The quest for uncertainty

The question of how to represent and process uncertainty is of fundamental importance to the scientific process, but also in everyday life. Currently there exist a lot of different calculi for managing uncertainty, each having its own advantages and disadvantages. Especially, almost all are defining the domain and structure of uncertainty values a priori, e.g., one real number, two real numbers, a finite domain, and so on, but maybe uncertainty is best measured by complex numbers, matrices or still another mathematical structure. Here we investigate the notion of uncertainty from a foundational point of view, provide an ontology and axiomatic core system for uncertainty, derive and not define the structure of uncertainty, and review the historical development of approaches to uncertainty which have led to the results presented here.