The Logic of Uncertainty with Irrational Agents

Modern axiomatic uncertainty theories (fuzzy logic, probability theory and others) provide a calculus for manipulating with probabilities, membership functions, and degrees of belief when the initial values such as probabilities of elementary events are already given. These theories do not include a mechanism for getting initial uncertainty values. The value of these theories is in computing uncertainties of complex events that follow a structure imposed by axioms of a specific uncertainty theory. The lack of internal mechanism for getting initial values often means in the end that the same mechanism is applied for getting initial probability values, fuzzy logic membership functions, and belief functions. This is a source of much confusion -what is the real difference between all of these theories. A resolution of this confusion is critical from both theoretical and practical viewpoints. We argue that adding an internal mechanism of getting uncertainty values means adding irrational, conflicting and interacting agents along with their contexts.