Greta Coraglia

I am a mathematician specializing in category theory, type theory, and theoretical computer science, with a strong drive to apply foundational ideas to real-world AI systems. My interest sits at the intersection of categorical and probabilistic reasoning: I am passionate about working out how compositionality can guide inference, enabling systems that are both expressive and transparent.

I co-founded MIRAI with industry experts, driven by the conviction that AI compliance should be built on transparency and fairness, not just on ticking boxes. At MIRAI I lead end-to-end R&D across several projects, combining applied research with hands-on development to turn ideas into concrete, working solutions.

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What I work on

My work sits at the bridge between research and engineering, ensuring theoretical insights become tested, maintainable, and explainable solutions aligned with regulatory requirements.

ML fairness & classification. In-depth assessments of classification algorithms, analysing performance, robustness, and fairness metrics to inform model selection and deployment decisions.

Generative AI & RAG. Designed and evaluated Retrieval-Augmented Generation pipelines, focusing on retrieval quality, answer faithfulness, and end-to-end system performance. Research findings translated directly into architectural and implementation improvements.

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Talks & Dissemination

A few of my tries at making math and AI for everyone.

• Dalle macchine alle persone: viaggio nel mondo dell’intelligenza artificiale (j/w I. Masnari, D. Posillipo), 2024 (video — Lecco, Segrate)
• Dati sì, ma dati da chi?, Museo Nazionale S&T Leonardo da Vinci, Open night, September 2024
• An open source tool to detect bias in your predictive algorithm (using logic!): BRIOxAlkemy (about, git repo, my slides at AIxIA 2023)
• Matematica da costruire, Archimede, December 2023
• Dissemination corner in The Reasoner, BRIO: From topology to a logic of uncertainty, November 2023 (here)
• Guest post, Identity types in context (j/w Shreya Arya), on the n-Category Café, July 2022 (here)
• Seminario permanente, Un numero finito di idee sulla definizione di infinito, ZEST!, 2020 (recording)

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Publications

AI, fairness & logic

• Semantics for trust in probabilistic and opaque systems (j/w Francesco A. Genco and Giuseppe Primiero), in progress

• Evaluating AI fairness in credit scoring with the BRIO tool (j/w Genco, Piantadosi, Bagli, Giuffrida, Posillipo, Primiero), arXiv:2406.03292, May 2024

• A bias detecting tool (j/w D’Asaro, Genco, Giannuzzi, Posillipo, Primiero, Quaggio), Proceedings of the 2nd Workshop on Bias, Ethical AI, Explainability and the role of Logic and Logic Programming, published v., January 2024

Category theory & type theory

• Fibrations of algebras (j/w Davide Castelnovo, Fosco Loregian, Ülo Reimaa), submitted for publication, arXiv:2408.16581
  • recording of a talk Fosco gave at the beginning of the project
  • my talk at HoTTEST, 14 March 2024 (slides, recording)
• A 2-dimensional analysis of context comprehension (j/w Jacopo Emmenegger), TAC, published v., October 2024
  • HoTT/UF Workshop, A 2-dimensional analysis of comprehension, 22 April 2023 (slides)
  • ItaCa Fest, Comonads for dependent types, online, 19 May 2022 (slides, recording)
• Categorical models of subtyping (j/w Jacopo Emmenegger), LIPIcs Proceedings of TYPES 2023, published v., December 2023
  • TYPES 2023, Categorical models of subtyping, 15 June 2023 (recording)
• Fuzzy type theory for opinion dynamics (Adjoint School project tutored by Paige North), ongoing
  • ItaCa Workshop, A fuzzy theory of types, Pisa, 21 December 2022 (slides)
• Context, judgement, deduction (j/w Ivan Di Liberti), arXiv:2111.09438, November 2021
  • TallCat, Coding deductive systems into a 2-category, Tallinn, 5 May 2022 — courtesy of the CSM group
  • Logic and higher structures, A 2-categorical representation of deduction, CIRM Marseille, 21 February 2022 (slides)
  • ItaCa Workshop, Context, judgement, deduction, Genova, 20 December 2021 (recording)
• A categorical perspective on Heyting-valued sets, Master’s thesis, awarded AILA’s Best Thesis in Logic prize, July 2019

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Background

Previously a postdoc with LUCI Lab at the University of Milan, on the BRIO project, and a member of the Scientific Committee of the ItaCa community. PhD from the Mathematics Department at the University of Genova, under the supervision of Pino Rosolini with the logic group.