4 Search Results for "Trotta, Davide"

Document
DOI: 10.4230/LIPIcs.CSL.2026.22
On the Algorithmic Structure of Dialectica Realisers

Authors: Davide Barbarossa and Thomas Powell

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

Abstract
Gödel’s Dialectica interpretation is a fundamental tool for the extraction of computational content from proofs, and plays a central role in today’s proof mining program. In the past decades, it has also been studied from the perspective of programming languages, and our contribution is in that direction. Specifically, we present Dialectica as a collection of rules in the style of Hoare logic, where Dialectica is now viewed as a language for specifying procedural programs that come with a forward and backward direction. This viewpoint captures the interesting dynamics of realisers extracted by the Dialectica interpretation, and we illustrate this by defining a generalised backpropagation semantics for a fragment of this language. We envisage this work as providing a base for several future developments, both theoretical and practical, which we outline at the end.
Cite as

Davide Barbarossa and Thomas Powell. On the Algorithmic Structure of Dialectica Realisers. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 22:1-22:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{barbarossa_et_al:LIPIcs.CSL.2026.22,
  author =	{Barbarossa, Davide and Powell, Thomas},
  title =	{{On the Algorithmic Structure of Dialectica Realisers}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{22:1--22:22},
  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.2026.22},
  URN =		{urn:nbn:de:0030-drops-254466},
  doi =		{10.4230/LIPIcs.CSL.2026.22},
  annote =	{Keywords: Dialectica interpretation, Hoare logic, Programs from proofs}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.30
When Lawvere Meets Peirce: An Equational Presentation of Boolean Hyperdoctrines

Authors: Filippo Bonchi, Alessandro Di Giorgio, and Davide Trotta

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
Fo-bicategories are a categorification of Peirce’s calculus of relations. Notably, their laws provide a proof system for first-order logic that is both purely equational and complete. This paper illustrates a correspondence between fo-bicategories and Lawvere’s hyperdoctrines. To streamline our proof, we introduce peircean bicategories, which offer a more succinct characterization of fo-bicategories.
Cite as

Filippo Bonchi, Alessandro Di Giorgio, and Davide Trotta. When Lawvere Meets Peirce: An Equational Presentation of Boolean Hyperdoctrines. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bonchi_et_al:LIPIcs.MFCS.2024.30,
  author =	{Bonchi, Filippo and Di Giorgio, Alessandro and Trotta, Davide},
  title =	{{When Lawvere Meets Peirce: An Equational Presentation of Boolean Hyperdoctrines}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{30:1--30:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.30},
  URN =		{urn:nbn:de:0030-drops-205867},
  doi =		{10.4230/LIPIcs.MFCS.2024.30},
  annote =	{Keywords: relational algebra, hyperdoctrines, cartesian bicategories, string diagrams}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2023.16
Weakly Markov Categories and Weakly Affine Monads

Authors: Tobias Fritz, Fabio Gadducci, Paolo Perrone, and Davide Trotta

Published in: LIPIcs, Volume 270, 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)

Abstract
Introduced in the 1990s in the context of the algebraic approach to graph rewriting, gs-monoidal categories are symmetric monoidal categories where each object is equipped with the structure of a commutative comonoid. They arise for example as Kleisli categories of commutative monads on cartesian categories, and as such they provide a general framework for effectful computation. Recently proposed in the context of categorical probability, Markov categories are gs-monoidal categories where the monoidal unit is also terminal, and they arise for example as Kleisli categories of commutative affine monads, where affine means that the monad preserves the monoidal unit. The aim of this paper is to study a new condition on the gs-monoidal structure, resulting in the concept of weakly Markov categories, which is intermediate between gs-monoidal categories and Markov ones. In a weakly Markov category, the morphisms to the monoidal unit are not necessarily unique, but form a group. As we show, these categories exhibit a rich theory of conditional independence for morphisms, generalising the known theory for Markov categories. We also introduce the corresponding notion for commutative monads, which we call weakly affine, and for which we give two equivalent characterisations. The paper argues that these monads are relevant to the study of categorical probability. A case at hand is the monad of finite non-zero measures, which is weakly affine but not affine. Such structures allow to investigate probability without normalisation within an elegant categorical framework.
Cite as

Tobias Fritz, Fabio Gadducci, Paolo Perrone, and Davide Trotta. Weakly Markov Categories and Weakly Affine Monads. In 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 270, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{fritz_et_al:LIPIcs.CALCO.2023.16,
  author =	{Fritz, Tobias and Gadducci, Fabio and Perrone, Paolo and Trotta, Davide},
  title =	{{Weakly Markov Categories and Weakly Affine Monads}},
  booktitle =	{10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)},
  pages =	{16:1--16:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-287-7},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{270},
  editor =	{Baldan, Paolo and de Paiva, Valeria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2023.16},
  URN =		{urn:nbn:de:0030-drops-188133},
  doi =		{10.4230/LIPIcs.CALCO.2023.16},
  annote =	{Keywords: String diagrams, gs-monoidal and Markov categories, categorical probability, affine monads}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2021.87
The Gödel Fibration

Authors: Davide Trotta, Matteo Spadetto, and Valeria de Paiva

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
We introduce the notion of a Gödel fibration, which is a fibration categorically embodying both the logical principles of traditional Skolemization (we can exchange the order of quantifiers paying the price of a functional) and the existence of a prenex normal form presentation for every logical formula. Building up from Hofstra’s earlier fibrational characterization of de Paiva’s categorical Dialectica construction, we show that a fibration is an instance of the Dialectica construction if and only if it is a Gödel fibration. This result establishes an intrinsic presentation of the Dialectica fibration, contributing to the understanding of the Dialectica construction itself and of its properties from a logical perspective.
Cite as

Davide Trotta, Matteo Spadetto, and Valeria de Paiva. The Gödel Fibration. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 87:1-87:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{trotta_et_al:LIPIcs.MFCS.2021.87,
  author =	{Trotta, Davide and Spadetto, Matteo and de Paiva, Valeria},
  title =	{{The G\"{o}del Fibration}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{87:1--87:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.87},
  URN =		{urn:nbn:de:0030-drops-145272},
  doi =		{10.4230/LIPIcs.MFCS.2021.87},
  annote =	{Keywords: Dialectica category, G\"{o}del fibration, Pseudo-monad}
}
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