S.D. Makhortov - D.Sc. (Phys.-Math.), Head of department, Voronezh State University (VSU). E-mail: sd@expert.vrn.ru A.N. Shmarin - Post-graduate Student, Voronezh State University (VSU). E-mail: tim-shr@mail.ru

The theory of LP-structures provides powerful algebraic tools for studying the processes of knowledge management, knowledge verification, and optimization of logical inference in several areas of computer science. In particular, the publications present the advanced algorithms for a backward inference based on the solution of production-logical equations in LP-structures. The strategy of the relevant LP-inference is aimed at minimizing the number of queries to external sources of information. This paper describes a new idea for optimizing the LP-inference. It lies in the construction of an additional data structure to store the results that have already been obtained, which saves time in traversing the knowledge base graph. The ability to process fuzzy rules is another feature of the present research. Reduced complexity of the traversing is achieved by the fact that it is sufficient to study just once the knowledge base subtrees rooted at a vertex, inferred by more than one rule, and to use the information obtained in traversing other connected vertices. The paper considers theoretical aspects of the construction of the optimized algorithm for LP-inference, maintaining fuzziness at the level of confidence factors. We propose a basis for improving the quality of solutions for the cluster relevant LP-inference. The effectiveness of the practical application of the method developed lies in a significant reduction of the amount of calculations, which enables the use of the LP-inference method in large knowledge bases, as well as in more complex logical information systems. In the future, the theoretical approaches presented will be implemented in a new version of the expert system LPExpert (http://sourceforge.net/projects/lpexpert). This product is cross-platform software distributed under GPL 2.1 license and applicable in operating systems Windows and Linux.