On (Anti)Conditional Independence in Dempster-Shafer Theory
  This paper verifies a result of {Shenoy:94} concerning graphoidal structure
of Shenoy's notion of independence for Dempster-Shafer theory of belief
functions. Shenoy proved that his notion of independence has graphoidal
properties for positive normal valuations.
  The requirement of strict positive normal valuations as prerequisite for
application of graphoidal properties excludes a wide class of DS belief
functions. It excludes especially so-called probabilistic belief functions. It
is demonstrated that the requirement of positiveness of valuation may be
weakened in that it may be required that commonality function is non-zero for
singleton sets instead, and the graphoidal properties for independence of
belief function variables are then preserved. This means especially that
probabilistic belief functions with all singleton sets as focal points possess
graphoidal properties for independence.
