Based on the principle of dialectic symmetry formulated by the philosophy of dialectic positivism, an interpretation of the concept of "artificial intelligence" is proposed. This principle assumes the existence of a hierarchy of information objects, similar to the hierarchy, which reflects different levels of organization of matter (mechanical, chemical, biological, social). The construction of a hierarchy of information objects - information processing systems - allows us to interpret in the same way the essence of both artificial intelligence and the intelligence that a human being is endowed with. These are information processing systems referring to the highest levels of the specified hierarchy.

Multivalued logics are becoming one of the most important tools of information technology. They are in great demand for creation of artificial intelligence systems that are close to human intelligence, since the functioning of the latter cannot be reduced to the operations of binary logic. At the same time, the problem of improving the efficiency of using the results of research in multivalued logics, as well as the problem of interpreting variables of multivalued logic, is acute. These problems create certain interdisciplinary barriers and make it difficult to implement the results of research in the field of multivalued logics in other fields of knowledge. It is shown that the problem of interpreting multivalued logic variables can be removed by establishing correspondence with fuzzy logic variables. Improving the efficiency of using of operations of multivalued logics and their variables can be provided by using their close connection to Galois fields. This connection, among other things, makes it possible to reduce any operations of multivalued logics, the number of variables in which is equal to a prime number, to algebraic functions whose arguments take values in Galois fields. This allows, among other things, to eliminate the very cumbersome constructions used in works on multivalued logic and make its apparatus convenient for use in related scientific disciplines in information technology. Direct verification of the adequacy of algorithms based on the use of Galois fields can be carried out by means of radio-electronic circuits, examples of which are presented in the present paper.

It is shown that the use of the representation of digital signals varying in the restricted amplitude range through elements of Galois fields and the Galois field Fourier transform makes it possible to obtain an analogue of the convolution theorem. It is shown that the theorem makes it possible to analyze digital linear systems in same way that is used to analyze linear systems described by functions that take real or complex values (analog signals). In particular, it is possibile to construct a digital analogue of the transfer function for any linear system that has the property of invariance with respect to the time shift. It is shown that the result obtained has a fairly wide application, in particular, it is of interest for systems in which signal processing methods are combined with the use of neural networks.

An analysis of the behavior of Internet users from the point of view of their preferences in the choice of information sources and the effectiveness of their impact is presented. It is shown that the modern infocommunication space has undergone qualitative changes in the most recent time, and these transformations are already having a pronounced impact on higher education, mainly through the factor of competition between information sources. It is shown that these transformations can be interpreted as the evolution of the noosphere, which is considered as a global infocommunication network, in which non-trivial transpersonal information objects are formed. Their existence leads to the fact that the human intellect has a dual nature - both individual and collective principles are present in it at the same time. The latter is responsible for such phenomena as the collective unconscious, understood in the sense of Jung. It is shown that the neural network model of the noosphere makes it possible to formulate a similar concept of "professional collective unconscious", which is responsible for professional intuition, acts of creativity, etc. In turn, the existence of the professional collective unconscious forces us to radically reconsider the content of what is called training and move to the concept of meta-learning, which, among other things, involves stimulating transitions from one level of interaction with transpersonal information structures that make up the professional collective unconscious to another.

It is shown that in order to increase the efficiency of using methods of abstract algebra in modern information technologies, it is important to establish an explicit connection between operations corresponding to various varieties of multivalued logics and algebraic operations. For multivalued logics, the number of variables in which is equal to a prime number, such a connection is naturally established through explicit algebraic expressions in Galois fields. It is possible to define an algebraic δ-function, which allows you to reduce any truth table to an algebraic expression, for the case when the number of values accepted by a multivalued logic variable is equal to an integer power of a prime number. In this paper, we show that the algebraic δ-function can also be defined for the case when the number of values taken by a multivalued logic variable is p − 1, where p is a prime number. This function also allows to reduce logical operations to algebraic expressions. Specific examples of the constructiveness of the proposed approach are presented, as well as electronic circuits that experimentally prove its adequacy.

The interpretation of the category of complex is given on the basis of dialectical positivism, in the framework of which the principle of dialectic symmetry is formulated. It, in turn, is based on the consideration of matter and information as paired dialectic categories. In accordance with this principle, information objects form a hierarchy similar to that which corresponds to different levels of matter organization (mechanical, chemical, biological, social). As “complex”, one should interpret the system that is the medium for the information object at least one level higher than the level related to trivial information (that is, one that is inextricably linked with the object itself). This level is the level corresponding to estranged information (simplifying information about a certain object recorded on another medium).