7 Search Results for "Fernández-Duque, David"

Document
DOI: 10.4230/LIPIcs.LICS.2026.81
Axiomatizability of Alexandrov Dynamic Topological Logic

Authors: Niels C. Vooijs and David Fernández-Duque

Published in: LIPIcs, Volume 380, 41st Annual Symposium on Logic in Computer Science (LICS 2026)

Abstract
Dynamical systems provide rigorous models of movement or evolution over time. Due to their abstract nature, they may be naturally employed for representing e.g. physical, biological, or financial phenomena. Specifically in the context of Computer Science, computational processes, machine learning algorithms, and multi-agent systems may be regarded as dynamical systems. This has sparked interest in designing formal specification languages for dynamical systems which could potentially be employed for automated or computer-assisted deduction, leading to the introduction of dynamic topological logic (DTL). When space is continuous but time is discrete, it is known that a sound and complete deductive calculus for DTL exists. However, discrete spaces are not uncommon in CS applications , and in this setting, whether such a calculus exists even in principle has been an open question for more than two decades. More precisely, it was unknown whether the DTL of Alexandrov spaces is computably enumerable. In this paper, we use model search techniques to provide an affirmative answer.
Cite as

Niels C. Vooijs and David Fernández-Duque. Axiomatizability of Alexandrov Dynamic Topological Logic. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 81:1-81:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{vooijs_et_al:LIPIcs.LICS.2026.81,
  author =	{Vooijs, Niels C. and Fern\'{a}ndez-Duque, David},
  title =	{{Axiomatizability of Alexandrov Dynamic Topological Logic}},
  booktitle =	{41st Annual Symposium on Logic in Computer Science (LICS 2026)},
  pages =	{81:1--81:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-434-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{380},
  editor =	{Faggian, Claudia and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.LICS.2026.81},
  URN =		{urn:nbn:de:0030-drops-268689},
  doi =		{10.4230/LIPIcs.LICS.2026.81},
  annote =	{Keywords: dynamic topological logic, Alexandrov spaces, computable enumerability, modal logic, temporal logic}
}
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
DOI: 10.4230/LIPIcs.CSL.2025.25
Exponential Lower Bounds on Definable Fixed Points

Authors: Konstantinos Papafilippou and David Fernández-Duque

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

Abstract
It is known that the μ-calculus is no more expressive than basic modal logic over the class of finite partial orders, as well as over the class of finite, strict partial orders. Nevertheless, we show that the μ-calculus is exponentially more succinct, even when a reflexive modality is added as primitive. As corollaries, we obtain a lower bound for the fixed-point theorem for Gödel-Löb logic and a variant for Grzegorczyk logic, as well as lower bounds on interpolants for the interpolation theorem of Gödel-Löb logic.
Cite as

Konstantinos Papafilippou and David Fernández-Duque. Exponential Lower Bounds on Definable Fixed Points. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 25:1-25:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{papafilippou_et_al:LIPIcs.CSL.2025.25,
  author =	{Papafilippou, Konstantinos and Fern\'{a}ndez-Duque, David},
  title =	{{Exponential Lower Bounds on Definable Fixed Points}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{25:1--25:19},
  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.2025.25},
  URN =		{urn:nbn:de:0030-drops-227827},
  doi =		{10.4230/LIPIcs.CSL.2025.25},
  annote =	{Keywords: Modal logic, Provability Logic, Fixed-Point Theorem, mu-calculus, Interpolation, Succinctness}
}
Document
Survey
DOI: 10.4230/TGDK.1.1.11
How Does Knowledge Evolve in Open Knowledge Graphs?

