A conventional systematic satisfiability logic suffers from a nonflexible logical structure that leads to a lack of interpretation. To resolve this problem, the advantage of introducing nonsystematic satisfiability logic is important to improve the flexibility of the logical structure. This paper proposes Random 3 Satisfiability ( RAN3SAT ) with three types of logical combinations ( $k = 1, 3, k =2, 3$ , and $k =1$ , 2, 3) to report the behaviors of multiple logical structures. The different types of RAN3SAT enforced with Discrete Hopfield Neural Network (DHNN) are included with benchmark searching techniques, such as Exhaustive Search algorithm. Additionally, to strengthen and certify the behavior of the proposed model, we extensively conducted several performance evaluation metrics with a specific number of neurons. In particular, the experimental results revealed that RAN3SAT was able to be implemented in DHNN, and each logical combination has its characteristics. Nonetheless, RAN3SAT provides more neuron variations in the whole solution space. The proposed model can also be applied in real-world applications such as the logic mining approach since RAN3SAT consists of various logic combinations that behave as input language to transform raw data into informative output.

Amazon.com Inc. seeks alternative ways to improve manual transactions system of granting employees resources access in the field of data science. The work constructs a modified Artificial Neural Network (ANN) by incorporating a Discrete Hopfield Neural Network (DHNN) and Clonal Selection Algorithm (CSA) with 3-Satisfiability (3-SAT) logic to initiate an Artificial Intelligence (AI) model that executes optimization tasks for industrial data. The selection of 3-SAT logic is vital in data mining to represent entries of Amazon Employees Resources Access (AERA) via information theory. The proposed model employs CSA to improve the learning phase of DHNN by capitalizing features of CSA such as hypermutation and cloning process. This resulting the formation of the proposed model, as an alternative machine learning model to identify factors that should be prioritized in the approval of employees resources applications. Subsequently, reverse analysis method (SATRA) is integrated into our proposed model to extract the relationship of AERA entries based on logical representation. The study will be presented by implementing simulated, benchmark and AERA data sets with multiple performance evaluation metrics. Based on the findings, the proposed model outperformed the other existing methods in AERA data extraction.

Recently, new variants of non-systematic satisfiability logic were proposed to govern Discrete Hopfield Neural Network. This new variant of satisfiability logical rule will provide flexibility and enhance the diversity of the neuron states in the Discrete Hopfield Neural Network. However, there is no systematic method to control and optimize the logical structure of non-systematic satisfiability. Additionally, the role of negative literals was neglected, reducing the expressivity of the information that the logical structure holds. This study proposed an additional optimization layer of Discrete Hopfield Neural Network called the logic phase that controls the distribution of negative literals in the logical structure. Hence, a new variant of non-systematic satisfiability named Weighted Random 2 Satisfiability was formulated. Thus, a proposed searching technique called the binary Artificial Bee Colony algorithm will ensure the correct distribution of the negative literals. It is worth mentioning that the binary Artificial Bee Colony has flexible and less free parameters where the modifications tackled on the objective function. Specifically, this study utilizes a binary Artificial Bee Colony algorithm by modifying the updating rule equation by using not and (NAND) logic gate operator. The performance of the binary Artificial Bee Colony will be compared with other variants of binary Artificial Bee Colony algorithms of different logic gate operators and conventional binary algorithms such as the Particle Swarm Optimization, Exhaustive Search, and Genetic Algorithm. The experimental results and comparison show that the proposed algorithm is compatible in finding the correct logical structure according to the initiate ratio of negative literal.

Existing satisfiability (SAT) is composed of a systematic logical structure with definite literals in a set of clauses. The key problem of the existing SAT is the lack of interpretability of a logical structure that leads to low variability of the retrieved neuron states. Thus, a new non-systematic SAT with higher interpretability is needed to reduce the repetition of the patterns of the final neuron states. This paper presents Major 2 Satisfiability (MAJ2SAT) by emphasizing a ratio of 2 Satisfiability (2SAT) clauses present in non-systematic SAT. Hence, different compositions of MAJ2SAT are implemented in a Discrete Hopfield Neural Network (DHNN) by adopting an Exhaustive Search as a training algorithm. Various performance metrics are utilized to measure the compatibility and behaviour of MAJ2SAT in DHNN. Overall, the formulation of MAJ2SAT offers an alternative logical structure in the field of data mining that involves a more dynamic composition of literals and clauses.