Usage of Neural Networks for Solving Applied Logic Problems

Abstract

The article deals with heuristic neural network-based solver for NP-hard problems (determining the (in)consistency of a system of logical equations). This problem is relevant and important, for example, when performing express analysis of the consistency of the knowledge base of an expert system, decision-ma king based on fuzzy logic models, recognition of multidimensional objects, etc. The trained neural network plays the role of a highly efficient heuristic solver, and the number of equations and variables used in the logical model has little effect on the speed of decision-making by the neural network, while the probability of an exact solution for a parametrically defined class of problems is close to one. A parametrically defined class of problems is understood as a set of problems described by multidimensional vectors of parameters that satisfy some general law of probability distribution. One such family of parameters, proposed and used for training a neural network, is given in the article. It is shown how to generate inconsistent and consistent instances of individual systems of logical equations. A series of more than 200 experiments to test the model was carried out, the limits of the confidence interval of the probability of a correct decision were obtained, which allows us to evaluate the effectiveness of the model. It is shown how to implement a neural network to check the (in)consistency of a logical knowledge model. The constructed model can be effectively supplemented with new parameter vectors and applied in various fields of applied research.