Quantifiers for Differentiable Logics in Rocq (Extended Abstract)

Jairo Miguel Marulanda-Giraldo, Ekaterina Komendantskaya, Alessandro Bruni, Reynald Affeldt, Matteo Capucci, Enrico Marchioni

Keywords: Neural Network Verification, Formal Specifications, Loss Functions, Differentiable Logics, Interactive Theorem Proving

TL;DR: We explore how to formalize semantics for first-order differentiable logics using the Rocq proof assistant to ease their integration into AI verification backends.

Abstract: The interpretation of logical expressions into loss functions has given rise to so-called differentiable logics. They function as a bridge between formal logic and machine learning, offering a novel approach for property-driven training. The added expressiveness of these logics comes at the price of a more intricate semantics for first-order quantifiers. To ease their integration into machine-learning backends, we explore how to formalize semantics for first-order differentiable logics using the Mathematical Components library in the Rocq proof assistant. We seek to give rigorous semantics for quantifiers, verify their properties with respect to other logical connectives, as well as prove the soundness and completeness of the resulting logics.

Submission Number: 26