Bolotova, S. D. Makhortov Voronezh State University 1, Universitetskaya pl., Voronezh, Russia, 394006 The relevant LP-inference, which is based on the solution of logical equations, is an effective tool that can be used for research and optimization of production-logical systems. <...> It significantly reduces the number of executed queries to an external source of information (either to a database or an interactive user). <...> The preference is given to testing the facts that are really needed in the inference. <...> However, experiments have shown that the process of using the relevant LP-inference may require an excessive amount of computational resources of the computer. <...> So, the relevant LP-inference method was modified to use parallel computing algorithms. <...> Multi-threading is a fundamentally new element in the implementation, which allows speeding up the process of constructing sets of facts that are required in the inference, and their further processing. <...> Key words and phrases: backward inference, relevant inference, logic equations, parallelism, multi-threading. 1. <...> Introduction in the field of artificial intelligence. <...> They are used in the theory of learning and problem solving systems, the development expert systems, covering a large variety of applications in several areas, such as medicine, engineering, exploration, and others [1]. <...> Production systems have very rich history and the fact that they are still of interest is confirmed by numerous modern applied and theoretical researches in this area [2–5]. <...> However, production system programs are very computationally intensive and run Production systems is an important area of the theoretical and applied research quite slowly. <...> In particular, they often require an exponential number of computation and intensive exchange with external memory. <...> This fact reduces their effectiveness, and therefore, many experts try to avoid working with programs that require extreme amounts of resources [1]. <...> Consequently, a significant increase of production systems performance is the important part in theoretical and applied research. <...> There are several possible ways for speeding up the execution of production systems. <...> Multi-threading is a fundamentally new element in the implementation. <...> A General Description of the Algorithm based on the solution of the production logical equations and for this purpose it uses mathematically-based algorithms for finding <...>