Big Data Mining: a Computer-Oriented Method of Working with the Semantics of Assertions

When analyzing large amounts of data with the involvement of experts of subject domain, the problem of knowledge representation arises, this problem lies in describing the semantic content of judgments with their subsequent formalization, automated construction of a logical inference and computer processing, the purpose of this computer processing is to transform judgments in accordance with their semantics. The article explores the problem of knowledge representation through the construction of the semantics of judgments based on intuitionistic logic. The computer-oriented method is proposed. It allows us to work effectively with the semantic content of judgments and at the same time to obtain computer-realized intuitionistic conclusions of statements on the basis of translational approach by converting classical conclusions into intuitionistic ones. The essence of the method is the semantic evaluation of each judgment by elements of a specially selected lattice. This method allows an automatic transition from the inferability (truth) of some judgment in classical theory to the inferability (respectively truth) of the judgment itself or the close in meaning judgment in the corresponding intuitionistic theory, if we choose the complete Boolean and complete Heyting algebras as lattices, respectively. This approach is especially relevant when processing large amounts of information, as it avoids the need to build complex intuitionistic conclusions, which, in turn, can significantly increase the speed of data processing. The article demonstrates the use of the proposed method in the construction of intuitionistic derivations in the language of lattice ordered rings and in the conversion of classical theory into intuitionistic one for many-sorted algebraic systems. The peculiarities of the method are also studied, and the respective statements are proved.