Integrating Belief Domains into Probabilistic Logic Programs

TL;DR

This paper extends Probabilistic Logic Programming under the Distribution Semantics by incorporating belief functions, enabling representation of epistemic uncertainty with interval probabilities, thus broadening practical reasoning capabilities.

Contribution

It introduces interval-based Capacity Logic Programs that extend existing semantics to include belief functions for better modeling of epistemic uncertainty.

Findings

Framework supports practical applications of belief functions

Extension allows modeling of hierarchical and epistemic uncertainties

Properties of the new logic enable implementation in existing systems

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.