7 Search Results for "Reutter, David"


Document
Automating Boundary Filling in Cubical Agda

Authors: Maximilian Doré, Evan Cavallo, and Anders Mörtberg

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)


Abstract
When working in a proof assistant, automation is key to discharging routine proof goals such as equations between algebraic expressions. Homotopy Type Theory allows the user to reason about higher structures, such as topological spaces, using higher inductive types (HITs) and univalence. Cubical Agda is an extension of Agda with computational support for HITs and univalence. A difficulty when working in Cubical Agda is dealing with the complex combinatorics of higher structures, an infinite-dimensional generalisation of equational reasoning. To solve these higher-dimensional equations consists in constructing cubes with specified boundaries. We develop a simplified cubical language in which we isolate and study two automation problems: contortion solving, where we attempt to "contort" a cube to fit a given boundary, and the more general Kan solving, where we search for solutions that involve pasting multiple cubes together. Both problems are difficult in the general case - Kan solving is even undecidable - so we focus on heuristics that perform well on practical examples. We provide a solver for the contortion problem using a reformulation of contortions in terms of poset maps, while we solve Kan problems using constraint satisfaction programming. We have implemented our algorithms in an experimental Haskell solver that can be used to automatically solve goals presented by Cubical Agda. We illustrate this with a case study establishing the Eckmann-Hilton theorem using our solver, as well as various benchmarks - providing the ground for further study of proof automation in cubical type theories.

Cite as

Maximilian Doré, Evan Cavallo, and Anders Mörtberg. Automating Boundary Filling in Cubical Agda. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 22:1-22:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{dore_et_al:LIPIcs.FSCD.2024.22,
  author =	{Dor\'{e}, Maximilian and Cavallo, Evan and M\"{o}rtberg, Anders},
  title =	{{Automating Boundary Filling in Cubical Agda}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{22:1--22:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.22},
  URN =		{urn:nbn:de:0030-drops-203514},
  doi =		{10.4230/LIPIcs.FSCD.2024.22},
  annote =	{Keywords: Cubical Agda, Automated Reasoning, Constraint Satisfaction Programming}
}
Document
homotopy.io: A Proof Assistant for Finitely-Presented Globular n-Categories

Authors: Nathan Corbyn, Lukas Heidemann, Nick Hu, Chiara Sarti, Calin Tataru, and Jamie Vicary

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)


Abstract
We present the proof assistant homotopy.io for working with finitely-presented semistrict higher categories. The tool runs in the browser with a point-and-click interface, allowing direct manipulation of proof objects via a graphical representation. We describe the user interface and explain how the tool can be used in practice. We also describe the essential subsystems of the tool, including collapse, contraction, expansion, typechecking, and layout, as well as key implementation details including data structure encoding, memoisation, and rendering. These technical innovations have been essential for achieving good performance in a resource-constrained setting.

Cite as

Nathan Corbyn, Lukas Heidemann, Nick Hu, Chiara Sarti, Calin Tataru, and Jamie Vicary. homotopy.io: A Proof Assistant for Finitely-Presented Globular n-Categories. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 30:1-30:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{corbyn_et_al:LIPIcs.FSCD.2024.30,
  author =	{Corbyn, Nathan and Heidemann, Lukas and Hu, Nick and Sarti, Chiara and Tataru, Calin and Vicary, Jamie},
  title =	{{homotopy.io: A Proof Assistant for Finitely-Presented Globular n-Categories}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{30:1--30:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.30},
  URN =		{urn:nbn:de:0030-drops-203594},
  doi =		{10.4230/LIPIcs.FSCD.2024.30},
  annote =	{Keywords: Higher category theory, proof assistant, string diagrams}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Decidability of Graph Neural Networks via Logical Characterizations

Authors: Michael Benedikt, Chia-Hsuan Lu, Boris Motik, and Tony Tan

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)


Abstract
We present results concerning the expressiveness and decidability of a popular graph learning formalism, graph neural networks (GNNs), exploiting connections with logic. We use a family of recently-discovered decidable logics involving "Presburger quantifiers". We show how to use these logics to measure the expressiveness of classes of GNNs, in some cases getting exact correspondences between the expressiveness of logics and GNNs. We also employ the logics, and the techniques used to analyze them, to obtain decision procedures for verification problems over GNNs. We complement this with undecidability results for static analysis problems involving the logics, as well as for GNN verification problems.

