Valeria de Paiva

Mathematician working at the intersection of category theory, logic, and natural language. I build bridges between abstract mathematics and real-world systems—especially in semantics, knowledge representation, and AI. My work spans academia and industry, from foundational logic to conversational systems and large-scale language technologies.

Research

My research explores how mathematical structure—especially from category theory and logic—can illuminate language, computation, and knowledge systems. A central theme is what I call Network Mathematics: extracting and organizing the implicit structure of mathematics and scientific knowledge using computational tools. This involves:

• category-theoretic semantics
• logical systems and proof theory
• natural language understanding
• knowledge graphs and structured representations

I am particularly interested in how these ideas scale—from foundational theory to real-world AI systems.

Current Projects

Network Mathematics

A long-term project to extract the structure of mathematics from large corpora and represent it as interconnected knowledge graphs. This includes in particular, MathGloss Building structured mathematical glossaries from text using NLP, with links to resources such as Wikipedia, nLab, and formal libraries.

Categorical Semantics and AI

Applying logical and categorical tools to improve semantic parsing, reasoning, and explainability in modern AI systems.

Selected Work

I have authored 100+ publications in category theory, logic, and computational semantics.

Key themes include:

• Dialectica categories and categorical logic
• Linear logic, modal logics and their models
• Semantics of natural language
• Knowledge representation and reasoning systems

Publication list from Google Scholar

My thesis is available here.

Experience

I have worked across academia and industry, including roles at:

• Samsung Research
• Nuance Communications
• Xerox PARC

My work focuses on bringing deep theoretical ideas into practical systems, particularly in conversational AI and semantic technologies. I work at Topos Institute.

A bit more

I am interested in how ideas travel between disciplines—especially how logic and category theory can inform modern AI. I also enjoy building communities, connecting researchers, and developing new research directions across fields.

I am deeply committed to supporting women in logic and computer science. I co-founded and help maintain the Women in Logic website, Women in Logic blog, and Facebook group, as well as a curated collection of Women in Logic talks. I serve on the steering committee for Women in Logic and help organize the Workshop on Women in Logic, which just had its ninth edition in Birmingham, UK. I also contribute to the ACM-W Scholarship Program, which supports women students in computing worldwide.

Events

A complete events list will be added in due course. In the meantime, you can find highlights of projects, talks, and workshops I am or have been involved in, recently.