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Measuring inconsistency is recognized as an important research issue for quantifying and handling inconsistencies in knowledge bases. Several logic-based inconsistency measures have been proposed. Minimal unsatisfiable and maximal satisfiable subsets are at the heart of the syntactic measures, while semantic inconsistency measures are often based on some paraconsistent semantics. In order to design interesting measures faithful to human rationality, many properties have been introduced to reach this goal. In this paper, we propose a new property called sub-additivity allowing to push further the ability to reorder knowledge bases according to their inconsistency degree. After pointing out the limitations of several measures to satisfy the sub-additivity property, we present a new measure based on a fine exploitation of the internal structure of the knowledge base, namely the structure of its associated minimal unsatisfiable subsets. Then, we show how its computation can be formulated as a nonlinear optimization problem. Finally, we prove that the new measure satisfies all the required properties while highlighting its interesting features.
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