  We formulate Dempster Shafer Belief functions in terms of Propositional Logic
using the implicit notion of provability underlying Dempster Shafer Theory.
Given a set of propositional clauses, assigning weights to certain
propositional literals enables the Belief functions to be explicitly computed
using Network Reliability techniques. Also, the logical procedure corresponding
to updating Belief functions using Dempster's Rule of Combination is shown.
This analysis formalizes the implementation of Belief functions within an
Assumption-based Truth Maintenance System (ATMS). We describe the extension of
an ATMS-based visual recognition system, VICTORS, with this logical formulation
of Dempster Shafer theory. Without Dempster Shafer theory, VICTORS computes all
possible visual interpretations (i.e. all logical models) without determining
the best interpretation(s). Incorporating Dempster Shafer theory enables
optimal visual interpretations to be computed and a logical semantics to be
maintained.
