The validity of Dempster-Shafer belief functions

Abstract This reply to papers by Pearl and Shafer focuses on two issues underlying the debate on the validity of using Dempster-Shafer theory, namely the requirement of a process-independent semantics and the a priori need for multiple uncertainty calculi. Pearl shows deficiencies of Dempster-Shafer theory in dealing with several instances of commonsense reasoning in a process-independent manner. Although this argument is correct under the assumptions stated, it is weakened somewhat by introducing questions of whether a process-independent semantics is always necessary or desirable. Another issue underlying both papers, whether multiple uncertainty representations are necessary, is also discussed. Shafer claims that multiple uncertainty representations are necessary. He presents a goal of developing all uncertainty representations in parallel and defining domains in which each representation is best suited. In contrast, Pearl implicitly claims that probability theory alone is necessary, unless the use of another representation (such as Dempster-Shafer theory) is shown to be clearly advantageous. These two perspectives lead to different approaches to defining the form of uncertainty best modeled by Dempster-Shafer theory or any other uncertainty calculus.