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

The gist The NeurOWL framework is an end-to-end neuro-symbolic system designed to verify and abduce missing axioms in incomplete OWL ontologies by integrating LLMs with ontology embeddings, which addresses the challenge of plausibility reasoning without requiring predefined hypothesis candidates.

Problem and Motivation

Ontologies expressed in the Web Ontology Language (OWL) provide a formal framework for representing structured knowledge and enable automated reasoning through Description Logics (DL) Owing to their precise and shareable representation of machine-interpretable semantics, OWL ontologies are widely used in knowledge-intensive domains such as biomedicine (Ashburner et al. 2000) and healthcare (Bos and Donnelly 2006). A fundamental reasoning task in ontology engineering is subsumption reasoning: determining whether a subsumption relationship holds between two concepts and providing explanations for such entailments For complete and consistent ontologies, subsumption can be determined by standard reasoners (Glimm et al. 2014; Kazakov, Krötzsch, and Simancik 2012), and explanations can be derived as justifications (i.e., minimal sets of axioms sufficient for the entailment). In practice, however, real-world ontologies are often incomplete due to different reasons like evolving domain knowledge and the high cost of expert curation. As a result, some valid subsumptions may not be entailed because some required axioms are missing. Abductive reasoning has been proposed as a natural solution to this problem (Du, Wan, and Ma 2017; Haifani et al. 2022; Wei-Kleiner, Dragisic, and Lambrix 2014; Del-Pinto and Schmidt 2019; Du et al. 2012; Du, Wang, and Shen 2014; Halland and Britz 2012; Klarman, Endriss, and Schlobach 2011; Koopmann 2021; Pukancová and Homola 2020; Elsenbroich, Kutz, and Sattler 2006; Koopmann et al. 2020; Bienvenu 2008; Haak et al. 2025). In this work, we concentrate on TBox abduction that aims to find a set of hypotheses (missing axioms) H such that, when added to an incomplete ontology O′, the target subsumption α becomes entailed (i.e., O′ ∪ H = α). Despite their promise, existing approaches exhibit several limitations: (1) they typically rely on a predefined hypothesis space, restricting candidate axioms to a fixed vocabulary (Haifani et al. 2022; Koopmann et al. 2020); (2) they often assume that the target subsumption is valid, preventing their applicability in more general settings where the validity of α is itself uncertain. Recently, there has been growing interest in using large language models (LLMs) for related ontology reasoning and construction tasks such as subsumption prediction and concept placement (He et al. 2023; Chen et al. 2023; He et al. 2024; Yang et al. 2025; Shi et al. 2024; Babaei Giglou, D’Souza, and Auer 2023; Zhang et al. 2025; Lo et al. 2024; Sun et al. 2024); however, these works generally lack explanatory capabilities.

NeurOWL Framework

NeurOWL is proposed as an end-to-end neuro-symbolic framework for explainable subsumption reasoning over incomplete OWL ontologies. It supports both positive and negative entailment scenarios and does not require a predefined hypothesis space. Instead, it automatically identifies meaningful missing components that are both compatible with the existing information and plausible in real-world contexts, by integrating textual information with formal semantics through LLMs and ontology embeddings. NeurOWL operates in both training-free and finetuned settings, making it adaptable across domains. Moreover, by iteratively applying NeurOWL, we can recover any subset- and entailment-minimal solutions as a set of missing axioms (see Theorem 1 and the case studies).

Core Idea and Structure

The core idea of NeurOWL is to uncover missing knowledge by identifying intermediate concepts that connect related noarXiv:2607.15776v2 [cs.AI] Consider a simple example (see Example 2 for the full version) with the ontology O′1:

O′1:

PersianCat ⊑ PetCat, Cat ⊑ Mammal, Mammal ⊑ Animal ⊓ ∃produces.Milk.

Intuitively, one expects the subsumption PersianCat ⊑ Animal to hold, but it cannot be derived from O′1 due to incompleteness. To address this, NeurOWL searches for intermediate concepts C such that PersianCat ⊑ C ⊑ Animal, which can be used to construct missing axioms and explanations. Candidate intermediate concepts are identified using ontology embeddings (Yang et al. 2025) and LLMs, which capture semantic similarity and verify likely missing connections. If no suitable intermediate concept is found, NeurOWL treats the target subsumption as a simple, indivisible axiom, proposes it directly, and validates it using an LLM (Stage 3b in Figure 1).

