# Nomological Deductive Reasoning for Trustworthy, Human-Readable, and Actionable AI Outputs
## 5 Nomological Deductive Reasoning (NDR): A Proposed Solution
### Ontology Design
#### 5.3.3 Experimental Results
To address this, future work will explore how LLMs can be coupled with the rule-based rigor of NDR--where LLMs serve as natural-language interfaces that translate formal rule-based deductions into user-friendly narratives. Such a hybrid approach aims to preserve the logical integrity of NDR while enhancing user engagement and interpretability through the expressive capabilities of LLMs. In conclusion, this research offers both practical contributions--a transparent, rule-based credit-scoring framework--and theoretical insights into the integration of symbolic reasoning with machine learning. The NDR approach not only strengthens the foundation of explainable AI but also points toward a future in which AI systems are both powerful and principled, ensuring that decisions are not just accurate but also aligned with human values and domain logic. Conceptualization, G.H. and A.LE. ; methodology, G.H. and A.LE. ; investigation, G.H. ; writing--original draft preparation, G.H. ; writing--review and editing, G.H. and A.LE. ; supervision, A.L.E. ; project administration, A.L.E. All authors have read and agreed to the published version of the manuscript. The work of Dr. [PERSON] was supported by Grant PID2021-124335 OB-C22 funded by MCIN/AEI 10.13039/501100011033 and the European Union. Data Availability Statement: The original contributions presented in the study are included in the article, and no new datasets were involved. Further inquiries can be directed to the corresponding author. We thank all the anonymous reviewers for their supportive comments for further improving this article. ## Appendix A

The literature up until the end of the twentieth century reflects a rich landscape of theoretical models aimed at characterizing scientific explanation. Among the most influential are the deductive-nomological (D-N) model proposed by [PERSON] [134], widely regarded as the most prominent philosophical account of explanation, and [PERSON]'s Statistical Relevance (SR) [153] and Causal Mechanical (CM) [154] models. Additional noteworthy contributions include the Unificationist models advanced by [PERSON] [155] and [PERSON] [156], as well as the Pragmatic theory of explanation developed by [PERSON] [157]. Despite the inevitable divergences inherent in philosophical discourse, a common evaluative criterion can be discerned across these models: adherence to empiricist standards of intelligibility and testability with respect to the concepts employed in explanatory statements. Notably, all these theories--each with its own unique formal structure--converge on the fundamental notion that explanation involves identifying factors or causes that underlie the occurrence of an event E. This is perhaps most explicitly formalized in [PERSON]'s model, which frames explanation through general laws and antecedent conditions serving as the premises of explanatory arguments. Table 14 provides a comparative overview of the principal tenets of each model. It also underscores the shared conceptual foundation across these diverse theories, thereby supporting the proposition that a generic framework of explanation may be viable, particularly within the emerging field of explainable Artificial Intelligence (XAI). \begin{table}
\begin{tabular}{p{56.9 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Explanation Theory** & **Author(s)** & **Main Idea of the Model** & **Common Element (with All Other Theories)** \\ \hline \multirow{4}{*}{\ \begin{tabular}{} \end{tabular}  } & \multirow{4}{*}{ \begin{tabular}{} \end{tabular}  } & Explanation involves showing that the phenomenon to be explained follows deductively from general laws or premises. It emphasizes logical reasoning and general laws. & Logical structure and relationships: Like other theories, it connects a phenomenon to its cause/effect, focusing on structure and relationships (causal, statistical, etc.). \\ \cline{1-1} \cline{3-4}  & & Explanations are based on showing the statistical relevance of factors.