Beyond Semantic Equivalence: Logical Graphs for LLM Uncertainty Quantification

2026-07-18

AI Summary

This work addresses the tendency of large language models (LLMs) to produce confident yet unreliable responses, a challenge exacerbated by existing uncertainty quantification methods that overlook logical relationships among candidate answers. Such approaches often overestimate uncertainty when answers exhibit semantic diversity but logical consistency. To remedy this, the paper introduces the Logical Graph Uncertainty (LGU) framework, which explicitly incorporates logical entailment and incompatibility into LLM uncertainty estimation for the first time. LGU constructs a logical graph, aggregates probability mass along entailment chains, computes entropy over logically maximal hypotheses, and integrates an incompatibility-based penalty mechanism. Empirical results demonstrate that LGU significantly outperforms current methods, achieving gains of up to 7.1% in AUROC and 3.5% in AUARC over semantic entropy baselines across multiple question-answering benchmarks.

Abstract

Large Language Models (LLMs) often produce confidently stated yet unreliable outputs, posing critical challenges for deployment in safety-sensitive applications. Existing uncertainty metrics such as semantic entropy capture agreement at the level of semantic equivalence, but largely ignore the logical relationships between distinct answers. As a result, they tend to overestimate uncertainty and falsely flag hallucinations in settings where generated responses are diverse in form yet logically compatible (e.g., differing only in granularity or specificity). We propose Logical Graph Uncertainty (LGU), a framework that explicitly models implication and incompatibility among answers. LGU aggregates probability mass along entailment chains, computes entropy over logically maximal hypotheses, and penalizes mutual incompatibility among them. Across multiple question-answering benchmarks, LGU consistently improves uncertainty estimation over existing methods, and outperforms the semantic entropy baseline by up to +7.1% AUROC and +3.5% AUARC across datasets.

Problem

• uncertainty quantification
• large language models
• logical relationships
• semantic equivalence
• hallucination

Innovation

• Logical Graph Uncertainty
• uncertainty quantification
• logical entailment
• semantic entropy
• large language models