The overall NeurOWL framework is illustrated in Figure 1. It integrates logical structure with neural verification to predict missing axioms and consists of three stages:

** Stage 1. Logical Checking: Determine whether the input query can be logically entailed by O′ using a standard ontology reasoner. If so, the system returns True with a justification derived from O′.**

** Stage 2. Logical Bridging: Identify potentially missing axioms using candidate concepts induced by the logical structure of O′, combined with LLM-based validation.**

** Stage 3. Bridging by Embedding: Generate candidates directly based on semantic similarity using embeddings when the previous stages fail.**

In Stage 2, there are two cases:

1. Stage 2a: Downward. Consider each child B′ of B in O′ (i.e., O′ = B′ ⊑ B) as candidate for a bridge concepts. Then, A ⊑ B′ is treated as a candidate missing axiom and will be verified by the LLM.

2. Stage 2b: Upward. Consider each parent A′ of A in O′ (i.e., O′ = A ⊑ A′) as candidate, and use the LLM to validate the corresponding potential missing axiom A′ ⊑ B.

In Stage 3, there are two sub-cases:

** Stage 3a (bidirectional search): We first perform a bidirectional search for an intermediate concept C such that A ⊑ C ⊑ B, where C is, by default, drawn from all atomic concepts in O′ (excluding A and B), but can be customized based on user interest. We then select the top-k candidates and verify them using the LLM. Each candidate is ranked by the scoring function s(C) = 1/2 s(A ⊑ C) + s(C ⊑ B), where s(A ⊑ C) denotes the plausibility score of the axiom A ⊑ C produced by the embedding model. If a valid C is identified, the system returns True with the justification A ⊑ C, B. Otherwise, the subsumption A ⊑ B is treated as an elementary assertion and as a potential missing axiom itself.**

** Stage 3b (Direct check): Then, NeurOWL uses LLM to check the correctness of the subsumption A ⊑ B directly in Stage 3b. If the LLM judges A ⊑ B to be correct, NeurOWL returns True along with the subsumption itself as the missing axiom and explanation. Otherwise, NeurOWL indicating that the input subsumption does not plausibly hold and returns False. The main contributions of this work are: (1) We introduce a generalized TBox abduction task that does not require predefined missing axioms candidates and handles cases where the given subsumption is incorrect. (2) We propose NeurOWL, an end-to-end neuro-symbolic framework for reasoning over incomplete ontologies, utilising ontology embedding and LLM. (3) We empirically evaluate our approach on real-world ontologies, demonstrating its effectiveness and robustness under varying degrees of incompleteness. The main results show that NeurOWL achieves strong performance in concept subsumption reasoning while also generating meaningful explanations for incomplete input ontologies on datasets constructed from the real-world ontologies FoodOn (Dooley et al. 2018), Gene Ontology (Ashburner et al.

1. End-to-end neuro-symbolic framework for explainable subsumption reasoning can be implemented to jointly perform verification and abduction. This allows an AI system to not only determine whether a given subsumption is semantically plausible but also provide a logically sound explanation containing potential missing axioms without requiring predefined hypothesis candidates.

2. The system can automatically identify meaningful missing components that are both compatible with the existing information and plausible in real-world contexts. This capability extends the AI's reasoning beyond simple entailment checking to infer necessary knowledge for incomplete ontologies.

3. Iterative application of NeurOWL can be used to recover any subset- and entailment-minimal solutions as a set of missing axioms, allowing the AI to progressively refine its understanding by recovering a weakest set of missing axioms sufficient to derive the target conclusion.

4. The system can handle complex concept reasoning by utilizing different stages, such as Stage 3a's bidirectional search for intermediate concepts C such that A is a subclass of C and C is a subclass of B, which allows it to infer missing axioms involving existential restrictions like ∃r.B1.

5. Performance can be optimized by fine-tuning the embedding model on the specific incomplete ontology, as demonstrated by NeurOWLOnT achieving significantly better performance due to its adaptation to the underlying logical structure through fine-tuning on complex datasets like Snomed∃.

6. The framework provides a structured way to analyze where errors occur, with ablation studies showing that using Stage 2a or 2b is substantially higher than that of Stage 3a alone, helping researchers focus computational effort on the most effective components for specific reasoning tasks.

OWL ontologies provide a formal knowledge representation framework that enables semantic reasoning, and have been widely adopted across domains such as healthcare and bioinformatics. In practice, however, real-world ontologies are often incomplete, which pose challenges for reasoning. In this work, we focus on a fundamental subsumption reasoning problem: given an incomplete ontology and a candidate (non-entailed) subsumption, determine whether the subsumption is semantically plausible and, if so, providing a logically sound explanation containing potential missing axioms. This task unifies subsumption verification with ontology abduction, and generalizes the latter by removing the need for a predefined candidate set of missing axioms. To address this subsumption reasoning problem, we propose NeurOWL, an end-to-end neuro-symbolic framework that jointly performs verification and abduction, leveraging both formally defined semantics and textual semantics through Large Language Models and ontology embeddings. We evaluate NeurOWL on real-world ontologies across multiple domains, demonstrating strong and robust performance across different domains.