The Paradigm of Complex Probability, Prognostic, and Dynamic Logic

What is it about?

The book topic The Paradigm of Complex Probability, Prognostic, and Dynamic Logic differs from most of other mathematical topics in its point of view. It attempts to analyze and to develop methods for simulating stochastic or deterministic phenomena and statistical processes and to relate them to a newly developed logic that I coined by the terms Dynamic Logic. Also, if the computer can be made to imitate an experiment or a process, then by repeating the computer simulation with different data, we can draw statistical conclusions. In such approach, the conclusions may lack a high degree of mathematical precision but still be sufficiently accurate to enable us to understand the process being simulated. Probability theory is a branch of statistics, a science that employs mathematical methods of collection, organization, and interpretation of data, with applications in practically all scientific areas. As a matter of fact, prognostic in science means to predict the failure of any system before its failure occurs whether in physics, in engineering, and in all disciplines of applied science. Hence, prognostic has tremendous consequences and crucial predictions as we shall see in the third chapter of the book where it was applied to petro-chemical pipelines and was successfully related to my complex probability paradigm as well to my novel dynamic logic. Thus, three fields were linked and were bonded together.

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Why is it important?

Computing probabilities is the main work of classical probability theory. Adding new dimensions to the stochastic experiments will lead to a deterministic expression of probability theory. This is the original idea at the foundations of this work. Actually, the theory of probability is a nondeterministic system in its essence; that means that the events outcomes are due to chance and randomness. The addition of novel imaginary dimensions to the chaotic experiment occurring in the real set R will yield a deterministic experiment and hence a stochastic event will have a certain result in the complex probability set C. If the random event becomes completely predictable then we will be fully knowledgeable to predict the outcome of stochastic experiments that arise in the real world in all stochastic processes. Consequently, the work that has been accomplished here was to extend the real probabilities set R to the deterministic complex probabilities set C = R + M by including the contributions of the set M which is the imaginary set of probabilities. Therefore, since this extension was found to be successful, then a novel paradigm of stochastic sciences and prognostic was laid down in which all stochastic phenomena in R was expressed deterministically in C. I called this original model ‘The Complex Probability Paradigm’ that was initiated and illustrated in my previous 25 research publications. Hence, this original probability paradigm will be applied in this work to the novel dynamic logic which is a development of the ordinary static logic and that was accomplished after adding the dimension of time to the classical system of axioms of logic.

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