5 Search Results for "Doczkal, Christian"

Document
DOI: 10.4230/LIPIcs.CSL.2026.18
A Modular Framework for Proof-Search via Formalised Modal Completeness in HOL Light

Authors: Antonella Bilotta, Marco Maggesi, and Cosimo Perini Brogi

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

Abstract
We extend the existing HOL Light Library for Modal Systems (HOLMS) to support a modular implementation of modal reasoning within the HOL Light proof assistant. We deeply embed axiomatic calculi and relational semantics for seven normal modal logics (K, T, B, K4, S4, S5, GL) and formalise modal adequacy theorems for these systems. We then leverage those formalisations to implement a mechanism for automated reasoning via proof-search in the associated labelled sequent calculi, which we shallowly embed in HOL Light’s goal-stack mechanism. This way, we equip the general-purpose proof assistant with (semi)decision procedures for these logics that, in case of failure to construct a proof for the input formula, return a certified countermodel within the appropriate class for the logic under consideration. On the methodological side, we propose a precise measure of the modularity of our approach by systematically adopting Christopher Strachey’s distinction between ad hoc and parametric polymorphism throughout the library.
Cite as

Antonella Bilotta, Marco Maggesi, and Cosimo Perini Brogi. A Modular Framework for Proof-Search via Formalised Modal Completeness in HOL Light. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 18:1-18:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bilotta_et_al:LIPIcs.CSL.2026.18,
  author =	{Bilotta, Antonella and Maggesi, Marco and Perini Brogi, Cosimo},
  title =	{{A Modular Framework for Proof-Search via Formalised Modal Completeness in HOL Light}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{18:1--18:29},
  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.2026.18},
  URN =		{urn:nbn:de:0030-drops-254427},
  doi =		{10.4230/LIPIcs.CSL.2026.18},
  annote =	{Keywords: Modal logic, HOL Light, Labelled sequent calculi, Logical verification, Interactive theorem proving, Automated proof-search}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.ITP.2025.37
LeanLTL: A Unifying Framework for Linear Temporal Logics in Lean (Short Paper)

Authors: Eric Vin, Kyle A. Miller, and Daniel J. Fremont

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
We propose LeanLTL, a unifying framework for linear temporal logics in Lean 4. LeanLTL supports reasoning about traces that represent either infinite or finite linear time. The library allows traditional LTL syntax to be combined with arbitrary Lean expressions, making it straightforward to define properties involving numerical or other types. We prove that standard flavors of LTL can be embedded in our framework. The library also provides automation for reasoning about LeanLTL formulas in a way that facilitates using Lean’s existing tactics. Finally, we provide examples illustrating the utility of the library in reasoning about systems that come from applications.
Cite as

Eric Vin, Kyle A. Miller, and Daniel J. Fremont. LeanLTL: A Unifying Framework for Linear Temporal Logics in Lean (Short Paper). In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 37:1-37:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{vin_et_al:LIPIcs.ITP.2025.37,
  author =	{Vin, Eric and Miller, Kyle A. and Fremont, Daniel J.},
  title =	{{LeanLTL: A Unifying Framework for Linear Temporal Logics in Lean}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{37:1--37:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.37},
  URN =		{urn:nbn:de:0030-drops-246356},
  doi =		{10.4230/LIPIcs.ITP.2025.37},
  annote =	{Keywords: Linear Temporal Logic, Interactive Theorem Proving, Lean 4}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.40
Completeness of First-Order Bi-Intuitionistic Logic

Authors: Dominik Kirst and Ian Shillito

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

Abstract
We provide a succinct and verified completeness proof for first-order bi-intuitionistic logic, relative to constant domain Kripke semantics. By doing so, we make up for the almost-50-year-old substantial mistakes in Rauszer’s foundational work, detected but unresolved by Shillito two years ago. Moreover, an even earlier but historically neglected proof by Klemke has been found to contain at least local errors by Olkhovikov and Badia, that remained unfixed due to the technical complexity of Klemke’s argument. To resolve this unclear situation once and for all, we give a succinct completeness proof, based on and dualising a standard proof for constant domain intuitionistic logic, and verify our constructions using the Coq proof assistant to guarantee correctness.
Cite as

