Bayesian Networks and Proof-Nets: a proof-theoretical account of Bayesian Inference

TL;DR

This paper establishes a proof-theoretical framework linking Bayesian Networks with Linear Logic Proof-Nets, providing a novel perspective on Bayesian inference through logical proof structures.

Contribution

It introduces a correspondence between Bayesian Networks and Proof-Nets, offering a new proof-theoretical approach to Bayesian inference.

Findings

Demonstrates a strong correspondence between Bayesian Networks and Proof-Nets.

Provides a proof-theoretical account of Bayesian inference.

Bridges probabilistic models with logical proof structures.

Abstract

We uncover a strong correspondence between Bayesian Networks and (Multiplicative) Linear Logic Proof-Nets, relating the two as a representation of a joint probability distribution and at the level of computation, so yielding a proof-theoretical account of Bayesian Inference.