Abstract: Apparatus and computer-implemented method for correcting inconsistent facts in a knowledge base. The method comprises providing an inconsistent fact, wherein the inconsistent fact comprises a subject and a predicate and an object, determining an input for a language model, wherein the input comprises the subject or a label provided for the subject, wherein the input comprises the predicate or a label provided for the predicate, wherein the object or a label provided for the object is masked in the input, determining an output of the language model depending on the input, wherein the output comprises a predicted object or a predicted label for a predicted object, and replacing the inconsistent fact with a fact comprising the subject, the predicate and the predicted object.

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 method for operating at least one trained classifier for measurement data. The classifier comprises a neural network with at least one feature extraction section and at least one classification section. The method includes: processing a record of measurement data with at least the feature extraction section of the classifier; determining a set of neurons in the feature extraction section that are activated by said processing; determining, from a given correspondence between activated neurons and attributes, a set of attributes whose presence in a scene captured by the measurement data is indicated by the activated neurons; comparing attributes to which classes are linked by a given knowledge graph with said determined set of attributes; and evaluating, from the result of this comparison, at least one estimated class as a class to which the scene captured by the record of measurement data is likely to belong.

Abstract: A device and a computer-implemented method for adding a quantity fact to a knowledge base, in particular a knowledge graph. The method includes: providing the knowledge base; providing a textual resource; providing an entity from the knowledge base; providing a relation from the knowledge base; providing a set of different units; determining a quantity comprising a unit within the set of different units that is within the textual resource depending on the entity, the relation, and the set of different units; determining a quantity fact comprising the entity, the relation, the quantity and the unit; and adding the quantity fact to the knowledge base.

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 device and a method for solving an answer set programming program. The method includes receiving constant symbols and a set of rules for the constant symbols that comprises the constant symbols, wherein the answer set programming program is defined depending on the set of rules, determining a solution to the answer set programming program that comprises at least one of the constant symbols, determining a constraint depending on a cost for the solution, selecting in the solution at least one constant symbol, redetermining the solution as a result of an answer set programming program that is defined depending on the set of rules, and the constraint, wherein when solving the answer set programming program for redetermining the solution, the at least one constant symbol is treated as variable in the set of rules.

Abstract: A device and a computer implemented method for explainable clustering of a scene. The method includes determining a first relation that relates a first object class to a second object class, wherein determining the first relation includes determining, depending on the first object class and the second object class, a pair of entities in a first knowledge graph, in particular a commonsense knowledge graph, that represents information about a domain, wherein the pair of entities is related with the first relation in the first knowledge graph, determining a cluster in that the scene belongs depending on the scene and depending on other scenes, determining a second relation that relates the scene with the cluster depending on at least one feature of digital image data representing the scene, determining a rule that maps the first relation to the second relation.

Abstract: A method for determining negative samples for training a knowledge graph embedding of a knowledge graph enhanced by an ontology including at least one constraint for distinguishing a fact of the knowledge graph from a spurious fact. The method comprises determining embedding predicted triples; determining a set of triples that comprises a triple of the knowledge graph and at least one of the predicted triples that are inconsistent with respect to the ontology; determining from the set of triples a replacement entity for the object entity in the at least one triple of the predicted triples; and determining the negative sample to comprise the relation, the subject entity and the replacement entity, or determining from the subset a replacement entity for the subject entity in the at least one triple of the predicted triples and determining the negative sample to comprise the relation, the object entity, and the replacement entity.

Abstract: A device, computer program, computer-implemented method for training a knowledge graph embedding model of a knowledge graph that is enhanced by an ontology. The method comprises training the knowledge graph embedding model with a first training query and its predetermined answer to reduce, in particular minimize, a distance between an embedding of the answer in the knowledge graph embedding model and an embedding of the first training query in knowledge graph embedding model, and to reduce, in particular minimize, a distance between the embedding of the answer and an embedding of a second training query in knowledge graph embedding model, wherein the second training query is determined from the first training query depending on the ontology.

Abstract: A device, computer implemented method, computer program and non-transitory computer-readable storage, for automatically generating negative samples for training a knowledge graph embedding model, The method includes providing at least one first triple, the first triple is a true triple of a knowledge graph, providing at least one second triple, training the knowledge graph embedding model to predict triples of the knowledge graph depending on a set of triples comprising the at least one first triple and the at least one second triple, determining vector representations of entities and relations with the knowledge graph embedding model, determining a plurality of triples with the vector representations of entities and relations, providing an ontology comprising constraints that characterize correct triples, determining with the ontology at least one triple that violates at least one constraint of the constraints or that violates a combination of at least some of the constraints.

Abstract: Machine scheduling for executing a set of jobs of a task with a set of machines. The scheduling includes determining in a first iteration a first schedule that solves an optimization problem, the optimization problem is defined by a set of rules that assign the set of jobs to the set of machines, the first schedule maps each job to one machine of the set that is capable of processing this job, an execution of jobs assigned to a machine are scheduled to be finished in a machine span, and in a second iteration either determining a constraint for a machine span and determining a second schedule that solves the optimization problem for the set of jobs and the set of machines under the constraint, or determining a second schedule that solves the optimization problem for a sub-set of the set of jobs and of the set of machines.

Abstract: A method for training a control strategy with the aid of reinforcement learning. The method includes carrying out passes, in each pass, an action that is to be carried out being selected for each state of a sequence of states of an agent, for at least some of the states the particular action being selected by specifying a planning horizon that predefines a number of states, ascertaining multiple sequences of states, reachable from the particular state, using the predefined number of states, by applying an answer set programming solver to an answer set programming program which models the relationship between actions and the successor states that are reached by the actions, selecting the sequence that delivers the maximum return, and selecting an action as the action for the particular state via which the first state of the selected sequence may be reached, starting from the particular state.

Abstract: A device and computer implemented method. The method includes determining an embedding of a first entity, in particular of a knowledge graph, inserting a first vertex for the embedding in an in particular weighted in particular undirected graph, determining in the graph a first cluster of vertices including the first vertex, determining for the first cluster a second entity, in particular in the knowledge graph, determining a semantic similarity between the first entity and the second entity, in particular in the knowledge graph, determining a rule for the first cluster depending on the semantic similarity between the first entity and the second entity.

Abstract: A computer-implemented method for grouping target entities into clusters. A base association in which a cluster is associated with each of the target entities is determined in a computation step for the target entities as a function of an association for entities. Inference rules are determined as a function of the association for entities and as a function of the base association, each of the inference rules defining an association of entities with one of the clusters. An altered association is determined as a function of the association for entities and the inference rules. A check is made as to whether a difference between the base association and the altered association falls below a threshold value. When it does, an association of the target entities with the clusters is output or stored. Otherwise, a feedback value is determined as a function of the difference.

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.