Cite as

Michael Benedikt, Chia-Hsuan Lu, Boris Motik, and Tony Tan. Decidability of Graph Neural Networks via Logical Characterizations. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 127:1-127:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{benedikt_et_al:LIPIcs.ICALP.2024.127,
  author =	{Benedikt, Michael and Lu, Chia-Hsuan and Motik, Boris and Tan, Tony},
  title =	{{Decidability of Graph Neural Networks via Logical Characterizations}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{127:1--127:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.127},
  URN =		{urn:nbn:de:0030-drops-202708},
  doi =		{10.4230/LIPIcs.ICALP.2024.127},
  annote =	{Keywords: Logic, Graph Neural Networks}
}
Document
Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282)

Authors: James P. Delgrande, Birte Glimm, Thomas Meyer, Miroslaw Truszczynski, and Frank Wolter

Published in: Dagstuhl Manifestos, Volume 10, Issue 1 (2024)


Abstract
Knowledge Representation and Reasoning is a central, longstanding, and active area of Artificial Intelligence. Over the years it has evolved significantly; more recently it has been challenged and complemented by research in areas such as machine learning and reasoning under uncertainty. In July 2022,sser a Dagstuhl Perspectives workshop was held on Knowledge Representation and Reasoning. The goal of the workshop was to describe the state of the art in the field, including its relation with other areas, its shortcomings and strengths, together with recommendations for future progress. We developed this manifesto based on the presentations, panels, working groups, and discussions that took place at the Dagstuhl Workshop. It is a declaration of our views on Knowledge Representation: its origins, goals, milestones, and current foci; its relation to other disciplines, especially to Artificial Intelligence; and on its challenges, along with key priorities for the next decade.

Cite as

James P. Delgrande, Birte Glimm, Thomas Meyer, Miroslaw Truszczynski, and Frank Wolter. Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282). In Dagstuhl Manifestos, Volume 10, Issue 1, pp. 1-61, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@Article{delgrande_et_al:DagMan.10.1.1,
  author =	{Delgrande, James P. and Glimm, Birte and Meyer, Thomas and Truszczynski, Miroslaw and Wolter, Frank},
  title =	{{Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282)}},
  pages =	{1--61},
  journal =	{Dagstuhl Manifestos},
  ISSN =	{2193-2433},
  year =	{2024},
  volume =	{10},
  number =	{1},
  editor =	{Delgrande, James P. and Glimm, Birte and Meyer, Thomas and Truszczynski, Miroslaw and Wolter, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagMan.10.1.1},
  URN =		{urn:nbn:de:0030-drops-201403},
  doi =		{10.4230/DagMan.10.1.1},
  annote =	{Keywords: Knowledge representation and reasoning, Applications of logics, Declarative representations, Formal logic}
}
Document
Survey
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
A Classical Groupoid Model for Quantum Networks

Authors: David Reutter and Jamie Vicary

Published in: LIPIcs, Volume 72, 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)


Abstract
We give a mathematical analysis of a new type of classical computer network architecture, intended as a model of a new technology that has recently been proposed in industry. Our approach is based on groubits, generalizations of classical bits based on groupoids. This network architecture allows the direct execution of a number of protocols that are usually associated with quantum networks, including teleportation, dense coding and secure key distribution.

Cite as

David Reutter and Jamie Vicary. A Classical Groupoid Model for Quantum Networks. In 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 72, pp. 19:1-19:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{reutter_et_al:LIPIcs.CALCO.2017.19,
  author =	{Reutter, David and Vicary, Jamie},
  title =	{{A Classical Groupoid Model for Quantum Networks}},
  booktitle =	{7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)},
  pages =	{19:1--19:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-033-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{72},
  editor =	{Bonchi, Filippo 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.CALCO.2017.19},
  URN =		{urn:nbn:de:0030-drops-80391},
  doi =		{10.4230/LIPIcs.CALCO.2017.19},
  annote =	{Keywords: groupoids, networks, quantum, semantics, key distribution}
}
Document
A 2-Categorical Approach to Composing Quantum Structures

Authors: David Reutter and Jamie Vicary

Published in: LIPIcs, Volume 72, 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)


Abstract
We present an infinite number of construction schemes for quantum structures, including unitary error bases, Hadamard matrices, quantum Latin squares and controlled families, many of which have not previously been described. Our results rely on the type structure of biunitary connections, 2-categorical structures which play a central role in the theory of planar algebras. They have an attractive graphical calculus which allows simple correctness proofs for the constructions we present. We apply these techniques to construct a unitary error basis that cannot be built using any previously known method.

Cite as

David Reutter and Jamie Vicary. A 2-Categorical Approach to Composing Quantum Structures. In 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 72, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{reutter_et_al:LIPIcs.CALCO.2017.20,
  author =	{Reutter, David and Vicary, Jamie},
  title =	{{A 2-Categorical Approach to Composing Quantum Structures}},
  booktitle =	{7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)},
  pages =	{20:1--20:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-033-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{72},
  editor =	{Bonchi, Filippo 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.CALCO.2017.20},
  URN =		{urn:nbn:de:0030-drops-80389},
  doi =		{10.4230/LIPIcs.CALCO.2017.20},
  annote =	{Keywords: quantum constructions, 2-category, graphical calculus, planar algebra}
}
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