Probabilistic Linear Logic Programming with an Application to Bayesian Network Computations (Extended Version)

TL;DR

This paper introduces probLO, a novel linear logic programming extension that embeds Bayesian network representations and computations, enabling internal probabilistic reasoning without external semantics.

Contribution

It presents probLO, integrating Bayesian networks into linear logic programming using multi-head methods and slicing, a novel approach for probabilistic reasoning.

Findings

Successfully embeds Bayesian networks within linear logic programming.

Enables internal probability computations without external semantics.

Supports complex network structures beyond trees.

Abstract

Bayesian networks are a canonical formalism for representing probabilistic dependencies, yet their integration within logic programming frameworks remains a nontrivial challenge, mainly due to the complex structure of these networks. In this paper, we propose probLO (probabilistic Linear Objects) an extension of Andreoli and Pareschi's LO language which embeds Bayesian network representation and computation within the framework of multiplicative-additive linear logic programming. The key novelty is the use of multi-head Prolog-like methods to reconstruct network structures, which are not necessarily trees, and the operation of slicing, standard in the literature of linear logic, enabling internal numerical probability computations without relying on external semantic interpretation.