Analysing and measuring inconsistency

Analysing and measuring inconsistency




Inconsistencies frequently occur in knowledge about the real-world. Some of these may be more significant than others, and some knowledgebases (sets of formulae) may contain more inconsistencies than others. This creates problems of deciding whether to act on these inconsistencies, and if so how. To address this, we need a general logic-based characterization of inconsistency. Unfortunately mathematical logic cannot be used directly, because in the presence of inconsistency, any formula of the language is an inference. However, there are adaptations of mathematical logic that are not trivialised in the presence of inconsistency. We analyse inconsistent knowledge by considering the conflicts adaptations. These are used for measures of coherence for each knowledgebase, and for a measure of significance of inconsistencies in each knowledgebase. These analystical techniques have significant potential in developing intelligent systems that can be tolerant to inconsistencies when reasoning with real-world knowledge.


  • A Hunter and S Konieczny (2008) Measuring inconsistency through minimal inconsistent sets, Proceedings of the 11th International Conference on Knowledge Representation (KR'08), AAAI Press (in press).


  • J Grant and A Hunter (2008) Analysing inconsistent first-order knowledge bases, Artificial Intelligence 172:1064-1093.


  • G Qi and A Hunter (2007) Measuring incoherence in description logic-based ontologies, Proceedings of the International Semantic Web Conference (ISWC'07), LNCS 4825, pages 381-394, Springer.


  • A Hunter and S Konieczny (2006) Shapley inconsistency values, Proceedings of the 10th International Conference on Knowledge Representation (KR'06), pagse 249-259, AAAI Press.


  • J Grant and A Hunter (2006) Measuring inconsistency in knowledgebases, Journal of Intelligent Information Systems, 27:159-184.


  • A Hunter (2006) How to act on inconsistent news: Ignore, resolve, or reject Data and Knowledge Engineering, 57:221-239.


  • A Hunter and S Konieczny (2004) Approaches to measuring inconsistent information, in Inconsistency Tolerance. Lecture Notes in Computer Science, Volume 3300, pages 189-234, Springer.


  • A Hunter (2004) Logical comparison of inconsistent perspectives using scoring functions Knowledge and Information Systems Journal, 6(5):528-543.


  • A Hunter (2003) Evaluating the significance of inconsistencies, in the Proc. of the International Joint Conference on AI (IJCAI'03), pages 468-473, Morgan Kaufmann.


  • A Hunter (2003) Probable consistency checking for sets of propositional clauses In Quantitative and Qualitative Approaches to Reasoning with Uncertainty. Lecture Notes in Computer Science, volume 2711, pages 464 - 476, Springer.


  • A Hunter (2002) Measuring inconsistency in knowledge via quasi-classical models in the Proceedings of the 18th American National Conference on Artificial Intelligence (AAAI'2002), pages 68-73, MIT Press, ISBN 0-262-51129-0.


  • A Hunter (2001), A semantic tableau version of first-order quasi-classical logic. Quantitative and Qualitative Approaches to Reasoning with Uncertainty, Lecture Notes in Computer Science, volume 2143, pages 544-556, Springer, ISBN 3-540-42464-4.


  • A Hunter (2000) Reasoning with conflicting information using quasi-classical logic, Journal of Logic and Computation, 10(5):677-703.