Research on Alessandro Bruni

Neurosymbolic AI

Mon, 01 Jan 0001 00:00:00 +0000

Overview

Neurosymbolic AI combines the pattern-recognition power of neural networks with the rigour of symbolic reasoning. My work in this area focuses on formally verifying correctness and robustness properties of neural networks and other machine learning systems using the Rocq proof assistant.

A central goal is to give machine learning systems the same level of trustworthiness that we expect from safety-critical software, by providing machine-checked proofs of their behaviour. This work builds on verified mathematical foundations, where formalized probability theory and concentration inequalities provide the rigorous basis for reasoning about learning algorithms.

Verified Math Foundations

Mon, 01 Jan 0001 00:00:00 +0000

Overview

Rigorous mathematics requires that theorems be provably correct. Proof assistants such as Rocq make this literal: every step of a proof is mechanically verified by a computer. I contribute to MathComp-Analysis, a large-scale formalization of mathematical analysis built on the Mathematical Components library.

My focus is on probability theory — building machine-checked foundations for the mathematics that underpins statistics, machine learning, and information theory.

Probability Theory and Lebesgue Integration

Classical probability theory rests on measure theory and the Lebesgue integral. Building on this infrastructure in MathComp-Analysis, I formalize probability theory in Rocq, including:

Proof Theory & Automation

Mon, 01 Jan 0001 00:00:00 +0000

Overview

Proof theory studies the structure of mathematical proofs themselves. My work in this area focuses on structural proof theory for substructural logics — particularly linear and intuitionistic logic — and on leveraging these insights to build better automation for interactive theorem provers.

Structural Proof Theory

Skolemization for intuitionistic linear logic. Classical Skolemization replaces existential quantifiers with function symbols, enabling efficient automated reasoning. Extending this to intuitionistic and linear settings requires care, because the structural rules that classical logic takes for granted are absent. I have developed Skolemization techniques for intuitionistic linear logic, opening the door to more efficient proof search in resource-sensitive logics.

Security Protocol Verification

Mon, 01 Jan 0001 00:00:00 +0000

Overview

Security protocols are the backbone of secure communication, but subtle design flaws can undermine their guarantees. My work applies formal methods — model checking, abstraction-based verification, and choreographic approaches — to prove that protocols meet their security goals.

Key Topics

Protocol analysis with AIF-ω. I co-developed AIF-ω, a tool for set-based abstraction of stateful security protocols with countable families of agents. AIF-ω has been applied to protocols in automotive (MaCAN) and IoT settings.