Measuring Inconsistency in Probabilistic Knowledge Bases

Matthias Thimm
Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, PMLR R7:538-545, 2009.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR7-thimm09a, title = {Measuring Inconsistency in Probabilistic Knowledge Bases}, author = {Thimm, Matthias}, booktitle = {Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence}, pages = {538--545}, year = {2009}, editor = {Bilmes, Jeff and Ng, Andrew Y.}, volume = {R7}, series = {Proceedings of Machine Learning Research}, month = {18--21 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r7/main/assets/thimm09a/thimm09a.pdf}, url = {https://proceedings.mlr.press/r7/thimm09a.html}, 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.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Measuring Inconsistency in Probabilistic Knowledge Bases %A Matthias Thimm %B Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2009 %E Jeff Bilmes %E Andrew Y. Ng %F pmlr-vR7-thimm09a %I PMLR %P 538--545 %U https://proceedings.mlr.press/r7/thimm09a.html %V R7 %X 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. %Z Reissued by PMLR on 04 October 2026.
APA
Thimm, M.. (2009). Measuring Inconsistency in Probabilistic Knowledge Bases. Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R7:538-545 Available from https://proceedings.mlr.press/r7/thimm09a.html. Reissued by PMLR on 04 October 2026.

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