Vladimir Serdyukov – författare
Algebraic Formalization of Smart Systems
Theory and Practice
1 115 kr
Skickas inom 10-15 vardagar
Algebraic Quasi—Fractal Logic of Smart Systems
Theory and Practice
1 779 kr
Skickas inom 10-15 vardagar
2 273 kr
Läs direkt efter köp
This book is a continuation of the Algebraic Formalization of Smart Systems. Theory and Practice, 2018, and Algebraic Identification of Smart Systems. Theory and Practice, 2021. Algebraic logic refers to the connection between Boolean algebra and classical propositional calculus. This connection was discovered by George Boole and then developed by other mathematicians, such as C. S. Peirce and Ernst Schroeder. This trend culminated in the Lindenbaum-Tarski algebras. Here we try to connect algebraic logic and quasi-fractal technique, based on algebraic formalization of smart systems to get facts about smart systems functioning and connections of their qualitative and quantitative indicators. Basic techniques we used: algebraic quasi-fractal systems, Erdős–Rényi algorithm, a notion of –giant component of an algebraic system, fixed point theorem, purities, i.e., embeddings preserving -property of an algebraic system. The book is aimed for all interested in these issues.
Algebraic Formalization of Smart Systems
Theory and Practice
1 115 kr
Skickas inom 10-15 vardagar
1 408 kr
Läs direkt efter köp
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 basedon 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.