Evidential Reasoning in a Categorial Perspective: Conjunction and
  Disjunction of Belief Functions
  The categorial approach to evidential reasoning can be seen as a combination
of the probability kinematics approach of Richard Jeffrey (1965) and the
maximum (cross-) entropy inference approach of E. T. Jaynes (1957). As a
consequence of that viewpoint, it is well known that category theory provides
natural definitions for logical connectives. In particular, disjunction and
conjunction are modelled by general categorial constructions known as products
and coproducts. In this paper, I focus mainly on Dempster-Shafer theory of
belief functions for which I introduce a category I call Dempster?s category. I
prove the existence of and give explicit formulas for conjunction and
disjunction in the subcategory of separable belief functions. In Dempster?s
category, the new defined conjunction can be seen as the most cautious
conjunction of beliefs, and thus no assumption about distinctness (of the
sources) of beliefs is needed as opposed to Dempster?s rule of combination,
which calls for distinctness (of the sources) of beliefs.
