From the 1 of 7 linked papers with an AI index.
7 papers
Adequate Losses via Quantitative Linear Logic
Matteo Capucci, Robert Atkey, Charles Grellois +2
The paper proposes a family of quantitative linear logics (pQLL) that combine logical specifications with differentiable loss functions for neural components, proving cut‑eliminati…
Quantitative Linear Logic for Neuro-Symbolic Learning and Verification
Thomas Flinkow, Ekaterina Komendantskaya, Matteo Capucci +1
Differentiable Logics are deployed in neuro-symbolic learning tasks as a way of embedding logical constraints in the training objective of neural networks. A differentiable logic c…
Classifying strict discrete opfibrations with lax morphisms
Matteo Capucci, David Jaz Myers
We study discrete opfibration classifiers in enhanced 2-categories and show how, under suitable hypotheses, such classifiers can be endowed with the structure of a (lax or pseudo-)…
Compositionality of Lyapunov functions via assume-guarantee reasoning
Matteo Capucci, David Jaz Myers
Assume-guarantee reasoning is a technique for compositional model checking in which system specifications are checked under certain assumptions on system parameters or inputs, and…
On Quantifiers for Quantitative Reasoning
Matteo Capucci
We explore a kind of first-order predicate logic with intended semantics in the reals. Compared to other approaches in the literature, we work predominantly in the multiplicative r…
Algorithmic and Extremal Obstructions Through the Language of Cohomology
Anny Beatriz Azevedo, Benjamin Merlin Bumpus, Matteo Capucci +2
We model problems as presheaves that assign sets of certificates to input instances, and we show how to use presheaf Äech cohomology to capture the precise ways in which local sol…