PRO2SAT: Systematic Probabilistic Satisfiability logic in Discrete Hopfield Neural Network. (January 2023) - Chen, Ju; Kasihmuddin, Mohd Shareduwan Mohd; Gao, Yuan; Guo, Yueling; Asyraf Mansor, Mohd.; Romli, Nurul Atiqah; Chen, Weixiang; Zheng, Chengfeng
Highlights: Establish a logical structure based on probability control 2SAT distribution in Discrete Hopfield Neural Network. The proposed PRO2SAT has the ability to control the distribution of the positive literals and allow lower-order logical structure surpasses the performance of higher-order logical structure. PRO2SAT acquire optimized learning phase and more effective retrieval capability. The probabilistic feature of PRO2SAT is a major breakthrough in creating a network system that has more flexibility especially in large scale automation. Abstract: Satisfiability is prominent in the field of computer science and mathematics because SAT provides an alternative to represent the knowledge of any datasets. Fueled by this nature, recent paradigm tends to converge towards modelling Artificial Neural Network (ANN) through SAT. Despite extensive implementation of SAT in ANN, there are severely limited strategy to control the distribution of negative and positive literals in the logical rule. One of the most feasible approaches in controlling the behavior of the literal is by employing probabilistic behavior to each neuron in the ANN. In this paper, a novel logical rule namely Probabilistic 2 Satisfiability was proposed by implementing the probability to each variable in the 2 Satisfiability clause. In this context, the negativity of each variable will be determined using the probability which leads to higher search space. The proposed Probabilistic 2 Satisfiability was implemented into the special single layered Discrete Hopfield Neural Network where the cost function of each variable was derived by minimizing the inconsistency of the logic. The behavior of the proposed Probabilistic 2 Satisfiability was assessed based on various performance metrics including several newly introduced metrics. According to the experimental results, the proposed model has a probability of at least 81.8% in outperforming the existing method. Interestingly, the proposed model was reported to have the largest solution space when the ratio of positive was within [0.1, 0.4]. The comparison of experimental results with other state of the art logical rule demonstrates that the proposed model is promising in retrieving global neuron state.