Quantifying Beliefs by Belief Functions: An Axiomatic Justification

Abstract

We present a set of axioms that justify the use of belief functions to quantify the beliefs held by an agent Y at time t and based on Y's evidential corpus. It is essentially postulated that degrees of belief are quantified by a function in [0,1] that give the same degrees of beliefs to subsets that represent the same propositions according to Y's evidential corpus. We derive the impact of the coarsening and the refinement of the frame on which the beliefs are expressed. The conditioning process is also derived. We propose a closure axiom that asserts that any measure of beliefs can be derived from other measures of beliefs defined on less specific frames.