The set of imaginary numbers is included in the probability system by extending the five axioms of Andrey Nikolaevich Kolmogorov, which he proposed in 1933. This is done by adding three new and supplementary axioms. This allows any random experiment to be performed in the extended complex probability set C = R + M, which is the sum of the real set R of real probabilities and the imaginary set M of imaginary probabilities. The goal is to determine complex probabilities by incorporating and considering additional imaginary dimensions to the event that occurs in the “real” laboratory.
The outcome of the stochastic phenomenon in C can be predicted perfectly, regardless of the probability distribution of the input random variable in R. This is because the corresponding probability in the whole set C is always equal to one. Hence, the implication is that randomness and chance in R are replaced by absolute determinism in C. This is due to the fact that the probability in C is calculated after removing the chaotic factor from our knowledge of the nondeterministic experiment. This new complex probability paradigm will be applied to a newly defined logic that I call “Dynamic Logic”.
Author(s) Details:
Abdo Abou Jaoudé,
Department of Mathematics and Statistics, Faculty of Natural and Applied Sciences, Notre Dame University-Louaize, Lebanon.
