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NeurOWL: An LLM-Based Neural-symbolic Framework for Incomplete OWL Ontology Reasoning

The paper introduces NeurOWL, an end-to-end neuro-symbolic framework that leverages Large Language Models and ontology embeddings to verify the semantic plausibility of subsumption in incomplete OWL ontologies and generate logically sound explanations with potential missing axioms.

Original authors: Hui Yang, Jiaoyan Chen, Yiping Song, Renate Schmidt, Wen Zhang

Published 2026-07-20

📖 7 min read🧠 Deep dive

CC BY 4.0

Original authors: Hui Yang, Jiaoyan Chen, Yiping Song, Renate Schmidt, Wen Zhang

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 massive, intergalactic mystery, but your clue book is missing several pages. You have a list of rules about how different characters relate to each other—like "All cats are mammals" or "All mammals produce milk"—but the book doesn't explicitly say "All Persian cats are animals." In the world of computer science, this is called an ontology. Think of an ontology as a super-organized, digital encyclopedia that teaches a computer how to understand the world. It uses a strict language called OWL (Web Ontology Language) to define rules so that machines can reason, or "think," about how things fit together.

However, real-world encyclopedias are rarely perfect. They are often incomplete because the world is too big to write down every single rule, or because experts haven't had time to finish the job. When a computer tries to use these "broken" encyclopedias, it gets stuck. It can't prove that a Persian cat is an animal because the specific rule connecting them is missing. This is a huge problem for fields like healthcare and biology, where missing a connection could mean missing a cure or a diagnosis. Scientists have tried to fix this by asking computers to guess the missing rules, but usually, they need a pre-written list of possible guesses, which is like trying to find a needle in a haystack when you're only allowed to look in a tiny, pre-defined box.

Enter NeurOWL, a new framework that acts like a detective with a superpower. Instead of being stuck with a tiny box of guesses, NeurOWL combines the strict logic of a computer with the creative intuition of a Large Language Model (an AI that reads and understands human text). It doesn't just check if a rule is true; it tries to figure out why it might be true even if the rulebook is missing a page, and then it writes down the missing page for you. It's like having a detective who can look at a crime scene, realize a witness is missing, and then use their knowledge of the neighborhood to guess exactly who that witness might be, all while making sure their guess makes logical sense.

The Detective's Toolkit: How NeurOWL Works

The paper introduces NeurOWL as a "neuro-symbolic" framework. That's a fancy way of saying it mixes two types of thinking: symbolic (the strict, mathematical logic of the computer) and neural (the fuzzy, pattern-matching intuition of the AI). The goal is simple: given a broken rulebook and a question like "Is a Persian Cat an Animal?", NeurOWL decides if the answer is likely "Yes" or "No," and if it's "Yes," it finds the missing pieces of the puzzle to explain why.

Here is how the detective solves the case, step-by-step:

Step 1: The Logic Check (The "Obvious" Test)
First, NeurOWL asks the strict computer logic: "Can I prove this using only the rules we have right now?" If the answer is yes, great! It gives you the proof. But if the answer is no (because the rulebook is incomplete), it doesn't give up. It assumes some rules are missing and moves to the next step.

Step 2: The Logical Bridge (The "Connect the Dots" Phase)
This is where the detective gets clever. If the path from "Persian Cat" to "Animal" is broken, NeurOWL looks for a "bridge" concept that could connect them.

Downward Search: It looks at the "children" of the target. If "Animal" has children like "Mammal" and "Cat," maybe the missing rule is "Persian Cat is a Cat"?
Upward Search: It looks at the "parents" of the starting point. If "Persian Cat" is a type of "Pet Cat," maybe the missing rule is "Pet Cat is a Cat"?
The system uses the computer's logic to find these potential bridges, but then it calls in the LLM (the AI detective) to verify them. The AI reads the names and descriptions and says, "Yes, that makes sense! A Pet Cat is definitely a Cat."

Step 3: The Semantic Bridge (The "Gut Feeling" Phase)
If the logical search fails, NeurOWL switches to pure intuition. It uses embeddings, which are like digital fingerprints for words. It asks the AI: "Is there any concept in the entire encyclopedia that feels like it sits between 'Persian Cat' and 'Animal'?" The AI scans its vast knowledge of language and suggests a candidate. If it finds one, it checks if the connection holds. If not, it might just guess that the rule "Persian Cat is an Animal" is missing entirely and needs to be added directly.

What They Found: A Detective's Success Story

The researchers tested NeurOWL on real-world data from two massive encyclopedias: FoodOn (about food and agriculture) and Snomed CT (a huge medical database). They created "broken" versions of these encyclopedias by randomly deleting 5% of the rules, just to see if NeurOWL could fix them.

