  The set of subsystems of a finite quantum system (with variables in Z(n))
together with logical connectives, is a distributive lattice. With regard to
this lattice, the (where P(m) is the projector to) obeys a supermodularity
inequality, and it is interpreted as a lower probability in the sense of the
Dempster-Shafer theory, and not as a Kolmogorov probability. It is shown that
the basic concepts of the Dempster-Shafer theory (lower and upper probabilities
and the Dempster multivaluedness) are pertinent to the quantum formalism of
finite systems.
