Probabilistic Linear Logic Programming with an application to Bayesian Networks computations

2026-01-19

AI Summary

This work proposes probLO, an extension of Linear Objects (LO) logic programming, to efficiently handle the complex dependency structures of Bayesian networks within a logical framework. By innovatively integrating multi-headed Prolog-style rules with the slicing operator from linear logic, probLO enables, for the first time, an embedded representation of non-tree-structured Bayesian networks and supports probabilistic inference without relying on external semantics. Leveraging a multiplicative-additive linear logic mechanism, probLO natively encodes Bayesian networks directly in the logic, significantly enhancing both model integration capabilities and the efficiency of probabilistic computation.

Technology Category

• Knowledge Representation and Reasoning: Logic Programming
• Reasoning under Uncertainty: Probabilistic Programming
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Bayesian Networks
• Logic Programming
• Probabilistic Reasoning
• Linear Logic
• Probabilistic Integration

Innovation

• probabilistic linear logic programming
• Bayesian networks
• multi-head rules
• slicing
• logic programming