8 papers
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…
Adequate Losses via Quantitative Linear Logic
Matteo Capucci, Robert Atkey, Charles Grellois +2
As neural components are increasingly embedded in existing symbolic software -- including safety-critical systems -- the question arises of how to specify and enforce the safety of…
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…
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-)…
Contextads as Wreaths; Kleisli, Para, and Span Constructions as Wreath Products
Matteo Capucci, David Jaz Myers
We introduce contextads and the Ctx construction, unifying various structures and constructions in category theory dealing with context and contextful arrows -- comonads and their…
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 Čech cohomology to capture the precise ways in which local solu…