A Logical Interpretation of Dempster-Shafer Theory, with Application to Visual Recognition

We formulate Dempster Shafer Belief functions in terms of Propositional Logic, using the im­ plicit notion of provability underlying Demp­ ster Shafer Theory. The assignment of weights to the propositional literals enables the Belief functions to be explicitly computed using Net­ work Reliability techniques. Also, the updat­ ing of Belief functions using Dempster's Rule of Combination corresponds to incremental up­ dating of the corresponding support clauses. This analysis formalizes the implementation of Belief functions within an ATMS. We describe VICTORS, a visual recognition system based on an ATMS extended with Belief functions. Without Dempster Shafer theory, VICTORS computes all possible visual interpretations (i.e. all logical models) without discriminating the best interpretations. Incorporating Dempster Shafer theory enables optimal visual interpre­ tations to be computed and a logical semantics to be maintained.