Abstract
When processing large volumes of information, obtaining an accurate solution often requires excessive resources or is even impossible at all. Therefore, in modern information systems, methods of artificial intelligence and inference are used, which allow to find approximate solutions with a given accuracy in an acceptable time. An important feature of such systems is the fuzzy nature of knowledge and reasoning. Knowledge bases with some simplified logic, for example, based on fuzzy production rules can serve as a basis for their construction. Effective formalism for the construction and study of data and knowledge models is provided by algebraic methods. In particular, the formal methodology for knowledge management in production-type systems is developed by the lattice-based algebraic theory of LP-structures (lattice production structures). Another achievement of the theory is the method of relevant backward inference (LP-inference), which significantly reduces the number of queries to external sources of information. This result is especially relevant when processing big data and managing large volumes of knowledge. The basis of LP-inference is the apparatus of production-logical equations. The article for the first time introduces an extended class of such equations for an algebraic model, the expressive capabilities of which cover logical inference systems with a fuzzy knowledge base. Some properties of these equations are proved that are useful for finding their solutions. Thus, the advantages of the theory of LP-structures extend to a fuzzy logical inference.
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The reported study was supported by RFBR project 19-07-00037.
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Makhortov, S. (2021). Algebraic Models for Big Data and Knowledge Management. In: Sychev, A., Makhortov, S., Thalheim, B. (eds) Data Analytics and Management in Data Intensive Domains. DAMDID/RCDL 2020. Communications in Computer and Information Science, vol 1427. Springer, Cham. https://doi.org/10.1007/978-3-030-81200-3_2
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