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.

翻译：本文研究贝叶斯网络与线性逻辑证明的图形表示之间的对应关系。本论文的目标有三：以证明论视角阐释贝叶斯推理（遵循证明与程序间的Curry-Howard对应思想），提供组合式图形化方法，并兼顾计算效率。我们利用以下事实：图的分解比证明树或类型推导的分解更具灵活性，尽管组合性因此面临更大挑战。