Dominik Kirst and Ian Shillito. Completeness of First-Order Bi-Intuitionistic Logic. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 40:1-40:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kirst_et_al:LIPIcs.CSL.2025.40,
  author =	{Kirst, Dominik and Shillito, Ian},
  title =	{{Completeness of First-Order Bi-Intuitionistic Logic}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{40:1--40:19},
  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.2025.40},
  URN =		{urn:nbn:de:0030-drops-227979},
  doi =		{10.4230/LIPIcs.CSL.2025.40},
  annote =	{Keywords: bi-intuitionistic logic, first-order logic, completeness, Coq proof assistant}
}
Document
DOI: 10.4230/LIPIcs.ITP.2021.17
A Variant of Wagner’s Theorem Based on Combinatorial Hypermaps

Authors: Christian Doczkal

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
Wagner’s theorem states that a graph is planar (i.e., it can be embedded in the real plane without crossing edges) iff it contains neither 𝖪_5 nor 𝖪_{3,3} as a minor. We provide a combinatorial representation of embeddings in the plane that abstracts from topological properties of plane embeddings (e.g., angles or distances), representing only the combinatorial properties (e.g., arities of faces or the clockwise order of the outgoing edges of a vertex). The representation employs combinatorial hypermaps as used by Gonthier in the proof of the four-color theorem. We then give a formal proof that for every simple graph containing neither 𝖪_5 nor 𝖪_{3,3} as a minor, there exists such a combinatorial plane embedding. Together with the formal proof of the four-color theorem, we obtain a formal proof that all graphs without 𝖪_5 and 𝖪_{3,3} minors are four-colorable. The development is carried out in Coq, building on the mathematical components library, the formal proof of the four-color theorem, and a general-purpose graph library developed previously.
Cite as

Christian Doczkal. A Variant of Wagner’s Theorem Based on Combinatorial Hypermaps. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{doczkal:LIPIcs.ITP.2021.17,
  author =	{Doczkal, Christian},
  title =	{{A Variant of Wagner’s Theorem Based on Combinatorial Hypermaps}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{17:1--17:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.17},
  URN =		{urn:nbn:de:0030-drops-139123},
  doi =		{10.4230/LIPIcs.ITP.2021.17},
  annote =	{Keywords: Coq, MathComp, Graph-Theory, Hypermaps, Planarity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2018.60
Treewidth-Two Graphs as a Free Algebra

Authors: Christian Doczkal and Damien Pous

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Abstract
We give a new and elementary proof that the graphs of treewidth at most two can be seen as a free algebra. This result was originally established through an elaborate analysis of the structure of K_4-free graphs, ultimately reproving the well-known fact that the graphs of treewidth at most two are precisely those excluding K_4 as a minor. Our new proof is based on a confluent and terminating rewriting system for term-labeled graphs and does not involve graph minors anymore. The new strategy is simpler and robust in the sense that it can be adapted to subclasses of treewidth-two graphs, e.g., graphs without self-loops.
Cite as

Christian Doczkal and Damien Pous. Treewidth-Two Graphs as a Free Algebra. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 60:1-60:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{doczkal_et_al:LIPIcs.MFCS.2018.60,
  author =	{Doczkal, Christian and Pous, Damien},
  title =	{{Treewidth-Two Graphs as a Free Algebra}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{60:1--60:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.60},
  URN =		{urn:nbn:de:0030-drops-96429},
  doi =		{10.4230/LIPIcs.MFCS.2018.60},
  annote =	{Keywords: Treewidth, Universal Algebra, Rewriting}
}
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