\section{Discussion}\label{sec:discussion}
\begin{comment}
- Interpret the experimental results in light of the research objectives.
- Analyze the impact of introducing noise on the performance of neurosymbolic ontology reasoners.
- Discuss the strengths and limitations of the benchmark dataset and methodology.
- Explore potential extensions or improvements for future research.
\end{comment}

Our study investigates the application of noise injection methods to ontologies, examining their impact on various reasoning tasks. The proposed noise injection techniques are designed to be applicable across a wide range of ontologies. Based on our findings, we observed that across all ontologies, tasks, and noise types, \textit{R-GCN} is consistently and substantially more robust to noisy test data than \textit{OWL2Vec*} and \textit{Box2EL}. Its neighborhood-aggregation mechanism enables it to preserve performance even when a large portion of the test triples is corrupted, while embedding-based models—especially Box2EL—degrade sharply. This robustness holds for both membership prediction and object property assertion (OPA), the latter being particularly challenging due to the need for multi-step reasoning and the dominance of inference-based triples in the test sets.

These findings suggest that graph neural network-based approaches like \textit{R-GCN} provide a more reliable foundation for reasoning over noisy, real-world ontologies, where data imperfections and complex inference paths are common.

However, the specific characteristics of each ontology significantly influence the effectiveness of noise injection, highlighting the need for tailored approaches in certain scenarios. For example, the specific relations in the test set may not effectively show the influence of noise introduced as these relations inherently resist noise. In \textit{OWL2Bench}, \texttt{knows} relation is defined as reflexive (i.e., every individual 'knows' themselves), making it less sensitive to object property assertion inferences. These inferences hold regardless of corrupted assertions unless the TBox is modified. This raises questions about the validity of evaluating noise effects in scenarios where axiomatic properties dominate reasoning outcomes. Future work should consider refining testing sets or introducing variations in TBox definitions to better capture the influence of noise.

An important factor underlying the differing behaviors across ontologies is the composition of the test sets, particularly the ratio of membership versus object property assertion triples. As shown in Table~\ref{tab:stat_triples}, these ratios vary dramatically between ontologies, which in turn affects how strongly noise impacts model performance. For example, in the \textit{Family} ontology, OPA triples constitute over $98\%$ of the test set. Since many of these OPAs arise from multi-step inferences produced by Pellet, the test set is dominated by structurally complex, inference-heavy triples—making it inherently challenging and causing all models to exhibit low OPA performance even without noise. In this setting, noise injected into test triples disproportionately affects OPAs, amplifying the performance gap between \textit{R-GCN} and embedding-based models.

In contrast, \textit{OWL2Bench} has a much more balanced distribution, with only around $12\%$ OPA triples and a substantially larger proportion of membership triples. This composition makes the test set less sensitive to inference-heavy corruption, which helps explain why \textit{OWL2Vec*} attains relatively strong OPA performance and why noise in OPAs produces less dramatic declines compared with the \textit{Family} ontology. The \textit{Pizza} ontologies occupy an intermediate position, with $85\text{--}90\%$ OPA triples, resulting in noise effects that are more severe than \textit{OWL2Bench} but less extreme than \textit{Family}. The relative stability of \textit{R-GCN} across these datasets stems from its reliance on learned neighborhood structure rather than isolated triple accuracy, allowing it to generalize across ontologies despite their differing test-set compositions.

These observations highlight that robustness cannot be interpreted independently of the structural properties of the evaluation set. Ontologies whose test splits are dominated by complex inference-derived triples amplify the impact of noisy test data, disproportionately penalizing embedding-based models. Conversely, datasets with more balanced triple ratios may under-reflect the challenges posed by noise. Future benchmarks should therefore consider standardizing or controlling test-set composition when evaluating noise robustness, or at minimum report such statistics to contextualize cross-ontology comparisons.

Furthermore, it should be noted that the results from previous works, such as the work of~\citep{semrec_hoehndorf}, are not comparable to ours because our proposed benchmark focuses on evaluating ontology reasoning rather than ontology completion. Ontology reasoning refers to inferring logically consistent relationships from existing data and rules, which is inherently more complex. This complexity arises because reasoning requires the system to consider all possible logical implications of the data, making it more sensitive to inconsistencies and noise in the dataset. Consequently, the metrics may reflect this added difficulty, leading to poorer results compared to approaches that focus solely on completing the ontology.

While our initial exploration centered on introducing noise through the addition of logical contradictions or corruption of triples with low probability of occurrence, many other types of axioms and noise patterns merit investigation. Future research could involve examining various inconsistencies, contradictions, and errors that frequently occur in real-world ontologies, thereby enhancing the diversity of noise generation techniques. In particular, introducing noise in the TBox (e.g., modifying class hierarchies, altering domain and range constraints, or introducing invalid equivalence axioms) could offer valuable insights into how structural and logical inconsistencies impact reasoning outcomes. Furthermore, future work could focus on establishing standardized metrics and evaluation frameworks to consistently measure the performance of neurosymbolic reasoning systems. 