Representation of belief in relation to randomness

Overview & Synopsis

In this technical note, we develop a belief representation that generalizes the vanilla possibility theory, extending it to a bi-dimensional representation where randomness is taken into account. This way, we revisit and extend the usual quantitative implementation of belief level. We state the basic requirements and discuss the difference with the vanilla possibility theory before investigating the compatibility with Boolean and Kleene’s three-valued logic calculus. We then relate this representation to the probability theory, based on the assumption that necessity and possibility provide bounds for probability values, and finally discuss how to define a relevant projection of real values onto an admissible representation. This provides the basic ingredients to implement such extension of belief representation in existing mechanisms using the basic representation. The operational part of this development is available as open-source code.