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Uncertainty Reasoning with Large Language Models for Explainable Disease Diagnosis

This paper proposes a neuro-symbolic framework that integrates Large Language Models with fuzzy logic and formal rules to enable explainable, verifiable, and human-aligned disease diagnosis by transforming unstructured clinical narratives into auditable reasoning chains.

Original authors: Xiaoyang Fan, Yufan Cai, Zhe Hou, Jin Song Dong

Published 2026-05-26

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Xiaoyang Fan, Yufan Cai, Zhe Hou, Jin Song Dong

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to solve a complex mystery, like figuring out why a car won't start. You have two very different tools to help you:

The Intuitive Detective (The LLM): This is a super-smart detective who has read every car manual and heard every story about broken cars. They can look at a messy, vague description like "it makes a weird clunking noise sometimes when it's cold" and instantly guess, "Ah, probably the starter motor!" They are great at understanding messy language and finding hidden clues. However, they sometimes make things up (hallucinate), can't always explain why they guessed that, and their confidence can be shaky.
The Strict Judge (The Symbolic Logic): This is a judge who follows a strict rulebook. If the rule says "If starter motor is broken AND battery is good, THEN car won't start," the judge follows it perfectly. They never make things up, and they can show you the exact page of the rulebook they used. But, they are terrible at understanding vague language. If you say "it makes a kind of clunking noise," the judge gets confused because their rules require exact, crisp facts.

The Problem:
Real-life medical diagnosis is like that car mystery, but with patients. Patients describe their symptoms in messy, vague ways ("I feel a little tired," "my chest feels tight like a belt"). Doctors need to combine the Detective's ability to understand this messy language with the Judge's ability to follow strict rules and explain their reasoning. Currently, AI systems usually pick one or the other, leaving them either too vague to trust or too rigid to understand.

The Solution: A "Neuro-Symbolic" Team-Up
This paper proposes a new system that teams up the Intuitive Detective and the Strict Judge to create a Medical Diagnosis Assistant. Here is how it works, step-by-step:

1. The Translation Phase (Detective to Judge)

First, the system uses the Large Language Model (the Detective) to read the patient's messy story.

The Magic: The Detective translates vague phrases like "tight belt around the chest" or "on-and-off pain" into structured, logical facts.
The Twist: Instead of turning these into simple "Yes/No" facts, the system turns them into Fuzzy Facts. Think of this as a dimmer switch rather than a light switch. Instead of saying "Pain = Yes," it says "Pain = 80% true." This captures the nuance of "mild" or "severe."

2. The Reasoning Phase (The Judge's Courtroom)

Once the messy story is translated into these fuzzy, weighted facts, they are passed to the Symbolic Logic engine (the Judge).

The Process: The Judge looks at a library of medical rules (e.g., "If chest pain + exertion + family history → check for Angina").
The Calculation: The Judge doesn't just say "Guilty" or "Not Guilty." They calculate a score based on how strong the evidence is. If the pain was "mild" (0.5 weight) but the family history is strong (1.0 weight), the system calculates a final probability score for the diagnosis.
The Output: It produces a ranked list of possible diseases (e.g., "Stable Angina: 72% likely," "Heart Attack: 10% likely").

3. The "Explainable" Superpower

This is the most important part. Because the system uses the Judge's strict rules, it can generate a step-by-step receipt for every decision.

Analogy: If a regular AI says, "You have a headache," it's like a magic 8-ball giving an answer. This system says, "You have a headache because: (1) You said your head hurts (80% confidence), (2) You mentioned stress (70% confidence), and (3) The rulebook says stress + headache = tension headache."
Audit Trail: If a doctor disagrees, they can look at the "receipt," see exactly which rule was triggered, and even tweak the weights (e.g., "Actually, the pain wasn't that severe, lower the score"). The system instantly recalculates the diagnosis based on that feedback.

4. The Learning Loop

The system isn't static. It has a "Neural-Symbolic Cycle":

Human Feedback: If a doctor corrects the system, the system updates its rule weights.
Data Learning: If the system sees that a specific symptom (like "sharp pain") keeps appearing with a specific disease in thousands of new cases, it automatically adjusts the rules to reflect that new pattern.

What the Paper Found (The Results)

The authors tested this "Team-Up" system against pure AI detectives (like GPT-4) and pure logic judges.

Accuracy: The hybrid system was just as good, and sometimes better, at getting the right diagnosis compared to the top AI models.
Trust: Unlike the pure AI models, this system could show its work. It provided clear reasons for its guesses.
Cost: Interestingly, while the system took a bit longer to run, it was significantly cheaper to use (less "token" usage) than asking a massive AI model to do the whole job alone.
Robustness: When the data was messy or vague, the system handled it well by using the "dimmer switch" (fuzzy logic) approach rather than getting stuck on exact matches.

In Summary:
This paper presents a way to build a medical AI that acts like a collaboration between a creative translator and a strict accountant. It uses AI to understand the messy human language of patients, converts it into a mathematically precise format, and then uses strict logic to diagnose the illness. The result is a system that is not only smart but also honest, transparent, and able to explain exactly how it reached its conclusion.

Technical Summary: Uncertainty Reasoning with Large Language Models for Explainable Disease Diagnosis

Problem Statement

Clinical decision-making frequently operates under conditions of uncertainty, where patient narratives are incomplete, temporally vague, and expressed through qualitative, graded terms (e.g., "mild fatigue" or "high fever") rather than crisp Boolean facts. While Large Language Models (LLMs) demonstrate strong capabilities in extracting latent information from natural language, they suffer from a lack of verifiability, interpretability, and reliable uncertainty calibration. Conversely, purely symbolic systems offer transparent rules and verifiable inference but often fail when faced with the ambiguity and noise inherent in real-world clinical descriptions. The core challenge addressed by this work is the development of a diagnostic system that combines the adaptability of LLMs with the rigor of formal logic to produce explainable, auditable, and trustworthy medical diagnoses.

