The Paradigm of Complex Probability and Analytic Nonlinear Prognostic for Unburied Petrochemical Pipelines – A Relation to Dynamic Logic

What is it about?

Andrey Nikolaevich Kolmogorov put forward in 1933 the five fundamental axioms of classical probability theory. The original idea in my complex probability paradigm is to add new imaginary dimensions to the experiment real dimensions which will make the work in the complex probability set totally predictable and with a probability permanently equal to one. Therefore, adding to the real set of probabilities R the contributions of the imaginary set of probabilities M will make the event in C = R + M absolutely deterministic. It is of great importance that stochastic systems become totally predictable since we will be perfectly knowledgeable to foretell the outcome of all random events that occur in nature. Hence, my purpose is to link my complex probability paradigm to unburied petrochemical pipelines analytic prognostic in the nonlinear damage accumulation case. Consequently, by calculating the parameters of the novel prognostic model, we will be able to determine the magnitude of the chaotic factor, the degree of knowledge, the complex probability, the system failure and survival probabilities, and the remaining useful lifetime probability, after that a pressure time t has been applied to the pipeline and which are all functions of the system degradation subject to random effects. Furthermore, we will apply the new paradigm to my novel ‘Dynamic Logic’ model.

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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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