Quasi fractal Propositional Algebra Digitalization of Propositional Algebra and NPC -- Quasi fractal Temporal Topological Logic with Time Parameter over Topological Space -- Application to Brownian Motion.

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.