Relative inconsistency measures Abstract   The literature on inconsistency measures has ignored a distinction, that is, differentiating absolute measures and relative measures. An absolute measure gives the total amount of inconsistency in the knowledge base but a relative measure computes, by some criteria, the proportion of the base that is inconsistent. To compare the inconsistency measures, researchers have proposed postulates for such measures. We split these postulates into three groups: ones (including two new postulates) that relative measures should satisfy, ones inappropriate for relative measures, and ones that relative measures may satisfy. We obtain some new results upon the relationships between these groups of postulates. On these grounds, we introduce a formal definition for relative inconsistency measures. We consider some relative measures previously proposed and define several new ones that serve as examples. We show that all of these measures satisfy the new formal definition.

Discovering Reliable Correlations in Categorical Data In many scientific tasks we are interested in finding correlations in our data. This raises many questions, such as how to reliably and interpretably measure correlation between a multivariate set of attributes, how to do so without having to make assumptions on data distribution or the type of correlation, and, how to search efficiently for the most correlated attribute sets. We answer these questions for discovery tasks with categorical data. In particular, we propose a correctedforchance, consistent, and efficient estimator for normalized total correlation, in order to obtain a reliable, interpretable, and nonparametric measure for correlation over multivariate sets. For the discovery of the topk correlated sets, we derive an effective algorithmic framework based on a tight bounding function. This framework offers exact, approximate, and heuristic search. Empirical evaluation shows that already for small sample sizes the estimator leads to lowregret optimization outcomes, while the algorithms are shown to be highly effective for both large and highdimensional data. Through a case study we confirm that our discovery framework identifies interesting and meaningful correlations.