Abstract: A system and computer implemented method for learning rules from a data base including entities and relations between the entities, wherein an entity is either a constant or a numerical value, and a relation between a constant and a numerical value is a numerical relation and a relation between two constants is a non-numerical relation. The method includes: deriving aggregate values from said numerical and/or non-numerical relations; deriving non-numerical relations from said aggregate values; adding said derived non-numerical relations to the data base; constructing differentiable operators, wherein a differentiable operator refers to a non-numerical or a derived non-numerical relation of the data base, and extracting rules from said differentiable operators.

Abstract: A method for training a polyhedral classifier is described including obtaining training data in a data space, the training data including first data points associated with a first label and second data points associated with a second label, determining a pair of hyperplanes by determining an orientation of the pair of hyperplanes based on a minimization of a distance between the pair of hyperplanes such that the first data points lie between the hyperplanes in relation to a distance between the pair of hyperplanes such that both the first data points and the second data points lie between the hyperplanes and determining the position of the pair of hyperplanes such that the first data points lie between the pair of hyperplanes and the second data points are at least partially separated from the first data points by the pair of hyperplanes.

Abstract: A computer-implemented method for computing inconsistency explanations in a first data set, enhanced with an ontology, the first data set comprising data elements, called individuals, and facts about the individuals; the facts are expressed according to an ontology language in terms of class assertions and/or property assertions, a class assertion relates one individual with a class and a property assertion relates one individual with a second individual. The ontology includes a formal explicit description of the classes and/or properties and further including axioms about the classes and/or properties; wherein the method includes the steps of: constructing a second data set being an abstract description of the first data set; computing inconsistency explanations in the second data set with regard to the axioms of the ontology, and computing inconsistency explanations for the first data set with regard to the ontology based on the computed inconsistency explanations in the second data set.