The results were impressive. When asked to guess if a missing rule was plausible, NeurOWL got it right about 97% of the time on the FoodOn dataset and 96.8% on the Snomed CT dataset. But the real magic was in the explanations. Unlike other methods that just say "Yes" or "No," NeurOWL actually wrote down the missing rules.

On the FoodOn dataset, it correctly identified the missing rules and explained them with a score of 89.3 (called X-F1).
On the medical dataset, it achieved a score of 84.7.

The paper also showed that NeurOWL is flexible. It can work without any extra training (using a pre-trained AI) or it can be "fine-tuned" (given a crash course on the specific encyclopedia) to get even better at complex medical terms. In fact, for the trickiest medical cases involving complex relationships, the fine-tuned version performed significantly better, proving that giving the detective a specialized training manual helps.

What NeurOWL Is Not (And What It Rules Out)

It is important to know what NeurOWL doesn't do. The paper explicitly rules out the idea that you need a pre-defined list of possible missing rules to solve the problem. Old methods required scientists to say, "Here are the 100 rules you can guess from." NeurOWL throws that rulebook away and says, "I'll look at the whole world and guess whatever fits."

The authors also clarify that they are not claiming to have "solved" ontology reasoning forever. They are not saying the computer is now smarter than a human expert. Instead, they suggest that this method is a powerful tool to assist experts. The system is designed to handle cases where the target rule might actually be wrong, too. If the AI thinks "Persian Cats are Rocks," it will say "No" and stop, rather than forcing a bad explanation.

The confidence in these results comes from rigorous testing on thousands of examples. The numbers aren't guesses; they are measured outcomes from running the system on real data. However, the paper notes that in extremely complex scenarios (like guessing rules involving very specific medical restrictions), the system's performance drops a bit, suggesting there is still room for improvement.

The Bottom Line

NeurOWL is like a detective that doesn't just solve the mystery but also writes the missing chapter of the story. By combining the strict logic of computers with the creative intuition of AI, it can look at a broken encyclopedia, figure out what's missing, and explain why it's missing. It doesn't need a cheat sheet of possible answers; it just uses its knowledge of the world to fill in the gaps. For anyone working with complex data, from doctors to food scientists, this means we might soon have AI assistants that can not only answer questions but also help us fix the books we use to ask them in the first place.

Technical Summary: NeurOWL

Problem Statement

OWL ontologies serve as a formal framework for structured knowledge representation and automated reasoning, widely used in domains like healthcare and bioinformatics. However, real-world ontologies are frequently incomplete due to evolving domain knowledge and the high cost of expert curation. This incompleteness leads to a specific reasoning challenge: given an incomplete ontology $O'$ and a candidate subsumption $\alpha$ (e.g., $A \sqsubseteq B$ ) that is not logically entailed by $O'$ , the system must determine:

Plausibility: Is the subsumption semantically plausible (i.e., would it hold if the ontology were complete)?
Abduction: If plausible, what are the missing axioms (hypotheses) that, when added to $O'$ , would entail $\alpha$ ?

Existing abductive reasoning approaches suffer from two main limitations: they typically rely on a predefined hypothesis space (restricting candidates to a fixed vocabulary) and often assume the target subsumption is valid, failing to handle cases where the subsumption itself is incorrect. Furthermore, while Large Language Models (LLMs) have been applied to ontology tasks, they generally lack the ability to provide logically sound explanations or integrate formal semantics effectively.

Methodology: The NeurOWL Framework

To address these challenges, the authors propose NeurOWL, an end-to-end neuro-symbolic framework that unifies subsumption verification and ontology abduction. The framework leverages both formally defined semantics (via ontology embeddings) and textual semantics (via LLMs) to operate without a predefined candidate set of missing axioms.

The core mechanism involves identifying intermediate concepts (bridges) that connect the subject ( $A$ ) and object ( $B$ ) of the subsumption, or verifying the subsumption directly. The process is structured into three sequential stages:

1. Logical Checking (Stage 1)

A standard Description Logic (DL) reasoner checks if $O' \models A \sqsubseteq B$ .

If true: The system returns True with a justification (minimal set of axioms from $O'$ ).
If false: The system assumes missing axioms exist and proceeds to subsequent stages.

2. Logical Bridging (Stage 2)

This stage attempts to find missing axioms by exploiting the existing logical structure of $O'$ . It uses an ontology embedding model (e.g., OnT) to retrieve top- $k$ candidates, which are then validated by an LLM.

