PRO2SAT: Systematic Probabilistic Satisfiability logic in Discrete Hopfield Neural Network

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 intro-duced 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.

Automated summary

This article introduces a method called Probabilistic 2 Satisfiability to control the distribution of negative and positive literals in Artificial Neural Networks by assigning probabilities to variables in logical rules. Experimental results show that the proposed model outperforms existing methods with a probability of at least 81.8%.