This book reveals the general laws of the theory of smart systems with the help of a very powerful and expressive language of algebraic formalization. It also shows how this language can be used to substantiate practical results in the field of smart systems, which previously had only an empirical justification. Further, it proposes a translation of the theory of smart systems from verbal language to a much more expressive language of algebraic formalization, allowing the laws of the theory of smart systems to be seen in a different light. In 1937 L. Bertalanffy proposed the concept of an algebraic system and the development of a mathematical apparatus for describing systems. In the 1970s, A.I. Mal'tsev developed a theory of algebraic systems connecting algebra and logic for studying algebraic and logical objects. In the 1990s, the concept of purities by predicates was introduced by one of the authors, and the book includes some of its applications. The concept, which is based on the theory of algebraic systems, allows clarification of the connections between quantitative and qualitative analysis of a system. The book is intended for readers who use elements of artificial intelligence in their work.
This book is a continuation of our recently published book “Algebraic formalization of smart systems. Theory and practice.” It incorporates a new concept of quasi-fractal algebraic systems, based on A.I. Maltsev’s theory of algebraic systems and the theory of fractals developed by Benoit Mandelbrot, to investigate smart systems in more detail. The main tool used in the book, quasi-fractal algebraic systems, helps us to see smart systems in more detail by adding new factors, which e.g. make it possible to describe the previously indivisible elements of the initial model of factors. The techniques presented include fixed-point theorem, theorems of group theory, theory of Boolean algebras, and Erdös-Renyi algorithms. Given its focus, the book is intended for anyone interested in smart system theory.
This book reveals the general laws of the theory of smart systems with the help of a very powerful and expressive language of algebraic formalization. It also shows how this language can be used to substantiate practical results in the field of smart systems, which previously had only an empirical justification. Further, it proposes a translation of the theory of smart systems from verbal language to a much more expressive language of algebraic formalization, allowing the laws of the theory of smart systems to be seen in a different light. In 1937 L. Bertalanffy proposed the concept of an algebraic system and the development of a mathematical apparatus for describing systems. In the 1970s, A.I. Mal'tsev developed a theory of algebraic systems connecting algebra and logic for studying algebraic and logical objects. In the 1990s, the concept of purities by predicates was introduced by one of the authors, and the book includes some of its applications. The concept, which is based on the theory of algebraic systems, allows clarification of the connections between quantitative and qualitative analysis of a system. The book is intended for readers who use elements of artificial intelligence in their work.
This book is a continuation of our recently published book “Algebraic formalization of smart systems. Theory and practice.” It incorporates a new concept of quasi-fractal algebraic systems, based on A.I. Maltsev’s theory of algebraic systems and the theory of fractals developed by Benoit Mandelbrot, to investigate smart systems in more detail. The main tool used in the book, quasi-fractal algebraic systems, helps us to see smart systems in more detail by adding new factors, which e.g. make it possible to describe the previously indivisible elements of the initial model of factors. The techniques presented include fixed-point theorem, theorems of group theory, theory of Boolean algebras, and Erdös-Renyi algorithms. Given its focus, the book is intended for anyone interested in smart system theory.
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