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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.

We propose two efficient algorithms for exploring topic diversity in large document corpora such as user generated content on the social web, bibliographic data, or other web repositories. Analyzing diversity is useful for obtaining insights into knowledge evolution, trends, periodicities, and topic heterogeneity of such collections. Calculating diversity statistics requires averaging over the similarity of all object pairs, which, for large corpora, is prohibitive from a computational point of view. Our proposed algorithms overcome the quadratic complexity of the average pair-wise similarity computation, and allow for constant time (depending on dataset properties) or linear time approximation with probabilistic guarantees.