**9. Conclusions and Future Work**

In this paper, we proposed a new perspective in obtaining the best induced logic from real-life datasets. As in a standard logic mining model, the attribute selection was chosen randomly which leads to non-essential attributes and reduces the capability of the HNN to represent the dataset. To address the issue of randomness, a novel supervised learning (S2SATRA) capitalized the correlation filter among variables in the logical rule with respect to the logical outcome. In this case, the only attribute that has the best association value will be chosen during the pre-processing stage of S2SATRA. After obtaining the optimal *Qbest*, HNN can obtain the synaptic weight associated with the *Qbest* which minimizes the cost function of the network. During the retrieval phase, the best combination of *Q<sup>B</sup> <sup>i</sup>* will be generated, thus creating the best *Q<sup>B</sup> <sup>i</sup>* that generalizes the logical rule of the datasets. The effectiveness of the proposed S2SATRA is illustrated by extensive experimental analysis that compares S2SATRA with several state-of-the-art logic mining methods. Experimental results demonstrate that S2SATRA can effectively produce more optimal *Qbest* which leads to the improved *Q<sup>B</sup> <sup>i</sup>* . In this case, S2SATRA was reported to outperform all the existing logic mining models in most of the performance metrics. Given the simplicity and flexibility of the S2SATRA, it is also worth implim3n5int other logical dimensions. For instance, it will be interesting to investigate the implementation of random *k* satisfiability proposed by [13,41] into the supervised learning-based reverse analysis method. By implementing the flexible logical rules, the generalization of the dataset will improve dramatically.

**Author Contributions:** Investigation, resources, funding acquisition, M.S.M.K.; conceptualization, methodology, writing—original draft preparation, S.Z.M.J.; formal analysis, writing—review and editing, M.A.M.; visualization, project administration, H.A.W.; theory analytical, validation, S.M.S.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by Ministry of Higher Education Malaysia for Transdisciplinary Research Grant Scheme (TRGS) with Project Code: TRGS/1/2020/USM/02/3/2.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors would like to express special dedication to all of the researchers from AI Research Development Group (AIRDG) for the continuous support.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

