Bayesian Networks and Proof-Nets: the proof-theory of Bayesian Inference
Logic in Computer Science
2026-02-05 v1
Abstract
We study the correspondence between Bayesian Networks and graphical representation of proofs in linear logic. The goal of this paper is threefold: to develop a proof-theoretical account of Bayesian inference (in the spirit of the Curry-Howard correspondence between proofs and programs), to provide compositional graphical methods, and to take into account computational efficiency. We exploit the fact that the decomposition of a graph is more flexible than that of a proof-tree, or of a type-derivation, even if compositionality becomes more challenging.
Cite
@article{arxiv.2602.04045,
title = {Bayesian Networks and Proof-Nets: the proof-theory of Bayesian Inference},
author = {Rémi Di Guardia and Thomas Ehrhard and Jérôme Evrard and Claudia Faggian},
journal= {arXiv preprint arXiv:2602.04045},
year = {2026}
}