Andrey Nikolaevich Kolmogorov laid down the system of axioms for probability theory back in 1933. It is possible to extend this system to include the imaginary set of numbers by adding three additional axioms to his original five. This results in the creation of the complex probability set C, which is a combination of the real set R with its corresponding probability and the imaginary set M with its corresponding imaginary probability. Stochastic experiments are now performed in the complex set C instead of the real set R. The objective is to evaluate complex probabilities by considering new imaginary dimensions to the event occurring in the real laboratory. As a result, the corresponding probability in the entire set C is always equal to one and the outcome of the random experiments that follow any probability distribution in R is now predicted entirely in C. This means that chance and luck in R are replaced by total determinism in C. By subtracting the chaotic factor from the degree of our knowledge of the stochastic system, we can evaluate the probability of any random phenomenon in C. My innovative Complex Probability Paradigm (CPP) will be applied to the established theory of logic to express it completely deterministically in the probability universe C = R + M. After adding the time dimension, we will relate and join this original paradigm to a newly defined logic that I call ‘Dynamic Logic.’ This will also be implemented to pipeline prognostic with the aim of illustrating CPP and this new kind of logic.

Author(s) Details:

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