Measuring Inconsistency in Probabilistic Knowledge Bases

TL;DR

This paper introduces a new inconsistency measure for probabilistic knowledge bases, grounded in theoretical principles, and uses the Shapley value to identify causes of inconsistency, aiding knowledge base correction.

Contribution

It presents a novel inconsistency measure for probabilistic knowledge bases and applies the Shapley value to diagnose causes of inconsistency.

Findings

The measure is theoretically sound and applicable to real examples.

The Shapley value effectively reveals causes of inconsistency.

Tools assist knowledge engineers in restoring consistency.

Abstract

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.