# The ICICS/CS Reading Room

## UBC CS TR-89-08 Summary

- No on-line copy of this technical report is available.

- A Logic-Based Analysis of Dempster Shafer Theory, December 1989 Gregory M. Provan
We formulate Dempster Shafer Theory in terms of Propositional Logic, using the
implicit notion of probability underlying Dempster Shafer Theory. Dempster Shafer
theory can be modeled in terms of propositional logic by the tuple $(\Sigma , \varrho )$, where $\Sigma $ is a
set of propositional clauses and $\varrho $ is an assignment of measure to each clause $\Sigma_i \in \Sigma $.
We show that the disjunction of minimal support clauses for a clause $i$ with respect to
a set $\Sigma $ of propositional clauses, $ \xi ( \Sigma_{i}, \Sigma )$, is a symbolic representation of the Dempster
Shafer Belief function for $\Sigma_{i}$. The combination of Belief functions using Dempster's Rule
of Combination corresponds to a combination of the corresponding support clauses. The
disjointness of the Boolean formulae representing DS Belief functions is shown to be
necessary. Methods of computing disjoint formulae using Network Reliability techniques
are discussed.
\n In addition, we explore the computational complexity of deriving Dempster Shafer
Belief functions, including that of the logic-based methods which are the focus of this
paper. Because of Intractability even for moderately-sized problem instances, we propose
the use of effluent approximation methods for such computations. Finally, we examine
implementations of Dempster Shafer theory, based on domain restrictions of DS theory,
hypertree embeddings, and the ATMS.

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