Admissible Generalizations of Examples as Rules

Rule learning is a data analysis task consisting of extracting rules to generalize examples. For a data scientist, some generalizations called here admissible generalizations, make more sense. We explore formal properties of admissible generalizations. A formalization for generalization of examples is proposed that allows to express rule admissibility. Some admissible generalizations are captured by topological operators. We examine selecting supersets of examples that induce these operators and we define classes of such choice functions. This formalization is particularly developed in the case of numerical attributes. Classes of such functions are associated with notions of generalization and they are used to comment some behaviours of the CN2 algorithm.