*2.1. Optimal Attribute Selection Strategy*

Optimal attribute selection is vital to ensure HNN learn the correct logical rule during the learning phase. Ref. [30] proposed logic mining that capitalize random attribute combination that leads to creation of 2SAT logic. In this study, the synaptic weight connection obtained from 2SAT is purely based on the most frequent logical incidence in the datasets. The main question to ask: what happen if the 2SAT logical rule selected the wrong attribute? Hence, there is a huge possibility of the logic mining to learn the wrong synaptic which leads to suboptimal induced logic. A similar observation was made in the study by [31] which proposed 3SAT for induced logic, with a heavy focus on the random attribute selection. It is agreeable that the induced logic might produce accurate induced logic, but this issue leads logic mining to choose the random attributes that reduce the interpretability of induced logic. To solve this issue, the latest study by [30] proposed permutation operator to optimize the random selection proposed by [20]. The permutation operator will increase the accuracy of the induced logic when we change the attribute in the logical formula. Despite the increase in the accuracy and other metrics, the interpretability issue remains unsolvable. This is due to the random selection that contributes to a lack of interpretability of the learned logic in HNN. In this paper, we capitalize the work of [20,30] by constructing the dataset in the form of 2SAT logical rule and permutation operator. By selecting the optimal attribute combination of 2SAT, we can obtain more search space which leads to optimal induced logic.
