A theory of diagnosis from first principles
Artificial Intelligence
On the complexity of propositional knowledge base revision, updates, and counterfactuals
Artificial Intelligence
Two Information Measures for Inconsistent Sets
Journal of Logic, Language and Information
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Artificial Intelligence - Special issue on nonmonotonic reasoning
Logical comparison of inconsistent perspectives using scoring functions
Knowledge and Information Systems
Measuring inconsistency in knowledgebases
Journal of Intelligent Information Systems
The Uncertain Reasoner's Companion (Cambridge Tracts in Theoretical Computer Science)
The Uncertain Reasoner's Companion (Cambridge Tracts in Theoretical Computer Science)
Information and Software Technology
Analysing inconsistent first-order knowledgebases
Artificial Intelligence
Quantifying information and contradiction in propositional logic through test actions
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Measures of inconsistency and defaults
International Journal of Approximate Reasoning
On the measure of conflicts: Shapley Inconsistency Values
Artificial Intelligence
Introduction to inconsistency tolerance
Inconsistency Tolerance
Measuring inconsistency in requirements specifications
ECSQARU'05 Proceedings of the 8th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Inconsistency-Tolerant Bunched Implications
International Journal of Approximate Reasoning
Measuring inconsistency through minimal proofs
ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Policy-based inconsistency management in relational databases
International Journal of Approximate Reasoning
Approaches to measuring inconsistency for stratified knowledge bases
International Journal of Approximate Reasoning
Inconsistency-tolerant reasoning with OWL DL
International Journal of Approximate Reasoning
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Measuring the degree of inconsistency of a belief base is an important issue in many real-world applications. It has been increasingly recognized that deriving syntax sensitive inconsistency measures for a belief base from its minimal inconsistent subsets is a natural way forward. Most of the current proposals along this line do not take the impact of the size of each minimal inconsistent subset into account. However, as illustrated by the well-known Lottery Paradox, as the size of a minimal inconsistent subset increases, the degree of its inconsistency decreases. Another lack in current studies in this area is about the role of free formulas of a belief base in measuring the degree of inconsistency. This has not yet been characterized well. Adding free formulas to a belief base can enlarge the set of consistent subsets of that base. However, consistent subsets of a belief base also have an impact on the syntax sensitive normalized measures of the degree of inconsistency, the reason for this is that each consistent subset can be considered as a distinctive plausible perspective reflected by that belief base, whilst each minimal inconsistent subset projects a distinctive view of the inconsistency. To address these two issues, we propose a normalized framework for measuring the degree of inconsistency of a belief base which unifies the impact of both consistent subsets and minimal inconsistent subsets. We also show that this normalized framework satisfies all the properties deemed necessary by common consent to characterize an intuitively satisfactory measure of the degree of inconsistency for belief bases. Finally, we use a simple but explanatory example in requirements engineering to illustrate the application of the normalized framework.