Measuring Inconsistency in Probabilistic Knowledge Bases
This work addresses inconsistency management for knowledge engineers building probabilistic expert systems, representing an incremental improvement with a novel method for a known bottleneck.
The paper tackles the problem of measuring inconsistency in probabilistic knowledge bases by developing a measure based on fundamental principles, and extends it using the Shapley value to reveal causes of inconsistencies, with applications illustrated through examples and formal results.
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.