A theory of belief.
In this very long paper a theory of belief is presented in which uncertainty has -- according to the author's terminology -- two dimensions. The two dimensions have a variety of interpretations. The article focuses on two of these interpretations. The first is that one dimension corresponds to probability and the other to ``definiteness'', which itself has a variety of interpretations. To accomplish this program the paper relies on a huge number of axioms, definitions, lemmas, theorems\dots which make it very cumbersome and difficult to read. Moreover, many statements (sometimes similar to rigmaroles) are not convincing both from a semantic and a syntactic point of view. A couple of examples (but there are many others) that the referee wants to challenge: ``To provide an account of experimental results in which for disjoint events \(A\) and \(B\) the probabilities of \(A|(A\cup B)\) and \(B|(A\cup B)\) do not sum to 1''; ``Traditional probability theory has two components to it: a probability function which is a finitely additive measure and an independence relation on events\dots I and others find this definition of independence problematic: in the most important applications of probabilistic independence, one has a very good idea of which key events are independent of one another without resort to calculations or often without knowing their probabilities and the probability of their intersections''.
scientific article; zbMATH DE number 1956104