Authors: Axel Polleres, Romana Pernisch, Angela Bonifati, Daniele Dell'Aglio, Daniil Dobriy, Stefania Dumbrava, Lorena Etcheverry, Nicolas Ferranti, Katja Hose, Ernesto Jiménez-Ruiz, Matteo Lissandrini, Ansgar Scherp, Riccardo Tommasini, and Johannes Wachs

Published in: TGDK, Volume 1, Issue 1 (2023): Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge, Volume 1, Issue 1

Abstract
Openly available, collaboratively edited Knowledge Graphs (KGs) are key platforms for the collective management of evolving knowledge. The present work aims t o provide an analysis of the obstacles related to investigating and processing specifically this central aspect of evolution in KGs. To this end, we discuss (i) the dimensions of evolution in KGs, (ii) the observability of evolution in existing, open, collaboratively constructed Knowledge Graphs over time, and (iii) possible metrics to analyse this evolution. We provide an overview of relevant state-of-the-art research, ranging from metrics developed for Knowledge Graphs specifically to potential methods from related fields such as network science. Additionally, we discuss technical approaches - and their current limitations - related to storing, analysing and processing large and evolving KGs in terms of handling typical KG downstream tasks.
Cite as

Axel Polleres, Romana Pernisch, Angela Bonifati, Daniele Dell'Aglio, Daniil Dobriy, Stefania Dumbrava, Lorena Etcheverry, Nicolas Ferranti, Katja Hose, Ernesto Jiménez-Ruiz, Matteo Lissandrini, Ansgar Scherp, Riccardo Tommasini, and Johannes Wachs. How Does Knowledge Evolve in Open Knowledge Graphs?. In Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 1, Issue 1, pp. 11:1-11:59, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{polleres_et_al:TGDK.1.1.11,
  author =	{Polleres, Axel and Pernisch, Romana and Bonifati, Angela and Dell'Aglio, Daniele and Dobriy, Daniil and Dumbrava, Stefania and Etcheverry, Lorena and Ferranti, Nicolas and Hose, Katja and Jim\'{e}nez-Ruiz, Ernesto and Lissandrini, Matteo and Scherp, Ansgar and Tommasini, Riccardo and Wachs, Johannes},
  title =	{{How Does Knowledge Evolve in Open Knowledge Graphs?}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{11:1--11:59},
  year =	{2023},
  volume =	{1},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.1.1.11},
  URN =		{urn:nbn:de:0030-drops-194855},
  doi =		{10.4230/TGDK.1.1.11},
  annote =	{Keywords: KG evolution, temporal KG, versioned KG, dynamic KG}
}
Document
DOI: 10.4230/LIPIcs.CSL.2022.19
Dynamic Cantor Derivative Logic

Authors: David Fernández-Duque and Yoàv Montacute

Published in: LIPIcs, Volume 216, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022)

Abstract
Topological semantics for modal logic based on the Cantor derivative operator gives rise to derivative logics, also referred to as d-logics. Unlike logics based on the topological closure operator, d-logics have not previously been studied in the framework of dynamical systems, which are pairs (X,f) consisting of a topological space X equipped with a continuous function f: X → X. We introduce the logics wK4C, K4C and GLC and show that they all have the finite Kripke model property and are sound and complete with respect to the d-semantics in this dynamical setting. In particular, we prove that wK4C is the d-logic of all dynamic topological systems, K4C is the d-logic of all T_D dynamic topological systems, and GLC is the d-logic of all dynamic topological systems based on a scattered space. We also prove a general result for the case where f is a homeomorphism, which in particular yields soundness and completeness for the corresponding systems wK4H, K4H and GLH. The main contribution of this work is the foundation of a general proof method for finite model property and completeness of dynamic topological d-logics. Furthermore, our result for GLC constitutes the first step towards a proof of completeness for the trimodal topo-temporal language with respect to a finite axiomatisation - something known to be impossible over the class of all spaces.
Cite as

