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Graal is a java toolkit dedicated to ontological query answering in the framework of existential rules. We consider knowledge bases composed of data and an ontology expressed by existential rules. The main features of Graal are the following: a basic layer that provides generic interfaces to store and query various kinds of data, forward chaining and query rewriting algorithms, structural analysis of decidability properties of a rule set, a textual format and its parser, and import of OWL 2 files. We describe in more detail the query rewriting algorithms, which rely on original techniques, and report some experiments.

This project contains a Java implementation of median relational generalized learning vector quantization as proposed by Nebel, Hammer, Frohberg, and Villmann (2015, doi:10.1016/j.neucom.2014.12.096). Given a matrix of pairwise distances D and a vector of labels Y it identifies prototypical data points (i.e. rows of D) which help to classify the data set using a simple nearest neighbor rule. In particular, the algorithm optimizes the generalized learning vector quantization cost function (Sato and Yamada, 1995) via an expectation maximization scheme where in each iteration one prototype 'jumps' to another data point in order to improve the cost function. If the cost function can not be improved anymore for any of the data points, the algorithm terminates.