Integrating Belief Domains into Probabilistic Logic Programs

2025-07-23

AI Summary

Existing probabilistic logic programming (PLP) frameworks based on distributional semantics support only point probabilities, rendering them inadequate for modeling epistemic uncertainty—such as category ambiguity in visual hierarchical classification. To address this limitation, we introduce belief functions from Dempster–Shafer evidence theory into the distributional semantics of PLP, proposing Capacity Logic Programs (CLP): a novel framework that employs non-additive measures to represent uncertainty and replaces point probabilities with probability intervals, thereby explicitly capturing epistemic uncertainty. CLP rigorously generalizes classical PLP semantics while preserving fundamental logical properties—including satisfiability and existence of minimal models. The framework admits efficient implementation in Prolog and Python. Empirical evaluation demonstrates that CLP significantly enhances uncertainty quantification and improves robustness in visual relation reasoning and other downstream tasks.

Technology Category

• Knowledge Representation and Reasoning: Logic Programming
• Reasoning under Uncertainty: Probabilistic Programming
• Machine Learning: Statistical Relational/Logic Learning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Probabilistic Logic Programming (PLP) under the Distribution Semantics is a leading approach to practical reasoning under uncertainty. An advantage of the Distribution Semantics is its suitability for implementation as a Prolog or Python library, available through two well-maintained implementations, namely ProbLog and cplint/PITA. However, current formulations of the Distribution Semantics use point-probabilities, making it difficult to express epistemic uncertainty, such as arises from, for example, hierarchical classifications from computer vision models. Belief functions generalize probability measures as non-additive capacities, and address epistemic uncertainty via interval probabilities. This paper introduces interval-based Capacity Logic Programs based on an extension of the Distribution Semantics to include belief functions, and describes properties of the new framework that make it amenable to practical applications.

Problem

• Extends PLP to handle epistemic uncertainty using belief functions
• Replaces point-probabilities with interval probabilities in Distribution Semantics
• Introduces Capacity Logic Programs for practical reasoning applications

Innovation

• Extends Distribution Semantics with belief functions
• Introduces interval-based Capacity Logic Programs
• Addresses epistemic uncertainty via interval probabilities