Methodology

The authors propose a neuro-symbolic reasoning framework that aligns LLMs with formal logic through a three-module architecture:

1. Formal Knowledge Construction

This module bridges unstructured text and symbolic logic:

Neural Embedding & Rule Induction: Clinical corpora (notes, guidelines) are encoded using a domain-tuned LLM. The model is prompted to propose Horn clause templates ( $H \leftarrow B_1, \dots, B_n$ ) for symptom-disease pairs. Templates exceeding a confidence threshold are concretized into a symbolic rule set $R$ , which evolves dynamically.
Symbolic Decoding: LLMs transform embedded text segments into structured triples (entity, relation, value). These are mapped to fuzzy predicates with truth degrees $w \in [0, 1]$ , reflecting linguistic hedges (e.g., "mild" maps to a specific weight).
Prolog Synthesis: Triples and rules are compiled into a symbolic knowledge base using a template library, enabling the generation of fine-grained proof trees for every inferred hypothesis.

2. Neural-Symbolic Cycle

The framework supports a continuous learning loop involving both data and human feedback:

Physician-Driven Editing: Clinicians can inspect reasoning traces, add exception rules, adjust predicate weights, or supply counter-examples. These edits are versioned, creating a transparent audit trail.
Automated Rule Updating: The system employs a two-stage mechanism for data-driven refinement:
- Online Passive-Aggressive Ranking: Adjusts symptom weights when ground-truth diseases are mis-ranked relative to false positives.
- Structural Add/Prune: Periodically analyzes aggregated statistics (co-occurrence counts and specificity ratios) to add new symptom-disease edges or prune existing ones based on evidence thresholds.
Versioned Knowledge Base: Every update creates a time-stamped snapshot $K(t)$ , allowing for counterfactual audits to explain why a diagnosis changed between versions.

3. Real-time Diagnostic Engine

This module executes the diagnosis:

Preprocessing: Notes are segmented and temporal expressions are normalized.
Hybrid Symptom Weighting: Symptom weights are derived from a blend of retrieval priors (similarity to nearest neighbor cases in a FAISS index) and intrinsic salience (LLM-derived weights from text hedges). A softmax blend allows clinicians to adjust the reliance on text vs. retrieval evidence.
Fuzzy Prolog Reasoning: Weighted facts are asserted in SWI-Prolog (augmented with a fuzzy logic library). Rules fire if their t-norm activation exceeds a threshold.
Epidemiological Prior Fusion: Final probabilities are calculated by combining rule activation scores with prevalence data conditioned on patient demographics (age, sex, region).

Key Contributions

Hybrid Architecture: A unified pipeline connecting LLM extraction, fuzzy symptom representation, symbolic deduction, and probabilistic ranking.
Inspectable Update Mechanism: A system that allows physician feedback and localized case evidence to revise rule weights and structure while maintaining a versioned, auditable history of the knowledge base.
Empirical Validation: Evaluation on public clinical benchmarks demonstrating that the hybrid design improves robustness and explainability over symbolic ablations while remaining competitive with strong LLM baselines.

Experimental Results

The framework was evaluated on three datasets: gretelai/symptom-to-diagnosis (single-label), lavita/ChatDoctor-iCliniq (multi-label), and MIMIC-IV (multi-label).

Accuracy: On the single-label dataset, the full hybrid method achieved the highest Top-1 accuracy (44.8%), outperforming both pure LLM baselines (e.g., GPT-4o at 39.0%) and ablated symbolic models.
Multi-Label Performance: On the iCliniq dataset, the hybrid method (42.0% Top-1) slightly trailed GPT-4o (48.6%). The authors attribute this to data quality issues (unreliable labels, non-symptom text) and the inherent difficulty of highly ambiguous contexts where LLMs excel. However, on the trimmed iCliniq dataset and the MIMIC-IV dataset (which features clearer symptom signals), the hybrid system demonstrated superior or comparable performance, achieving 57.2% Top-1 accuracy on MIMIC-IV compared to GPT-4o's 53.3%.
Consistency & Explainability: The system demonstrated low error rates in symptom extraction (<1.3%) and high explainability scores (3.20–3.67/4.00), confirming that intermediate reasoning aligns with final conclusions.
Efficiency: While the hybrid system required more runtime (48.69 min vs. 26.61 min for GPT-4o on 1,000 samples), it was significantly more cost-efficient ($7.61 vs. $14.68) and used fewer tokens (2.87M vs. 5.75M).

Significance and Claims

The paper claims that by grounding neural extraction in explicit fuzzy and symbolic representations, the proposed framework offers a practical route toward diagnostic AI that can reason over ambiguous patient narratives while preserving traceability.

The authors emphasize that their system does not merely rank diagnoses by confidence but provides auditable inference paths and formally verifiable conclusions. Unlike purely statistical methods, the system supports iterative refinement where misalignments between LLM-generated diagnoses and ground truth can be traced, explained, and corrected through formal rules. The work positions itself as a step toward AI that is not only accurate but also interpretable, robust, and aligned with human reasoning, addressing the critical need for transparency in high-stakes clinical decision support.

The authors acknowledge limitations, including reliance on manually curated rules which may limit scalability to new domains, dependence on expert-crafted membership functions for fuzzy logic, and a current lack of explicit temporal modeling for symptom evolution.