This paper analyzes the theoretical under pinnings of recent proposals for computing Dempster-Shafer Belief functions from ATMS labels. Such proposals are intended to be a means of integrating symbolic and numeric rep resentation methods and of focusing search in the ATMS. This synthesis is formalized us ing graph theory, thus showing the relation ship between graph theory, the logic-theoretic ATMS description and the set-theoretic Demp ster Shafer Theory description. The computa tional

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... ty of calculating Belief functions from ATMS labels using algorithms originally derived to calculate the network reliability of graphs is analyzed. Approximation methods to more efficiently compute Belief functions using this graphical approach are suggested.