Andrey Nikolaevich Kolmogorov introduced the five fundamental axioms of classical probability theory in 1933. My complex probability paradigm builds on this by adding new imaginary dimensions to the experiment’s real dimensions. This addition makes the work in the complex probability set entirely predictable, with a probability that is always equal to one. By including the contributions of the imaginary set of probabilities M to the real set of probabilities R, the event in C = R + M becomes entirely deterministic. This is essential because it allows us to predict the outcome of all random events that occur in nature, making stochastic systems entirely predictable.

The goal of my complex probability paradigm is to connect it to unburied petrochemical pipelines’ analytic prognostic in the nonlinear damage accumulation case. By calculating the parameters of the new prognostic model, we can determine the chaotic factor’s magnitude, the degree of knowledge, the complex probability, the system’s failure and survival probabilities, and the remaining useful lifetime probability. All these factors are functions of the system degradation subject to random effects after applying a pressure time t to the pipeline.

Furthermore, we will apply this new paradigm to my novel “Dynamic Logic” model.

**Author(s) Details:**

** Abdo Abou Jaoudé, **

Department of Mathematics and Statistics, Faculty of Natural and Applied Sciences, Notre Dame University-Louaize, Lebanon.