Measuring Inconsistency in Probabilistic Knowledge Bases
  This paper develops an inconsistency measure on conditional probabilistic
knowledge bases. The measure is based on fundamental principles for
inconsistency measures and thus provides a solid theoretical framework for the
treatment of inconsistencies in probabilistic expert systems. We illustrate its
usefulness and immediate application on several examples and present some
formal results. Building on this measure we use the Shapley value-a well-known
solution for coalition games-to define a sophisticated indicator that is not
only able to measure inconsistencies but to reveal the causes of
inconsistencies in the knowledge base. Altogether these tools guide the
knowledge engineer in his aim to restore consistency and therefore enable him
to build a consistent and usable knowledge base that can be employed in
probabilistic expert systems.
