AN APPROACH TO FUNCTIONAL MODELING OF MARKOV NETWORKS (Part 1)

The provisions of the theory of Markov algorithms are being developed. The inference, which cannot be considered normal according to Markov, is investigated. The individual schemes of the Markov algorithm are combined into systems, and the systems into a network. A method of combining individual algorithm schemes into systems and networks is introduced into scientific circulation, for which the concept of “mathematical composition” is introduced, its properties are investigated. An innovative approach to modeling objects and systems of the world around us using such mathematical compositions is proposed for consideration. Within the framework of this approach, a functional model of interaction between artificial intelligence, mathematical compositions and objects, and systems of the world around us is synthesized in order to formalize a complete list of interactions represented by categorical morphisms. The functional model is not synthesized in advance, but is built in the processor of processing words and morphisms from input samples of data from objects and systems of the world around us in the form of a diagram of Markov occurrences of words into each other. At the same time, a functional model of the Markov network itself is being built. It is shown that since the composition of objects and systems of the world around us is established as words are processed, their interaction as their morphisms are processed, then mathematical composition is considered a Markov system without creativity, until it is established that there are more than one data sources from objects and systems and the interface of creativity is not found in them. This interface is detected as a control element of an object or system of the world around us by values and known types of their morphisms, unknown types of morphisms are recorded and analyzed for classification. If none is detected, then the Markov system is understood as a finite state machine, if detected, then the Markov network. It is established that the concept of “mathematical composition” generalizes two different mathematical objects, the Markov system and the Markov network. It is concluded that mathematical compositions are not artificial intelligence, they are a separate mathematical and technical entity.