David Fernández-Duque and Yoàv Montacute. Dynamic Cantor Derivative Logic. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 19:1-19:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fernandezduque_et_al:LIPIcs.CSL.2022.19,
  author =	{Fern\'{a}ndez-Duque, David and Montacute, Yo\`{a}v},
  title =	{{Dynamic Cantor Derivative Logic}},
  booktitle =	{30th EACSL Annual Conference on Computer Science Logic (CSL 2022)},
  pages =	{19:1--19:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-218-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{216},
  editor =	{Manea, Florin and Simpson, Alex},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.19},
  URN =		{urn:nbn:de:0030-drops-157397},
  doi =		{10.4230/LIPIcs.CSL.2022.19},
  annote =	{Keywords: dynamic topological logic, Cantor derivative, temporal logic, modal logic}
}
Document
DOI: 10.4230/LIPIcs.TIME.2019.6
The Second Order Traffic Fine: Temporal Reasoning in European Transport Regulations

Authors: Ana de Almeida Borges, Juan José Conejero Rodríguez, David Fernández-Duque, Mireia González Bedmar, and Joost J. Joosten

Published in: LIPIcs, Volume 147, 26th International Symposium on Temporal Representation and Reasoning (TIME 2019)

Abstract
We argue that European transport regulations can be formalized within the Sigma^1_1 fragment of monadic second order logic, and possibly weaker fragments including linear temporal logic. We consider several articles in the regulation to verify these claims.
Cite as

Ana de Almeida Borges, Juan José Conejero Rodríguez, David Fernández-Duque, Mireia González Bedmar, and Joost J. Joosten. The Second Order Traffic Fine: Temporal Reasoning in European Transport Regulations. In 26th International Symposium on Temporal Representation and Reasoning (TIME 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 147, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{dealmeidaborges_et_al:LIPIcs.TIME.2019.6,
  author =	{de Almeida Borges, Ana and Conejero Rodr{\'\i}guez, Juan Jos\'{e} and Fern\'{a}ndez-Duque, David and Gonz\'{a}lez Bedmar, Mireia and Joosten, Joost J.},
  title =	{{The Second Order Traffic Fine: Temporal Reasoning in European Transport Regulations}},
  booktitle =	{26th International Symposium on Temporal Representation and Reasoning (TIME 2019)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-127-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{147},
  editor =	{Gamper, Johann and Pinchinat, Sophie and Sciavicco, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2019.6},
  URN =		{urn:nbn:de:0030-drops-113649},
  doi =		{10.4230/LIPIcs.TIME.2019.6},
  annote =	{Keywords: linear temporal logic, monadic second order logic, formalized law, transport regulations}
}
Document
DOI: 10.4230/LIPIcs.CSL.2017.14
A Decidable Intuitionistic Temporal Logic

Authors: Joseph Boudou, Martín Diéguez, and David Fernández-Duque

Published in: LIPIcs, Volume 82, 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)

Abstract
We introduce the logic ITL^e, an intuitionistic temporal logic based on structures (W,R,S), where R is used to interpret intuitionistic implication and S is an R-monotone function used to interpret temporal modalities. Our main result is that the satisfiability and validity problems for ITL^e are decidable. We prove this by showing that the logic enjoys the strong finite model property. In contrast, we also consider a 'persistent' version of the logic, ITL^p, whose models are similar to Cartesian products. We prove that, unlike ITL^e, ITL^p does not have the finite model property.
Cite as

Joseph Boudou, Martín Diéguez, and David Fernández-Duque. A Decidable Intuitionistic Temporal Logic. In 26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{boudou_et_al:LIPIcs.CSL.2017.14,
  author =	{Boudou, Joseph and Di\'{e}guez, Mart{\'\i}n and Fern\'{a}ndez-Duque, David},
  title =	{{A Decidable Intuitionistic Temporal Logic}},
  booktitle =	{26th EACSL Annual Conference on Computer Science Logic (CSL 2017)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-045-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{82},
  editor =	{Goranko, Valentin and Dam, Mads},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2017.14},
  URN =		{urn:nbn:de:0030-drops-77016},
  doi =		{10.4230/LIPIcs.CSL.2017.14},
  annote =	{Keywords: intuitionistic logic, temporal logic, products of modal logics}
}
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