roberto and Geatti, Luca and Montali, Marco and Montanari, Angelo},
  title =	{{On Cascades of Reset Automata}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{20:1--20:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.20},
  URN =		{urn:nbn:de:0030-drops-228453},
  doi =		{10.4230/LIPIcs.STACS.2025.20},
  annote =	{Keywords: Automata, Cascade products, Regular expressions, Krohn-Rhodes theory}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.10
The Complexity of Second-Order HyperLTL

Authors: Hadar Frenkel and Martin Zimmermann

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
We determine the complexity of second-order HyperLTL satisfiability, finite-state satisfiability, and model-checking: All three are equivalent to truth in third-order arithmetic. We also consider two fragments of second-order HyperLTL that have been introduced with the aim to facilitate effective model-checking by restricting the sets one can quantify over. The first one restricts second-order quantification to smallest/largest sets that satisfy a guard while the second one restricts second-order quantification further to least fixed points of (first-order) HyperLTL definable functions. All three problems for the first fragment are still equivalent to truth in third-order arithmetic while satisfiability for the second fragment is Σ₁¹-complete, i.e., only as hard as for (first-order) HyperLTL and therefore much less complex. Finally, finite-state satisfiability and model-checking are in Σ₂² and are Σ₁¹-hard, and thus also less complex than for full second-order HyperLTL.
Cite as

Hadar Frenkel and Martin Zimmermann. The Complexity of Second-Order HyperLTL. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 10:1-10:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{frenkel_et_al:LIPIcs.CSL.2025.10,
  author =	{Frenkel, Hadar and Zimmermann, Martin},
  title =	{{The Complexity of Second-Order HyperLTL}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{10:1--10:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.10},
  URN =		{urn:nbn:de:0030-drops-227679},
  doi =		{10.4230/LIPIcs.CSL.2025.10},
  annote =	{Keywords: HyperLTL, Satisfiability, Model-checking}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.17
Description Complexity of Unary Structures in First-Order Logic with Links to Entropy

Authors: Reijo Jaakkola, Antti Kuusisto, and Miikka Vilander

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
The description complexity of a model is the length of the shortest formula that defines the model. We study the description complexity of unary structures in first-order logic FO, also drawing links to semantic complexity in the form of entropy. The class of unary structures provides, e.g., a simple way to represent tabular Boolean data sets as relational structures. We define structures with FO-formulas that are strictly linear in the size of the model as opposed to using the naive quadratic ones, and we use arguments based on formula size games to obtain related lower bounds for description complexity. For a typical structure the upper and lower bounds in fact match up to a sublinear term, leading to a precise asymptotic result on the expected description complexity of a randomly selected structure. We then give bounds on the relationship between Shannon entropy and description complexity. We extend this relationship also to Boltzmann entropy by establishing an asymptotic match between the two entropies. Despite the simplicity of unary structures, our arguments require the use of formula size games, Stirling’s approximation and Chernoff bounds.
Cite as

Reijo Jaakkola, Antti Kuusisto, and Miikka Vilander. Description Complexity of Unary Structures in First-Order Logic with Links to Entropy. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 17:1-17:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jaakkola_et_al:LIPIcs.CSL.2025.17,
  author =	{Jaakkola, Reijo and Kuusisto, Antti and Vilander, Miikka},
  title =	{{Description Complexity of Unary Structures in First-Order Logic with Links to Entropy}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{17:1--17:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.17},
  URN =		{urn:nbn:de:0030-drops-227749},
  doi =		{10.4230/LIPIcs.CSL.2025.17},
  annote =	{Keywords: formula size, finite model theory, formula size games, entropy, randomness}
}
Document
Resource Paper
DOI: 10.4230/TGDK.2.2.7
Whelk: An OWL EL+RL Reasoner Enabling New Use Cases

Authors: James P. Balhoff and Christopher J. Mungall

Published in: TGDK, Volume 2, Issue 2 (2024): Special Issue on Resources for Graph Data and Knowledge. Transactions on Graph Data and Knowledge, Volume 2, Issue 2

Abstract
Many tasks in the biosciences rely on reasoning with large OWL terminologies (Tboxes), often combined with even larger databases. In particular, a common task is retrieval queries that utilize relational expressions; for example, “find all genes expressed in the brain or any part of the brain”. Automated reasoning on these ontologies typically relies on scalable reasoners targeting the EL subset of OWL, such as ELK. While the introduction of ELK has been transformative in the incorporation of reasoning into bio-ontology quality control and production pipelines, we have encountered limitations when applying it to use cases involving high throughput query answering or reasoning about datasets describing instances (Aboxes). Whelk is a fast OWL reasoner for combined EL+RL reasoning. As such, it is particularly useful for many biological ontology tasks, particularly those characterized by large Tboxes using the EL subset of OWL, combined with Aboxes targeting the RL subset of OWL. Whelk is implemented in Scala and utilizes immutable functional data structures, which provides advantages when performing incremental or dynamic reasoning tasks. Whelk supports querying complex class expressions at a substantially greater rate than ELK, and can answer queries or perform incremental reasoning tasks in parallel, enabling novel applications of OWL reasoning.
Cite as