2a (Downward): Identifies child concepts $B'$ of $B$ in $O'$ ( $O' \models B' \sqsubseteq B$ ). The system hypothesizes a missing axiom $A \sqsubseteq B'$ .
2b (Upward): Identifies parent concepts $A'$ of $A$ in $O'$ ( $O' \models A \sqsubseteq A'$ ). The system hypothesizes a missing axiom $A' \sqsubseteq B$ .
Verification: An LLM validates the plausibility of the candidate missing axiom. If valid, the justification is constructed as $\{A \sqsubseteq B'\} \cup J_{B' \sqsubseteq B}$ (or the symmetric case).

3. Bridging by Embedding (Stage 3)

If Stage 2 fails, the system searches for missing axioms based purely on semantic similarity.

3a (Bidirectional Search): Searches for an intermediate concept $C$ such that $A \sqsubseteq C \sqsubseteq B$ . Candidates are drawn from atomic concepts (or complex concepts like $\exists r.B_1$ in specific settings) and ranked by a scoring function $s(C) = \frac{1}{2}(s(A \sqsubseteq C) + s(C \sqsubseteq B))$ . The top candidates are verified by the LLM.
3b (Direct Check): If no suitable bridge is found, the system treats $A \sqsubseteq B$ as an elementary assertion. The LLM directly verifies the plausibility of the subsumption itself. If deemed correct, it is returned as the missing axiom; otherwise, the system returns False.

Implementation Details:

Embeddings: The framework utilizes OnT (fine-tuned on the target ontology) or SBERT (pre-trained) to encode concepts and roles.
LLM: The Qwen3.5-9B model is used for prompt-based verification of candidate axioms and bridges.
Iterative Capability: The framework can be applied iteratively, using predicted missing axioms as new inputs to refine the reasoning chain.

Key Contributions

Generalized TBox Abduction Task: The authors define a task that does not require a predefined candidate set of missing axioms and explicitly handles cases where the given subsumption is incorrect (negative entailment).
NeurOWL Framework: An end-to-end neuro-symbolic system that jointly performs verification and abduction, integrating ontology embeddings and LLMs to operate in both training-free and fine-tuned settings.
Empirical Evaluation: Comprehensive evaluation on real-world ontologies (FoodOn and Snomed CT) demonstrating effectiveness across varying degrees of incompleteness and complexity (atomic vs. existential restriction concepts).

Experimental Results

The authors evaluated NeurOWL on datasets constructed from FoodOn and Snomed CT, simulating incompleteness by removing 5% of TBox axioms. The evaluation included both "Standard" settings (atomic concepts as bridges) and "Complex" settings (existential restrictions $\exists r.B$ as bridges).

Key Findings:

Performance: NeurOWL consistently outperformed baselines (LLM-only, SBERT, and OnT classifiers) in terms of F1-score.
- On FoodOnA, NeurOWL (OnT) achieved an F1 of 0.960 (Hard Neg: 0.845).
- On SnomedA, NeurOWL (OnT) achieved an F1 of 0.968 (Hard Neg: 0.862).
- On Snomed $\exists$ (complex concepts), NeurOWL (OnT) achieved an F1 of 0.924, significantly outperforming the SBERT variant (0.906) and demonstrating the necessity of fine-tuning for complex logical structures.
Explanation Quality: The framework achieved high X-F1 (correct prediction + correct explanation) and X-F1* (all predicted bridges correct) scores.
- On FoodOnA, NeurOWL (OnT) reached X-F1: 0.893 and X-F1: 0.793*.
- The fine-tuned OnT variant significantly outperformed the training-free SBERT variant in explanation accuracy, particularly in complex settings.
Stage Analysis: Stages 2a and 2b (Logical Bridging) yielded the highest retrieval performance (H@1 > 0.9 for Stage 2b on SnomedA). Stage 3a (Bidirectional) had lower retrieval performance due to the larger candidate space but remained crucial for cases where logical bridges were absent.
Iterative Application: Case studies demonstrated that iterative application of NeurOWL could generate progressively finer-grained chains of missing axioms (e.g., refining a subsumption from a broad disorder to a specific malignant tumor).

Significance and Claims

The paper claims that NeurOWL represents a significant step forward by unifying subsumption verification with ontology abduction in a single framework. Its primary significance lies in:

Removing the Predefined Hypothesis Constraint: Unlike prior work, NeurOWL does not rely on a fixed vocabulary or signature, allowing it to discover missing axioms involving any concept in the ontology.
Handling Uncertainty: It explicitly addresses the scenario where the validity of the target subsumption is uncertain, distinguishing between "plausible but missing" and "incorrect" subsumptions.
Explainability: It provides not just a binary decision but a logically sound explanation containing the specific missing axioms and the justification chain, bridging the gap between neural semantic understanding and symbolic logical reasoning.

The authors conclude that while the current work focuses on EL ontologies and existential restrictions, the framework is adaptable and sets a foundation for future extensions to more complex logical operators (e.g., $\forall$ , $\neg$ ) and iterative reasoning capabilities.