## Section: New Results

### Admissible Generalizations of Examples as Rules

Rule learning is a data analysis task that consists in extracting rules that generalize examples. This is achieved by a plethora of algorithms. Some generalizations make more sense for the data scientists, called here admissible generalizations. The purpose of our work in [8] is to show formal properties of admissible generalizations. A formalization for generalization of examples is proposed allowing the expression of rule admissibility. Some admissible generalizations are captured by preclosure and capping operators. Also, we are interested in selecting supersets of examples that induce such operators. We then define classes of selection functions. This formalization is more particularly developed for examples with numerical attributes. Classes of such functions are associated with notions of generalization and they are used to comment some results of the CN2 algorithm [22].