James P. Balhoff and Christopher J. Mungall. Whelk: An OWL EL+RL Reasoner Enabling New Use Cases. In Special Issue on Resources for Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 2, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{balhoff_et_al:TGDK.2.2.7,
  author =	{Balhoff, James P. and Mungall, Christopher J.},
  title =	{{Whelk: An OWL EL+RL Reasoner Enabling New Use Cases}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{7:1--7:17},
  ISSN =	{2942-7517},
  year =	{2024},
  volume =	{2},
  number =	{2},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.2.7},
  URN =		{urn:nbn:de:0030-drops-225918},
  doi =		{10.4230/TGDK.2.2.7},
  annote =	{Keywords: Web Ontology Language, OWL, Semantic Web, ontology, reasoner}
}
Document
Survey
DOI: 10.4230/TGDK.2.1.3
Semantic Web: Past, Present, and Future

Authors: Ansgar Scherp, Gerd Groener, Petr Škoda, Katja Hose, and Maria-Esther Vidal

Published in: TGDK, Volume 2, Issue 1 (2024): Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge, Volume 2, Issue 1

Abstract
Ever since the vision was formulated, the Semantic Web has inspired many generations of innovations. Semantic technologies have been used to share vast amounts of information on the Web, enhance them with semantics to give them meaning, and enable inference and reasoning on them. Throughout the years, semantic technologies, and in particular knowledge graphs, have been used in search engines, data integration, enterprise settings, and machine learning. In this paper, we recap the classical concepts and foundations of the Semantic Web as well as modern and recent concepts and applications, building upon these foundations. The classical topics we cover include knowledge representation, creating and validating knowledge on the Web, reasoning and linking, and distributed querying. We enhance this classical view of the so-called "Semantic Web Layer Cake" with an update of recent concepts that include provenance, security and trust, as well as a discussion of practical impacts from industry-led contributions. We conclude with an outlook on the future directions of the Semantic Web. This is a living document. If you like to contribute, please contact the first author and visit: https://github.com/ascherp/semantic-web-primer
Cite as

Ansgar Scherp, Gerd Groener, Petr Škoda, Katja Hose, and Maria-Esther Vidal. Semantic Web: Past, Present, and Future. In Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 1, pp. 3:1-3:37, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{scherp_et_al:TGDK.2.1.3,
  author =	{Scherp, Ansgar and Groener, Gerd and \v{S}koda, Petr and Hose, Katja and Vidal, Maria-Esther},
  title =	{{Semantic Web: Past, Present, and Future}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{3:1--3:37},
  ISSN =	{2942-7517},
  year =	{2024},
  volume =	{2},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.1.3},
  URN =		{urn:nbn:de:0030-drops-198607},
  doi =		{10.4230/TGDK.2.1.3},
  annote =	{Keywords: Linked Open Data, Semantic Web Graphs, Knowledge Graphs}
}
Document
Survey
DOI: 10.4230/TGDK.2.1.4
Logics for Conceptual Data Modelling: A Review

Authors: Pablo R. Fillottrani and C. Maria Keet

Published in: TGDK, Volume 2, Issue 1 (2024): Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge, Volume 2, Issue 1

Abstract
Information modelling for databases and object-oriented information systems avails of conceptual data modelling languages such as EER and UML Class Diagrams. Many attempts exist to add logical rigour to them, for various reasons and with disparate strengths. In this paper we aim to provide a structured overview of the many efforts. We focus on aims, approaches to the formalisation, including key dimensions of choice points, popular logics used, and the main relevant reasoning services. We close with current challenges and research directions.
Cite as

Pablo R. Fillottrani and C. Maria Keet. Logics for Conceptual Data Modelling: A Review. In Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 1, pp. 4:1-4:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{fillottrani_et_al:TGDK.2.1.4,
  author =	{Fillottrani, Pablo R. and Keet, C. Maria},
  title =	{{Logics for Conceptual Data Modelling: A Review}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{4:1--4:30},
  ISSN =	{2942-7517},
  year =	{2024},
  volume =	{2},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.1.4},
  URN =		{urn:nbn:de:0030-drops-198616},
  doi =		{10.4230/TGDK.2.1.4},
  annote =	{Keywords: Conceptual Data Modelling, EER, UML, Description Logics, OWL}
}
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