# An Information–Theoretic Model of Abduction for Detecting Hallucinations in Explanations

## TL;DR

This paper introduces a new model that detects hallucinations in AI-generated explanations by combining information theory and abductive reasoning.

## Contribution

The novel contribution is a neuro-symbolic framework using entropy-based inference and abductive reasoning for hallucination detection.

## Key findings

- The model outperforms existing neural and symbolic methods in hallucination detection accuracy and interpretability.
- It successfully identifies hallucinations in GPT-5.1 outputs through abductive reasoning and information divergence.
- Discourse structure integration improves differentiation between valid and unsupported claims.

## Abstract

We present an Information–Theoretic Model of Abduction for Detecting Hallucinations in Generative Models, a neuro-symbolic framework that combines entropy-based inference with abductive reasoning to identify unsupported or contradictory content in large language model outputs. Our approach treats hallucination detection as a dual optimization problem: minimizing the information gain between source-conditioned and response-conditioned belief distributions, while simultaneously selecting the minimal abductive hypothesis capable of explaining discourse-salient claims. By incorporating discourse structure through RST-derived EDU weighting, the model distinguishes legitimate abductive elaborations from claims that cannot be justified under any computationally plausible hypothesis. Experimental evaluation across medical, factual QA, and multi-hop reasoning datasets demonstrates that the proposed method outperforms state-of-the-art neural and symbolic baselines in both accuracy and interpretability. Qualitative analysis further shows that the framework successfully exposes plausible-sounding but abductively unsupported model errors, including real hallucinations generated by GPT-5.1. Together, these results indicate that integrating Information–Theoretic divergence and abductive explanation provides a principled and effective foundation for robust hallucination detection in generative systems.