Quasi - Fractal NPC: Digitalization of Connections of Smart Systems (Expressed in the Language of NPC), Quasi - Fractal Smart Systems with Uncountable Levels Number

This chapter deals with issues related to quasi - fractal temporal logic. A new operator QF is introduced for quasi - fractal algebraic systems of any infinite ordinal number of levels. So, to describe temporal logic from the point of view of algebra to clear up (to measure) the truth value of closed formulas of the first order language of the finite signature with equality and to clear up connections between various kinds of temporal logics while considering temporal logic we can define quasi - fractal time scale, or simply quasi - fractal time. Quasi - fractal temporal logic can be considered as complex system with binary connections defined by logics values—true and false, or as more complicated connections which are defined by digitalization functions. Quasi - fractal construction and fixed - point theorem helps one to highlight sustainable parts of temporal logic. The purpose of this chapter is to present the following main results: In more details: In Sect. 2.2 we begin to consider quasi - fractal first order logic and application of fixed - point theorem to it. We begin from measures, homomorphisms, metric, quasi - fractal metric spaces and contractions mapping examples. Then we consider interpretation of a distance of Boolean ring and fixed - point theorem. Also, in this chapter we have introduced the notion of Quasi - fractal First Order Logic and have considered connections between different first order logics: Sect. 2.3.1 Kripke timeline and fixed - point, Relevance logic, Fixed - point logic. After that we shall consider sustainable logical subsystems of First Order Logic and digital estimation of their true values, risk sustainable subsystems and quasi - fractal digitalization function, and then again, refinement of estimates of a quasi - fractal NPC using the digitalization function.